Charles R. Cowley
Professor of Astronomy
University of Michigan
January 3, 2000
Since this book deals with the history of matter, it is well to ask what we are talking about. What is matter? The Random House Unabridged Dictionary (2nd ed. 1987) lists 24 different definitions! We need not work through them all, but it will be interesting to look at a few. The first definition listed in this dictionary is supposed to reflect the meaning of the word as it is most commonly used. Here is what the editors of this dictionary say: 1. the substance or substances of which any physical object consists or is composed. They go to give an example of this meaning ``the matter of which the earth is made.''
The definition just given might be enough for our purposes. Of course, it begs the question of what a `substance' is. Another definition that I like comes third in the list. Matter is: 3. something that occupies space. I remember this definition from elementary school. It sounded very impressive then; maybe that is why I have liked it. Actually, it sounds rather abstract now, in addition to raising the possible question of what is meant by space.
Definition number 15a. is qualified as Philos. Presumably this means it is a technical usage in the discipline of philosophy. It says that matter is `that which by integrative organization forms chemical substances and living things'. This definition might well serve as an example of poor writing! My first comment on it would be to ask if the abstract phrase `by integrative organization' is really necessary. Does it add anything to `that which forms chemical substances and living things'? Again, since living things are presumably composed of chemical substances, do we need to add `and living things'? Finally, we might ask what the difference between a substance and a chemical substance is. By this time we have defined matter as `that which forms substances', and we are back to definition 1, above.
If these definitions have not particularly increased your notion of what we shall mean by matter, I am not surprised. In science we tend to take a pragmatic approach, and simply assume that we have a general notion of what certain abstract words like space and time mean. Ultimately, our edifice of science is built on undefined terms, words that we accept as meaningful even though we are unable to give them precise definitions. This may seem a bit strange at first, but it is the only way to avoid circularity. In physics, mass, length, and time are undefined terms.
Ask physicists what is meant by time, and they are likely to say that it is what we measure with certain instruments. They may freely admit that this is not a rigorous definition, but may add that it works for them.
Let us take the same attitude about matter.
In the last section, we decided that it was possible to talk about matter without being especially rigorous about the definition. Perhaps we will find the lack of a rigorous definition a problem, but we are prepared to deal with it should the need arise.
Ultimately, we might want to say that matter is composed of the elementary building blocks of particle physics. These come in two main families called bosons and fermions. The most familiar bosons are the light quanta called photons. Electrons, protons, and neutrons are fermions. For the present, we shall not concern ourselves with the breakdown of fermions into leptons (e.g. electrons) and quarks, the building blocks of protons and neutrons.
Atoms are made of nuclei consisting of protons and neutrons, surrounded by clouds of electrons. We have to think of matter at the atomic level in terms of the quantum theory. It is interesting to note that in the 21st century physicists still speak of the quantum `theory.' Does this imply that the ideas of quantum physics are not firmly established? No, it's just a phrase that lingers from earlier days. Quantum principles are as firmly established in physics as any `laws' of physics, such as Newton's or Einstein's laws. Indeed, while it is still common to speak of the quantum theory, we often hear of the `laws' of quantum mechanics.
According to the quantum theory, it is more accurate to think of the electrons as a fuzzy cloud of charge than little spheres that circle the nucleus the way planets go around the sun. The number of protons determines the chemical element to which a specific atomic nucleus belongs. If the atom is electrically neutral, then the number of electrons is the same as the number of protons, and we can also tell the element by counting the number of electrons.
The atom is the smallest amount of a chemical element that can exist. The number of neutrons in a nucleus does not determine the element. Atoms or atomic nuclei with the same number of protons but different numbers of neutrons are called isotopes. The familiar chemical elements can have one or more stable isotopes, and an important part of the history of matter can be deciphered from the relative amounts of isotopes that occur in nature.
Atoms may combine to form molecules. We shall have more to say on how this happens in a later section. A chemical compound is formed from one or more molecules of the same kind. Thus a molecule is the smallest possible division of a chemical compound, and we have the logical scheme atom:element::molecule:compound.
It takes a great many atoms or molecules to make the
quantities of matter that we experience in everyday life. For
example, a pint of pure water contains about 1025 molecules of
. Even a drop of water on the threshold of invisibility
contains some 20 billion molecules. Matter is said to exist in three
phases, solid, liquid, and gaseous. These phases are
meaningless for single atoms or molecules, and become practically
meaningful only when there is enough matter to ``see.''
Sometimes, it is useful to speak of a fourth phase of matter, the plasma. In physics and astronomy this term means a gas that contains many charged particles. The atmospheres of the sun and most stars are plasmas because the temperatures are high enough to separate at least one electron from many of the atoms. Plasmas have special properties, mostly associated with the interactions of their particles and magnetic fields.
The word ``phase'' is used in another technical sense, with a meaning slightly different from that in ``the three (or four) phases of matter.'' If we put oil and water in a container, they will separate into two distinct phases. Since both oil and water are liquid, the meaning of the word ``phase'' is used here in a new sense. The Nobel Laurate Linus Pauling (1901-1995) defines a phase as a ``...homogeneous part of a system, separated from other parts by physical boundaries.''
We shall have occasion to use both meanings of the word ``phase.''
Most of the matter in the universe is now thought to be an unknown form often called ``dark matter.'' There appears to be more mass in dark matter than in visible matter about an order of magnitude--ten times more dark than visible matter.
The only evidence we have of the presence of this dark matter comes from the motions of ``visible'' matter on large, astronomical scales. Indeed, the most convincing evidence comes from the general motions of entire galaxies, or clusters of galaxies. Briefly, the law of gravitation tells us how this material should move. What we find is that the law of gravitation is violated--unless we postulate the presence of additional, unseen matter.
No evidence for dark matter has emerged from experiments in terrestrial laboratories. There are certain theoretical ideas that account for the existence of dark matter, but they are still in the realm of theory, and some might even say speculation. But it is now well established in the astronomical domain that the law of gravitation is in trouble unless we postulate large amounts of dark matter. We shall explore the evidence in a later chapter.
Dark matter presents one of the greatest challenges to our current understanding of the physical world. However, it is difficult to discuss its history, since we don't know what it is. We can't even be positive there is such a thing as dark matter. A few scientists think the laws of gravitation may be flawed, and there is no way to be sure that isn't the case. For the present, mainstream scientific thinking assumes some form of unseen matter permeates the universe, and that we will eventually know its nature.
In this book, we concentrate on visible matter, since that is something we know a great deal about. Most of the visible matter in the universe is in the gaseous phase. The solid and liquid phases occur in planets, satellites, comets, and interstellar dust. The total mass in these objects is probably less than one percent of that in the gaseous form, in stars and nebulae.
Before we leave the subject of various kinds of matter, we should mention the divisions of matter into organic and inorganic. Sometimes it is useful to do this. Usually by organic matter, one means material that is now or was once a part of living organisms. Other matter is inorganic.
Organic chemistry is defined to mean the chemistry of the element carbon and its compounds. It is therefore possible to use the term `organic' with a slightly modified meaning from the one given above. Then one might speak of organic matter to simply mean material made of carbon compounds, with no necessary connection to living matter.
There was a time when it was thought that carbon compounds could only be formed by living things, but this was a long time ago. Many organic molecules have been identified in the depths of space. In a later chapter, we shall come to the intriguing questions of whether they have any relation to life, or are just organic in the sense of being compounds of carbon.
There are 92 chemical elements from the simplest, hydrogen, to uranium. There are also elements heavier than uranium. There are no stable isotopes of uranium, but two live long enough to be important. The two isotopes are written 235U and 238U, where the raised prefix gives the number of protons plus neutrons in the nuclei of these two isotopes. We shall not discuss isotopes in this chapter, but will briefly review the chemical properties of the elements that will be necessary for an understanding of the history of matter.
Many of the things we need to know about the chemical elements can be found on the periodic table. We should say just a few words about the history of this interesting construct. The periodic table emerged in the middle decades of the nineteenth century through the work of chemists. The names of Mendeleév (1834-1907) and Lothar Meyer (1830-1895) are usually mentioned as inventors of the table, but it is useful to see their work in the light of the contributions of their contemporaries. In the decades prior to the first periodic tables, chemists had just begun to understand the difference between elements and compounds, building on the atomic hypothesis of John Dalton (1766-1844).
The great German chemist Friedrich August Kekulé (1829-1896) initiated the first International Chemical Congress, which met at Karlsruhe in 1860. Many of our modern concepts of chemistry may be traced to that congress, for example, the way of writing formulae for chemical compounds. Both Lothar Meyer and Dimitri Mendeleév were influenced by what they learned in Karlsruhe. Nowadays, conference-going is a part of the life of every scientist, but some meetings are much more fruitful than others. Kekulée's conference would rank among the very best even if it had only stimulated work on the periodic table.
In the nineteenth century, the nature of isotopes was unknown,
and the early periodic tables were constructed with the help of
atomic weights. The atomic weight of an element is the weight or
mass (in grams) of a fixed number of atoms. The particular number
chosen is known for another of the famous old chemists, Avogadro
(1776-1856). Avogadro's number is about 
.
Consider an example. The atomic weight of carbon is 12.011. This
means that if you have 12.011 grams of carbon, you have carbon atoms.
What Mendeleév and Meyer noted was that if you arranged the chemical elements in order of their atomic weight, similar chemical properties emerged periodically. Thus, if you listed the elements in an order so that those with similar chemical properties occupied columns, you obtain a rudimentary version of the modern periodic table. For example, the alkali metals lithium, sodium, potassium, rubidium, (etc.) all have similar chemical properties, as do the noble gases helium, neon, argon, and xenon.
Nowadays, we order the elements in the periodic table by their atomic numbers rather than by their atomic weights. The atomic number of an element is the number of protons in the atomic nucleus, or alternately, the number of electrons in a neutral atom.
It might seem straightforward to find these periodicities in the chemical properties of elements, but look again. There are six elements between the lightest alkali element lithium, and the heavier noble gas, neon. Again, there are six elements between the next alkali element, sodium, and the noble gas congener of neon, argon (see Table 1-1). But hydrogen, which is in some ways similar to the alkali elements is followed immediately by the noble gas helium, and there are sixteen elements between potassium and krypton (Table 1-2). And, when the early work on the periodic table was done, not all sixteen of these elements were known. Gallium (Ga), germanium (Ge) and their properties were predicted by Mendele! How did these fellows manage to get the idea right in the face of so many difficulties? Did they just have the exceptional insight we associate with genius?
Genius is difficult to define, but one of the aspects of those with its gifts seems to be the ability to see beyond the difficulties such as those mentioned in the above paragraph. These early chemists cut the Gordian knots with bold hypotheses. Generally speaking, the geniuses are the ones who turn out to be right. Some equally bold, brilliant, and even beautiful hypotheses turn out to be wrong. They end up on the scrap heap of scientific history, but we should not be scornful of the minds responsible for them. Our current notion of the creation of the universe in a Big Bang was once rivaled by a theory in which the universe did not change with time. This ``steady-state'' theory of the universe is an example of a brilliant but discarded theory. We shall have a little more to say about the steady-state theory of the universe in a later chapter.
A chemist learns columns of the periodic table, because the elements in a column have similar chemical properties. We pointed out the chemical similarities of elements in the first and last columns. Be, Mg, Ca, etc. have similar properties, as do F, Cl, and Br. Things become more complicated for elements located at the center of the periodic table.
People who study the origin and history of the chemical elements tend to learn the periodic table in rows rather than in columns. This is because the processes that make the elements create heavier ones by adding particles to lighter ones, so helium is created from hydrogen, and carbon from helium. It turns out that you can't make carbon by adding protons to helium. We'll get to that in a bit.
The periodic table also becomes more complicated as you consider heavier elements. The first period has only two elements, the second and third eight, and the fourth and fifth have eighteen. Now the periodic table is often set up so it looks like the sixth and seventh periods also have eighteen elements, but that's just dodge. Actually, these periods have 32 elements. An extra fourteen elements that belong in the sixth and seventh periods are written below the ``body of the table.''
It turns out that the number of elements that might go in the
nth period is 2n2. This accounts for only hydrogen and
helium in the first period, and eight elements in the second
(
). There might be eighteen elements already in
the third period, but in our world, we don't get eighteen until the
fourth period, where there might be thirty-two!
In order to understand what is going on, you need to know about shells and subshells. It's a little involved, but no more so than you learn in high school chemistry. Let's take a crack at it.
The periods, first, second, third, etc., correspond to electron shells. Hydrogen and helium have electrons in the first (n = 1) shell, while lithium through neon have electrons in both the first and the second. Elements in the third period have electrons in shells 1, 2, and 3. So this continues for elements in the nth period, which have electrons in shells 1 through n. Helium and neon have all of their main shells filled, but that's not true for argon. To see what's happening here, we have to consider subshells.
Electron shells have names consisting of one upper case letter. The n = 1 shell is called the K-shell. The n = 2, and 3 shells are called the L, and M shells. Subshells also have one-letter names, but now lower case is used: s, p, d, and f. There are subshells beyond the f, for example, g and h, but we won't use them much here. The thing to remember about the subshells is that there are as many subshells as number that describes the main shell. The n = 1 shell has only one subshell, namely, the s or 1s shell. The n = 2 shell has two subshells, called the 2s and 2p.
It goes on like this. The n = 3 shell has three subshells, and the n = 4 has four. What's really tricky is that not all of the subshells get filled in order, but there is a scheme that will tell us which order the shells get filled in. In order to make this scheme work, you have to make a list of all of the possible subshells in a kind of a triangle. This is shown in figure 1.
Follow the arrows in the figure to get the order of the subshell filling. The order is: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, etc,. So note that the 3d subshell doesn't start filling until electrons are already in the n = 4 shell (or 4s subshell). Similarly, the 4d subshell doesn't start filling until the n=5 shell has already started to fill.
The n = 6 shell rather complicated. It starts easy enough with two 6s electrons, but then the atoms go back and fill the 4f subshell, and after that fills, they fill the 5d. Finally, the 6p shell fills. This would be hard to remember if we didn't have figure 1-1 to help us. All you have to do is get the arrows going at the right angle for the easy cases--for the lightest elements. Then you automatically get the complicated stuff like the 4s filling before the 3d, and the 3d filling between the 4s and 4p.
We need one more bit of information before all pieces of the puzzle fall into place. There are whole numbers associated with the names of the subshells. This is just like the numbers 1, 2, 3, that are associated with the K, L, and M shells. With the subshells, the numbers start with zero. So the numbers 0, 1, 2, 3, 4, etc. are associated with subshells named s, p, d, f, or g. These whole numbers tell us how many electrons it takes to fill a subshell. We let the letter l stand for the whole numbers associated with the subshells. There is a historical reason for the use of the symbol `l' (rather than x) that we don't need to go in to now. So electrons in the s-subshell have l = 0, those in the p-subshell have l = 1, and so on. These relations aren't changed by the main shell the electrons are in, so 2p and 4p electrons both have l = 1.
The maximum number of electrons that can occupy a subshell is
given by the simple formula 
, or 4l+2. This is
the last piece of the puzzle. With it, we see that we can have
two s electrons, six p electrons, ten d electrons, and
fourteen f electrons. So the first period fills with helium,
because there can be only one subshell, the 1s, and it can have
only two electrons. The second period fills with a full complement
of 2s (2), and 2p (6), or 8 electrons. This takes us to neon.
Likewise, the third period ends with the 3s and 3p shells
filled. We need figure 1-1 to see that while there
is a 3d shell, it isn't filled in the third period.
Figure 1-1 shows that the 3d shell gets filled in the fourth period. The noble gas krypton, which ends the fourth period, has filled 4s (2 electrons), 3d (10 electrons), and 4p (6 electrons) for a total of 18 electrons. Of course, 10 of these electrons are in the n = 3, 3d shell. We need the figure to keep this straight.
The fifth period is not shown in Table 1-1, so for a reference, you need to look at the full periodic table shown in Table 1-2. It has shell fillings just like the fourth period, except that the relevant shell integers are increased by unity. So the subshells are 5s, 4d, and 5p, again with 2, 10, and 6 electrons for a total of 18.
The seventh and final period runs, in principle, like the sixth, but this time, all of the elements are unstable. A few have long half-lives and are well known. Certainly, the names uranium (U), radium (Ra), and thorium (Th) are household words. The radioactive noble gas radon (Rn) is a danger to some households!
It turns out that there are a few departures from the shell-filling scheme of figure 1-1. We don't need to take them up here, but if you consult an appropriate reference, you'll find them. These irregularities don't change the overall structure of the periodic table as we have explained it, so we'll leave the details to specialists in atomic structure.
History books begin at the earliest times and work forward. We could do that with the history of matter. However, there are reasons why this might not be the best thing to do. First, our history of matter will be primarily a discussion of the discoveries of the physical sciences. Although we shall attempt to describe scientific results in a nontechnical language, we will adhere to certain scientific principles.
In any field of science, there are concepts that are considered firmly established. Theoretical ideas that fit into this category are often called laws, while experimental or observational results may be called facts. Most scientific endeavors will start from these laws or facts, and work toward new relationships. In some ways, doing science is like groping in the dark. We begin with our immediate area, and feel our way toward regions that are unfamiliar.
If we apply these notions to the history of matter, it would not make a great deal of sense to start at the very beginning of time. At this point, the conditions of our universe would be so different from those known at present that our laws and facts might be irrelevant or wrong. There is a general, though not unanimous agreement among cosmologists that our universe began as a ``Big Bang,'' with matter squeezed to arbitrarily high densities. As far as the current ideas go, there is no limit to how high the densities became, but we can say that at some point the laws of physics as we use them today would break down.
While the conditions at the beginning of time are fascinating in many ways, our current understanding of them is not on the same firm foundation as our understanding of the motions of the planets about the sun. These motions are understood in terms of Newton's Laws, and in most cases, the modifications associated with Einstein's theory are so small that we may safely neglect them.
After we discuss some preliminary matters, we shall begin with a brief survey of the earth, the solar system, and the astronomical universe as they are known today. We'll discuss the composition of these bodies in a general way, and will postpone a more technical discussion until we have finished our broad outline of what's out there.
Once these facts are laid out, we may begin to ask how these things came into being. The current composition of planets, stars, and galaxies are like a book in which the history of matter is written. This is the key idea of this book, so it is worth repeating it: The history of matter is written in its abundance patterns. The language of that writing is not simple English, and it is up to us to learn how to read it.
The relative numbers of atoms or isotopes of the chemical elements are often spoken of as their abundances. A table of ``standard'' abundances of the chemical elements (or SAD) may be found in an appendix to this book. We may assign abundances, these relative numbers, in various ways. Typically, some fixed number is chosen for one element, and then all the other numbers are assigned relative to that one. In astronomy, because hydrogen is usually dominant, we set its number at 1012.
If you look at
tabulated SAD abundances,
you will find that the abundance of helium is set
at 
. By taking the ratio of the numbers for hydrogen
and helium, we see that we should find slightly
less than 1 helium atom for every 10 hydrogens in the sun.
Iron's abundance is set at
, so we would expect to find that many iron atoms
in any volume that contained 1012 hydrogen atoms.
Geochemists use abundances with silicon set at 106. This is
because there is typically lots of silicon in rocks, but not much
hydrogen. There are various ways of translating the abundances
of one scale to that of another. In principle, you could pick any
element, and just multiply by the appropriate factor to convert.
For example, on the astronomer's scale, silicon is 3.581
.So to convert silicon, and all other numbers to the geochemists'
scale, you would multiply by 
. However,
it is common to use more than a single element for conversions
of this type.
Tables 10.1 and 10.2 were actually obtained from
a compilation where silicon was set at 106. When the conversion
was made, it turned out that hydrogen came out close, but not
exactly 1012. We did not bother to make further adjustments
when assembling the abundance tables. This is why the hydrogen
abundance is listed as 9.991
instead of 1012.
We shall have more to say about the way abundance tables are made in subsequent chapters.
The general endeavor of reading the history of earth materials from its chemistry is a part of the discipline of geochemistry. Analogous work in the broader context of the universe itself has come to be known as cosmochemistry.
In the early sections of this chapter we tried to clarify the notion of ``matter,'' whose history we take up in this book. There are various kinds of matter, and it comes in solid, liquid, and gaseous form as well as in the ionized state known as a plasma. We also mentioned the mysterious dark matter studied by astronomers. There probably is much more of this dark matter than familiar, visible, matter in our universe.
Familiar matter is made up of the chemical elements. We talked about the structure of atoms, their nuclei and electrons, and distinguished between chemical elements and compounds. In some technical sections, we showed how the shells and subshells of atoms accounted for the structure of the periodic table of the elements.
We decided we would start our history of matter by taking stock of the way things look to us at the present.
Geologists divide the earth into three spherical zones. There is an inner zone that is mostly metallic. The diameter of this core is roughly half that of the entire earth. Most of the rest of the earth is a rocky mantle, covered by a relatively thin crust. We have a very limited amount of direct information about the composition of the core and mantle, but there is a great deal of indirect information about these unseen layers. Most of this information is derived from ``listening'' to earthquakes with the help of instruments known as seismometers.
Above the crust of the earth are the oceans and the earth's atmosphere. These are the regions of the earth important to us, but they make up a tiny fraction of the mass of the whole earth. If we add all the mass in the oceans and polar caps, and throw in the atmosphere, the result is less than 6% of the mass of the earth's crust. And the crust is about 0.4% of the mass of the earth itself! Nevertheless, we will have to look rather closely at the chemistry of this trace amount of matter within which we live, because it will give important clues to the formation and history of the earth.
We can get a hint that the earth can't be made up just of rocky materials from its mean density--the quotient of its mass by its volume. This density is about 5.5 times that of water. Now if we compare this figure with the densities of rocks, there is a considerable discrepancy. Rocks rarely have densities much more than 3 times that of water. We will give a few more precise figures later, but for the present, we ask how an earth could be nearly twice the density of typical rocks. The most likely explanation is a core made of iron or a similar metal.
Certain rocks known as meteorites fall from the sky. Much of our current ideas about the composition of the planets comes from the study of these meteorites. Most meteorites are rocky in composition with small admixtures of dense metal inclusions. Others are almost entirely metallic in composition, with densities of the order of 8 times that of water. A few meteorites have comparable fractions of both metal and rock. The metal in these meteorites is typically quite high grade. If you cut the meteorite with a diamond saw, you can polish the face until it will reflect like a mirror. We shall often refer to this metal as `iron,' even though it is strictly a nickel-iron alloy.
Geologists have long believed these rocks came from one or more planets that had an iron cores and a rocky mantles, but were broken up somehow. It is interesting that astronomers resisted this notion for a long time. Even some rather recent textbooks written by astronomers soft-pedal the notion of meteorite parent bodies. But the earth is the special provence of the geologist, and only peripherally belongs to the astronomer. So these geologists have argued rather early on that the earth's core is probably made of material similar to the iron in meteorites. If some long destroyed parent body could have an iron core, why not the earth? Because the density of iron is much higher than that of rock, it is natural to think it would sink to form a core.
The earth's mantle is thought to be composed of rocky material that is, again, similar to that found in many meteorites. A few samples of the upper mantle come to us in pipes known as diatremes, and in regions where faults in the crust must have allowed extrusions of deeper rock. These materials, as well as the analyses of seismic waves are entirely consistent with a mantle composition similar to that of stony meteorites.
While the earth's core and mantle are each rougly 3000 km thick, the crust is as thin as 5 km, and rarely thicker than 20 km. The composition of this crust is considerably more complicated than we think the core or mantle to be. We shall discuss the origin of this complexity in due time. The crust of the earth is pushed about by forces internal to the earth, giving rise to continental drift. A more technical phrase describing these motions of crustal fragments is plate tectonics.
The earth's Moon is unusual among planetary satellites. Basically, it's big. While there are satellites of the giant planets that are even bigger than our Moon, they are not bigger relative to these planets.
As a result of the space program, we know an enormous amount about the Moon and its structure. When I began to study astronomy in the late 1950's, we didn't even have a very precise notion of the Moon's mass. Now we know the mass of the Moon quite accurately, and we even know of irregularities in its distribution of mass. For example, irregularities in the motions of space vehicles have indicated concentrations of masses that correspond roughly to the regions called maria. Maria are the darker regions that can be seen on the face of the moon, even with the naked eye. The mascons were discovered by the early Lunar Orbiters in the prior to the Apollo missions.
The Moon's bulk mass and density are about the same at that of rocks of the earth's upper mantle. Extensive analyses of moon rocks have told us that their overall composition resembles our estimates for the upper mantle. There are important differences. Lunar rocks are dryer, that is, they contain less water or other volatile substances. The also have a higher content of reduced, or metallic iron than mantle rocks. There are highly significant differences in the distribution of rock types in the crust of the Moon and the earth that will lead us to infer very different histories for the formation of these surficial regions. It will be easier for us to be specific after we have had a chance to review rocks and minerals in a later chapter.
Mercury is the innermost planet of the solar system. It is less massive than the earth or Venus, but 4.49 times the mass of the Moon. In size, Mercury is only a little bigger than the Moon. Its radius is 1.403 times the lunar radius. Now since volume depends on the cube of the radius, we might expect Mercury to have a mass of 1.403 cubed, or 2.76 times that of the Moon. Instead, the correct figure is 4.49. The obvious conclusion is that Mercury is made of much denser material than the Moon. It is easy to calculate from the figures here, that Mercury is 1.63 times more dense than the Moon.
We think Mercury has a relatively high density because of its iron core. This core is larger, relative to the size of the planet, than the cores of the earth or Venus.
One aspect of the comparative densities of the planets needs to be discussed at this point. Gravity squeezes even solids when pressures get as large as they can be in planetary interiors. This means if we want to compare the materials from which the planets were originally formed, we have to allow somehow for this squeezing. The task is not easy, because we don't know for certain what it is that's being squeezed! But we can certainly make some reasonable estimates. We have already mentioned using the composition of meteorites. A reasonable guess for the squeezing properties--compressibilities--of the earth's material is that it is about the same as that of stony and iron meteorites.
| Mean | |||
| Planet | Distance from | Density | Decompressed |
| Sun(AU) | (gm/cm3) | Density | |
| Mercury | 0.39 | 5.43 | 5.3 |
| Venus | 0.72 | 5.24 | 3.9-4.7 |
| Earth | 1.00 | 5.52 | 4.0-4.5 |
| Moon | 3.34 | 3.3 | |
| Mars | 1.52 | 3.94 | 3.7-3.8 |
| granite | 2.6-2.8 | ||
| basalt | 2.4-3.1 | ||
| kamacite | 7.8 | ||
| taenite | 8.2 |
Estimated decompressed densities are shown in Table 2-1. We can see that the biggest changes are for the earth and Venus--the larger pair of the four terrestrial planets. The smaller planets, Mercury and Mars, and the Moon are not squeezed much. But the table shows a remarkable trend of the decompressed densities. They decrease steadily from Mercury through Mars. Indeed, if we were to tack on the outer or Jovian planets, we would see that all have much lower densities still.
In the lower part of Table 2-1, we give the densities of two common rock types, and the metallic minerals, taenite and kamacite. The latter minerals are often described as nickel-iron alloys--they are the major minerals of the iron meteorites. It is readily seen that any of the decompressed densities of the planets of the upper part of the table are bracketed by the materials in the lower part. We can therefore make a general inference from the densities alone.
We may simply assume that the ratio of rock to iron in the terrestrial planets decreases with distance from the sun. This density decrease should be a significant clue to the way in which these planets formed, and we will return to it when we discuss planetary formation.
Our considerations, based on densities and on the pieces of interplanetary debris known as meteorites lead us to quite different conclusions about the bulk composition of the Moon and Mercury. This may be surprising, in view of the similarity of their surfaces. Nevertheless, we may conclude that Mercury has a dominant metal core, while the Moon has a small core, or possibly no core at all. This structural difference reflects the very different histories of the two bodies.
One might expect the properties of Venus and Mars to bracket those of the earth. This is not really the case. The earth is more massive, and larger than both planets, although Venus is nearly as large as the earth. Mars is about half the size of the earth, and as we can see from its density (Table 2-1), it is mostly rock and little iron.
Venus is the closest planet to the earth, and most like it in
size and mass. For many years the surface of Venus was hidden by
the thick atmosphere. Of the four terrestrial planets, Venus has
by far the most atmosphere. At the surface of the planet, the
gas pressure is about 90 times that of the earth's atmosphere.
The chemistry of the
atmosphere is quite different from ours, though. Venus's
atmosphere is mostly 
gas. There is about 3% 
,and only trace quantities of other gases. This is not unlike the
composition of the atmosphere of Mars, but the pressure of the
latter is slightly less than 0.01 earth atmospheres.
As far as gas goes, there is essentially none on Mercury, lots on Venus, enough (for humans!) on earth, and piddling amounts on Mars. This gas nevertheless presents a challenge to our understanding of the chemical evolution of the planets. We may understand the history of this gas even less well than the much more massive rocky and metal phases of these planets, but when the time comes we shall consider this difficult problem.
Models of the interior of Venus pretty well parallel those of the earth, just scaled down a little. It's metal to rock ratio may be assumed to be the same as ours. The surface of Venus is quite different, of course. At the bottom of its thick atmosphere, the temperature, about 730 Kelvin, is more than high enough to melt lead (m.p. 601K). From numerous investigations from spacecraft, we know a good deal about the surface of this planet. Russian missions to Venus included landers that sent back a few pictures of rock-strewn surfaces. Radar from orbiters has allowed much of the surface to be mapped--we have ``pictures'' of Venus not unlike those available for Mars.
While the bulk properties of Venus and the Earth may be similar, the surfaces could not be more different. The Venusian surface temperature is above the so-called critical temperature of water, that is, the temperature at which water can only exist as a gas. And there is no water to speak of in the atmosphere of the planet either. Venus is not a particularly pleasant place to think about visiting.
Mars, on the other hand is not so disagreable. A typical place on its surface is cold, but no colder than some places on the earth. Mars is certainly more likely to be explored in a manned space mission than Venus.
From its bulk properties--its size and density--it is not unreasonable to regard Mars as some kind of transition object, from the innermost planets to the very different giant or Jovian planets that lie considerably further from the sun. We might include among those transition objects the many smaller minor planets or asteroids.
It is useful to review at this point the scale of the distances of the planets from the sun. There is a simple algorithm that will give approximate distances known as Titius-Bode's law after two German astronomers of the late sixteenth century.
One way to express the algorithm of Titius-Bode's law is as follows. Write down a string of 4's, and beneath the fours write the sequence 0, 3, 6, 12, 24, 48, 96, 192. Add these numbers, and divide them by 10. These numbers are worked out in table 2-2. The actual distances from the sun are also shown. These distances are given in units of the earth-sun distance, called the astronomical unit or AU.
We have omitted Pluto from table 2-2. With a mean distance of 39.5, it fits the Titius-Bode prediction better than Neptune. For the present, it is best simply to remember that the scheme works pretty well for Mercury through Uranus.
The Titius-Bode law is not a law at all--in the sense of Newton's laws or the laws of quantum mechanics. It may be best to think of it as only a mnemonic, even though a good deal of theoretical work has been done attempting to ``explain'' it. The law predicts that there should be something between Mars and Jupiter. Eventually, the asteroids or minor planets were found to occupy a ``belt'' roughly between 2.2 and 3.2 astronomical units from the sun.
The four terrestrial planets, Mercury, Venus, earth, and Mars are all relatively close together as planets go. The mean separations of Mercury and Mars is just a little over one AU. So the average separations of these four planets is only about 0.4 AU. On the other hand, the mean distance to the asteroid belt from Mars is about 1.5 AU. In other words, the asteroids are rather far away from the inner planets, and it is not difficult to imagine a rather different history for them.
There isn't much material in these asteroids. The largest, Ceres, is only about a quarter the size of the Moon. All together, the mass of the asteroids is thought to be less than 1% of the Moon's mass. On the other hand, there are a lot of little asteroids, and we can tell from the light reflected from their surfaces that they must vary in composition.
Our best guesses are that the asteroids are mostly rocky objects. However, if we are going to explain the iron of meteorites as originating in this belt, some asteroids must have been large enough to form cores. This is a reasonably involved question, since the ability to form a metallic core depends not only on the size of the body but also on the availability of heat sources to melt it. There are two main sources of heat that have been considered in this context, energy from the decay of radioactive materials, and gravity. It will be necessary for us to consider these heat sources in some detail.
We can see from table 2-2 that the distance between Mars and Jupiter is about twice the distance from the sun to Mars. Putting this another way, Jupiter is a good distance beyond Mars, and we might expect on this account alone, that it might be quite different in nature from the inner planets. It certainly is.
Jupiter dominates the planetary system by virtue of its mass. The planet is 318 times the mass of the earth and 3.3 times the mass of the next largest planet, Saturn. It is well known that the orbits of the asteroids are strongly influenced by Jupiter's gravity. And there has long been speculation that a major planet could not have formed at the distance predicted by the Titius-Bode law because of perturbations from Jupiter.
The Jovian planets have a variety of satellite systems as well as rings. Prior to the space program, only Saturn was known to have rings. We now know that all Jovian planets have rings, although none as spectacular as those of Saturn. Unfortunately, we shall not have time to treat these highly interesting bodies in great detail. Their compositions mostly span the gamut from icy to rocky, and we shall already have dealt with this general topic in connection with the planets.
With the planet Jupiter, we encounter two more divisions
of the materials that formed the planets--ice, or ices. Jupiter's
density is 1.33, much too low to be dominated by any kind of rocky
material. The ices that we speak of are frozen gases, predominantly
water but with some ammonia (
), carbon dioxide
(), and trace species.
Actually, we think that Jupiter and Saturn have compositions not very different from that of the sun--mostly hydrogen and helium. So we shall add a fourth and final composition to our rough characterization of cosmic materials, the SAD. By definition, the SAD means the solar composition, primarily hydrogen and helium, with all other elements amounting to only 2% by mass.
All four planets are thought to have rocky cores, with some admixture of metal. In the case of the outer two these cores are more significant than for the inner two. All four Jovian planets have substantial magnetic fields, so their cores must be composed of material capable of conducting electricity.
Within substantial distance between Mars and Jupiter some significant change must have taken place when the planets were forming to explain the very great differences in the natures of the terrestrial and Jovian planets. We shall deal with this problem in later chapters, but we may look ahead briefly. We believe that in its earliest times, the planetary system was a flattened mixture of gas and dust which has been called the solar nebula. Within some 3 to 4 AU, the temperature was too high for water to freeze. The water remained mostly in the gaseous phase, and was swept away by violent winds from the young sun. Beyond this distance, recently called the snow line water froze, making snowballs around which the giant planets formed.
Pluto is rather small and curious. It is difficult to know how fits into the general scheme of planet formation. Fortunately, because it is so small, we may pass it by on a first consideration of the chemistry of the solar system.
Of the nine planets, only the innermost two, Mercury and Venus are without satellites. The earth has the familiar Moon, while Mars has two rather small satellites.
The giant planets are surrounded by a very complicated system of orbiting bodies. The spectacular rings of Saturn have more mundane counterparts that surround Jupiter, Uranus, and Neptune. The ring systems about the latter three planets were unknown until the advent of the space program. Jupiter's ring system was discovered by the Voyager mission in 1979. Rings about the outer giant planets were discovered by ground based observations, and later confirmed by Voyager.
We shall not comment on the details of the ring systems. Though spectacular, they do not contain much mass, and therefore are relatively unimportant insofar as the bulk chemistry of the solar system is concerned. Perhaps they contain significant clues to the chemical history of the bodies about which they revolve. This possibility has not been actively pursued, and for the present, the interest in rings centers on their form and stability.
When it comes to the satellites of the major planets, there is a great deal of material to study. One of the Jovian satellites, Ganymede, and one of the Saturnian ones, Titan, are actually larger than the planet Mercury. Another Jovian satellite, Callisto, is only a bit smaller than Mercury. These are giant systems, and a great deal of attention has been paid to them.
The so-called Galilean satellites of Jupiter, Io, Europa, Ganymede, and Callisto, were discovered by Galileo (1564-1642). The objects were among the paroxysm of discoveries that followed his first application of a telescope to problems of astronomy. Galileo was incredibly gifted. It may be recalled that he did not invent the telescope, but having heard of its invention, immediately set out to construct one. Galileo's discoveries got him into trouble with officials of the Catholic Church. It is a fascinating story. We will have a little more to say about it in Chapter 3.
Galileo suggested that the moons he discovered about Jupiter were a miniature solar system, similar to the one suggested by Copernicus. This was a profound notion, still of value today, and not only because the Galilean satellites circle their parent body just as the planets do. For example, the densities of the Galilean satellites decrease from the innermost--from 3.57 gm/cm3 at Io to 1.86 gm/cm3 at Callisto. Planetary scientists have suggested that this density decline might occur for reasons similar to the density decrease of the planets themselves, from Mercury through the Jovian planets.
The densities of these giant Jovian satellites give us immediate insight into their chemistry. Io is slightly more dense than the earth's Moon (3.30 gm/cm3). We have already concluded that the Moon is composed primarily of rocky material, similar in nature to the earth's mantle. Clearly, the composition of Io must be similar. Just why Io is even more dense than the earth's Moon is a fascinating question. It may be related to the extraordinary activity that takes place on the body--volcanism and outgassing.
Io's ``geological'' activity may exceed that of the earth. Volcanic mountains and lava flows resurface the satellite at an estimated rate of one meter per 1,000 years. An estimate for erosional rates on the earth is about 0.1 meter per 1000 years. Major changes of the earth's surface, such as the ``drift'' of the continents or carving to major canyons take some 100,000 years. Io may have been resurfaced as many as ten times during this period.
Telescopic observations of Io had indicated to astronomers that this was a most unusual body, but it was not until the Voyager missions in 1979 that we knew for sure just how strange it was. Interestingly, theoretical calculations by the American planetary physicists had predicted that Io's surface would be melted as a result of tidal forces between the satellite and Jupiter. The authors of this work, Peale, Cassen, and Reynolds, had the unusual experience of having their theory confirmed--in spades--the same year their paper was published.
The basic theory of Peale et al. was that Io would be subject to similar forces to those that act between the earth and Moon to raise the familiar oceanic tides. Less spectacular body tides occur on the Moon and the body of the earth, slightly changing their shape. The tidal forces are not constant, so the material gets squeezed and can then relax. This squeezing and unsqueezing deposits heat in the bodies, and this heat can be the cause of volcanic activity.
It is possible, but by no means certain, that the geological activity has boiled off enough of the volatile content of Io so that it is even denser than the Moon. This is no small feat, because we know that the Moon is a very dry body already. In this chapter where we have simplified the chemistry of the solar system to three basic ingredients, metal, rock, and ices, in decreasing order of density. Io must be mostly rock. As we move outward, to Europa, Ganymede, and Callisto, the fraction of rock to ice must steadily decrease. Callisto is still too dense to be entirely ice, and models show a rocky core about halfway to the center of this satellite.
Saturn's giant moon Titan has a density nearly the same as that of Callisto, so its structure must be just about the same--a rocky core and an ice mantle. Interestingly, the surface of Titan is enclosed in a nitrogen-rich atmosphere. Indeed, this satellite is the only one in the solar system with a substantial atmosphere. Why should this be so? Perhaps it is just a matter of the temperature.
We shall not dwell here on the myriad minor satellites of the Jovian planets. They are fascinating in a number of ways, but like the rings, their relationship to the overall chemistry of the solar system is probably minor. We cannot rule out that some significant clue remains hidden in the composition of these objects, but for the present, we must move on.
Comets have been known since ancient times. They appear as bright streaks of light in the sky, that move with respect to the stars. Most comets have a bright head, and a tail that may be several tenths of an astronomical unit in length. The known ones have orbits that take them to the inner solar system, where interaction with sunlight causes their often striking luminous features. Modern electric lighting, especially in cities, makes the night sky bright so comets appear relatively fainter than they would 100 or more years ago.
Some comets have orbits that cause them to return periodically to the inner solar system. The most famous of these is Halley's Comet. This object made spectacular appearances in Mark Twain's time, but was something of a dud when it most recently neared the sun in 1986. Our skies were too bright, and the comet itself may have mostly burned out. We know this happens to periodic comets because meteor showers or shooting stars are seen on nights when the earth intersects orbits of old comets.
The comets are primarily icy bodies. Sunlight causes the ices to boil off, and luminesce. Most comets are located very far from the sun. There are two reservoirs, one only a little beyond Pluto and a second one at the limits of the solar system. The furthest reservoir is called the Oort Cloud, after a Dutch astronomer who first postulated it. The inner cloud is also named after a Dutch astronomer who spent most of his career in the United States. It is called the Kuiper belt.
The names reveal what we believe the geometry of these clouds to be. The Oort cloud is spherical, while the Kuiper belt is flattened, and in the plane of the solar system. In both cases, gravitational perturbations may cause a comet to approach the sun, allowing it to be observed from the earth. In the case of the Oort cloud, passing stars are believed responsible for the perturbations.
Kuiper belt comets feel significant gravitational pulls from the planets themselves, especially Jupiter. Accumulated perturbations over many-many orbital cycles may dislodge a comet from its position in the belt and cause it to enter the inner solar system. Once set on such a path, the comet may become periodic like the famous Halley's comet, and return after a fixed number of years. The new orbit would take the comet from the inner solar system, and back out to the Kuiper belt.
We would like very much to have a piece of a comet that we could analyze in our laboratories. There are a variety of reasons for thinking this material might reflect most closely the composition of the original solar nebula. This composition, of course, would be the starting point for any attempt to make models of the structure and history of the solar system itself. So keenly have researchers sought this composition, that others have facetiously referred to it as the Holy Grail.
Surely, we know a lot about the materials that comets are made of. Astronomers have observed the spectra of comets and identified various atoms and molecules. During the most recent Halley approach, spacecraft flew near the comet and made numerous observations. Unfortunately, no samples were returned to earth, so that what we learned is much less detailed than we would like.
The big problem with the bulk composition of comets is that we do not know their mass.
Newton's laws of gravity allow you to tell the mass of the body that is being orbited very precisely. So planetary motions tell us the mass of the sun. Similarly, the motions of satellites tell the mass of the parent planets. Prior to the space program, we only had an estimate of the Moon's mass from studies of the three body problem--the sun, the earth, and the Moon. This is the problem Newton said made his head ache. By modern times, the Moon's mass was known to somewhat more than three significant figures.
The Moon is sufficiently massive to interact rather strongly with the earth. Minor bodies of the solar system are much less massive, and their paths are determined primarily by the sun and nearby major planets.
We know relatively little about the masses of the asteroids, and consequently, we can only estimate their densities by assuming they are mostly rocky in nature. If we assume that we know the density of an asteroid, we can estimate its mass once its volume is known.
Some information on the sizes of asteroids is available. We know how bright they are, and we can make reasonable estimates of their relfectivities. Generally, their reflected light is consistent with the light that would be reflected from one kind of meteorite or another. Combining this information with their distances, and the energy they receive from the sun, we can tell how big they must be to have the brightnesses we observe. For a very few asteroids, we can also determine their sizes by making measurements as they pass in front of stars. Crudely speaking, the larger the asteroid, the longer time it will dim the light of a star.
When it comes to comets, it is very difficult to determine even the size of the solid nuclei. Unlike they asteroids, comets are surrounded by extensive gaseous material that conceals their central regions. The flyby missions to Comet Halley in 1986 did see a murky, potato- shaped nucleus about 15 x 8 km in cross section. Estimates of the density, however, had to be made from the measured gas/dust ratios ejected by the comet's activity, which was induced by the sunlight.
It turns out that comets are subject to ``non-gravitational forces'' due to jets of material coming from the nuclei. It is possible to ask how massive the comets must be in order to have their orbits affected by these jets. This gives one of the better estimates of the mass of Halley's Comet, about 1017 gm. Density estimates for the nucleus, then range from 0.1 to 0.5 gm/cm3--uncertain by a factor of five!
So for comets, we cannot use densities as an indication of the percentage of rock to ice, but perhaps an equally good idea of this can be obtained from the material that was ejected. The latter was thoroughly sampled. Dust to gas ratios in the ejecta fall in the range of 1/2 to 1/5. If we identify the dust with rocky material, and the gas with (mostly) vaporized ice, we see that comets have a higher percentage of ices than the outer planets or satellites. This is consistent with the notion that comets may be the most sun-like in composition of all bodies in orbit about the sun.
The sun is more massive, by slightly more than a thousand, than the giant planet Jupiter. While we know its mass and volume quite accurately, we cannot use its density to infer its composition because the sun is highly compressed.
The part of the sun from which the light comes to us is a gas with a mean temperature of about 5800K. The total pressure is about a tenth that at the earth's surface. There are a few molecular fragments, but most molecules are dissociated. These are mean conditions. At any point on the surface of the sun, conditions can vary wildly. Hot gas from below flows upward, while cooler gas descends. Conditions in the hot and cold streams can fluctuate wildly, and it is amazing that the solar surface seems so uniform and constant.
One of Galileo's many discoveries was sunspots. It is not difficult to see sunspots with some optical aid. Of course, one should never look directly at the sun with binoculars or a telescope, but it is easy to project the solar image on a white card, and then sunspots are readily found. These are regions a thousand or more degrees cooler than the 5800K mentioned above. They are incredibly complex regions, with strong concentrations of magnetic fields, and complicated gas flows.
Probably no one would have predicted sunspots if they hadn't been observed. It is perhaps a lesson for anyone who does science to realize that nature can be very complex. Regions of the sun that we cannot observe directly are thought to be considerably simpler than the surface.
What the astronomer does to understand the interior of the sun, and indeed all stars, is to make mathematical models of them. The procedure is similar in nature to models of planetary interiors. These models are constructed by requiring that the pressures at any depth must be enough to hold up the mass of the overlying layers. We start at the ``top'' where the pressure is very low, and consider a slab of material with the conditions we think exist there--the temperature and pressure. This slab has a certain mass, so we ask what the pressure must be at the bottom to support it. Along with this pressure, there is usually an increase in temperature.
Some atoms may lose electrons as a result of the increased temperature, for example. So we have slightly new conditions for the material that makes up the next slab. We take these into account in calculating its mass, and we add this mass to that of the slab(s) above it in order to get the pressure at the bottom of the new slab. These procedures are followed until we get to the center, where the pressure must be sufficient to hold up the entire star--or planet.
The structure of the solar interior is thought to be rather well understood, although a few mysteries remain. If the sun were originally uniform in composition, then theoretical models predict the rate at which hydrogen is being converted into helium in the regions near the center. This conversion, of course, takes place by nuclear reactions, whose rates are believed to be rather well understood. However, it may be that we don't quite know all that we need to know.
For some twenty years now, there has been a discrepancy between the observed and predicted numbers of elementary particles known as neutrinos which should be produced in the solar interior. This discrepancy is one of the major unsolved problems of stellar astrophysics.
The neutrinos are produced by the nuclear reactions that supply the sun's energy. They interact only very weakly with matter, so they emerge from the solar interior and stream out into space. A certain number of them must pass through the earth, and with very careful measurements, physicsts have been able to detect them.
Much recent discussion has centered around the possibility that the problem may not lie in the astronomical domain at all, but in that of particle physics. Roughly half the neutrinos that should have been detected actually were. It is possible that some of the neutrinos changed their form in flight from the sun, and this might account for the low measurements.
Neutrinos come in three flavors, and if they ``oscillate'' from one form to another, the consequences could be of considerable importance for the dark matter problem that we have mentioned earlier. The neutrino oscillations might occur because these particles have what is known as a rest mass.
According to special relativity, the mass of a particle will increase as its velocity approaches that of the speed of light. If a particle has any mass, no matter how small, when it is at rest, it cannot be accelerated to the speed of light. Therefore, photons, which by definition travel at the speed of light, can have no mass when they are at rest, and therefore, there is no such thing as a photon at rest.
It is not known if neutrinos are like photons, with no rest mass at all, or if they have very small masses, and travel at nearly (but not exactly) at the speed of light. If the latter situation turns out to be true, we may not only solve one of the outstanding problems of the structure of the sun. We may also solve one of the main problems of the structure of the universe itself, for it might be that the missing or dark matter could be explained by massive neutrinos.
We have simplified the composition of materials by only considering four categories of matter--metals, rock, ices, and the solar composition, or SAD. We find the inner or terrestrial planets consist of metals and rock, with the metal/rock ratio diminishing from Mercury through Mars and the asteroids. The Jovian planets consist of small portions of metal and rock, ices, and substantial amounts of hydrogen and helium. Jupiter and Saturn may have compositions rather closely resembling the SAD. The densities of the planets give crude indications of what their compositions must be. We do not know the masses of many of the minor bodies of the solar system, and therefore do not know their densities. This situation applies to many satellites, to asteroids, and to comets. For these bodies, we may get some information about the chemistry of surficial matter, or in the case of comets, from material that has boiled off the surface.
We shall begin our survey with the universe itself. Perhaps the reader will find this an audacious, if not impudent notion. Isn't the universe the domain of philosophy if not religion? There is a way out of this difficulty.
The way was shown many years ago to the great pioneer Galileo Galilei by Cardinal Bellarmino (1542-1621). Galileo wanted badly to convince the world that the earth was not at the center of what was then thought to be the universe--what we now call the solar system. Copernicus (1473-1543) had proposed, and Galileo firmly believed, that the sun was central. However, this idea was not popular with the power centers of Rome, and Bellarmino advised Galileo to take a different approach. He suggested that Galileo treat the notion of a heliocentric universe as a hypothesis, and not as something that was necessarily ``true'' in some fundamental sense. Galileo might have saved himself consederable grief if he had heeded this advice.
A modern name for what Bellarmino called `hypothesis' is model. Models are usually ideas that are thought to have approximate reality, but are not expected to have the full complexity of natural objects. Astronomers make model planets, model stars, and model universes. The models are scaled in such a way that the mind is not overwhelmed by the vastness of the distances and times. If the notion of the universe as a whole seems formidible, then think about a model of it. Our model universe may be pictured as a large volume of space. For many purposes it is permissible to think of it as a big sphere, and we may scale the radius of the sphere down in our model until we can think of ourselves viewing the whole thing from the outside.
The sphere that may serve as our model universe will not have all the same properties as a cloud of gas such as a star. But many properties will be similar. In some ways our model universe will be similar to an exploding star. It may be helpful to think of models, and for the present, not to worry too much about the ``real'' universe.
People who work with models of the universe, cosmologists, may believe sincerely that their models are realistic. That's OK, perhaps they are. We can adopt that attitude too, if we want. If this notion is a bit too heavy, we can always say to ourselves, we are just considering models.
The devil is in the details. Cosmologists have a variety of ideas about how the universe behaves, so they propose different models. Some of these models appear more likely than others. At the present time, the favored models start with matter in an incredibly dense state that has expanded to the vast system we view today.
Galaxies are giant systems of stars, gas, and dust. In our own Galaxy there are perhaps 1011 stars. Astronomers use an upper-case G to distinguish our Galaxy from other galaxies. Until fairly recently, one might have said that the basic bricks from which the universe was constructed were clusters of galaxies but modern work, probing the depths of the universe, has revealed gigantic structures comparable in size to the largest volumes surveyed.
The largest distances that we may realistically consider are relatively easy to remember, because they are about the distance that light can travel in a time equal to the age of the universe. Our guesses about how old the universe is, and therefore how large it is are uncertain. Until quite recently it would have seemed safe to say the universe was between 10 and 20 billion years old. There is some recent evidence that it is somewhat younger than 10 billion years, but we shall keep the round numbers.
The corresponding radius of the universe is then between 10 and 20
billion light years. A light year is a popular unit of astronomical distances,
equal to the distance light travels in a year.
Astronomers use another distance unit called the
parsec. It is a bigger unit than the light year, and arises
from measurements of distances to stars. We shall discuss them in
a moment. A parsec is 
centimeters, or 3.1
billion billion centimeters.
There are 3.26 light years in a parsec, so in round numbers,
the radius of the universe
is some 3 to 6 billion parsecs. Intergalactic distances are measured in
units of millions of parsecs, or megaparsecs. Thus the universe
is some 3,000 to 6,000 megaparsecs in radius.
It is still uncertain whether, if we look on a large enough scale, if the universe smooths out. One of the pillars of the modern theory of the universe is that this must be the case. The universe must look the same in every direction, for every observer. Experts in the field call this the cosmological principle, and all modern theories of the universe assume it. Observations reported in the summer of 2000 by a consortium of astronomers support the notion that there is a maximum size of large scale structures. On a larger scale, these structures merge into a smoother background, as required by the cosmological principle.
There is, of course, no proof of the cosmological principle any more than there is a proof of any scientific ``law.'' Like all science, the notion rests on observations (or experiments) for its confirmation. The current situation is that on scales up to about 30 megaparsecs, galaxies and clusters of galaxies seem to form a network of walls, columns, and voids. The structure has sometimes been compared to that of a spunge.
We need not concern ourselves with these larger structures, because little is known of their chemistry beyond the composition the galaxies and clusters of galaxies that form them. Some very new information is becoming available through the use of distant quasars, but we shall only mention it briefly, when the time comes. The largest aggregate that we shall deal with is the cluster of galaxies. For historical reasons these are not called galactic clusters. The term was already used for certain clusters of stars in our own Galaxy.
The nearest large cluster of galaxies is about 20 megaparsecs away in the direction of the constellation of Virgo. It contains several thousand galaxies, and is perhaps 3 megaparsecs in radius. Another well known cluster is in the direction of Comae Bernices, and is about 5 times further. One of the strangest properties of these giant clusters is that the galaxies are imbeded in an envelope of very hot, diffuse gas. The temperature of this gas is so high that it is best observed by satellites that can sample photons at X-ray wavelengths.
The hot gas in clusters of galaxies was unknown prior to space astronomy. The first research dates from the early 1970's. What is so strange about this material is that its mass is significantly greater than that of the galaxies in the clusters! Even though the density of this gas is very low, it is found over such immense volumes that its total mass is impressive. If we average over the entire universe of galaxies as we know it, a substantial fraction of the material, perhaps as much as half(!!), may be in the form of this hot gas. This recently discovered material surely deserves to be called a major constituent of the universe.
Unlike the mysterious, and even more massive dark matter, the hot gas is composed of atomic ions and electrons whose nature we understand relatively well. What is the composition of this gas, and where did it come from? These are significant questions that we must answer.
Galaxies come in so many varieties that it is impossible to say that ours is typical. Giant galaxies may be several hundred times smaller in diameter than the Virgo or Coma clusters. Their diameters are several tens of kiloparsecs rather than megaparsecs. The largest may contain some 1012 times the mass of the sun in stars and interstellar matter in the form of dust and gas. There are also dwarf galaxies some 10 to 100 times smaller than the giants.
Possibly the most useful description of the different forms of galaxies is that of the American astronomer Edwin Hubble (1889-1953). His ``tuning fork'' scheme is by no means inclusive, but gives us a good start.
There are two main kinds of galaxies, ellipticals and spirals. The spirals divide into two families, as shown in figure 3-1.
Figure 3-1: Hubble's Tuning Fork Classification of Galaxies. The spirals form two families, one called regular and the other barred spirals. The transition type called S0 may be a spiral that has lost its gas.
Figure 3-2 shows photographs of a few representative types. The designations, refer to numbers in catalogues. The M stands for the early catalogue of the French astronomer Messier in the late eighteenth century. This catalogue differed from previous astronomical catalogues. Since the time of Hipparchus, astronomical catalogues had featured stars or planets. Messier's catalogue featured clusters of stars, and diffuse, bright regions called nebulae. We now know that some of the nebulae are external galaxies, while others are gasseous clouds in our own Milky Way.
Nearly a century later, a ``New General Catalogue'' (NGC) of stars and nebulae was compiled by the Danish-born astronomer J. L. E. Dreyer.
Figure: 3-2: Representative galaxies. Upper left: M100 an Sc; upper right:
NGC 1300, an SBc; lower left: M84, an elliptical;
lower right: M104, an edge-on spiral showing a dust lane.
Elliptical galaxies are rounded or flattened stellar systems. They contain relatively little gas, probably less than a per cent of the total stellar mass. Spiral systems may be rich in gas, especially in the arms, were the star-to-gas mass may be of comparable orders of magnitude. Star formation is clearly going on in spiral arms. If it is occurring in the centers, or bulges of spirals, or in elliptical systems, it is at a relatively low rate.
We can now turn to an overview of the abundances of the elements in galaxies. In our discussion of the solar system, we used four broad categories, metal, rock, ices, and the sun's composition or SAD. These will not suitable for the present purposes. What basically happens as large stellar systems evolve is that hydrogen and helium are converted into heavier elements. Astronomers have traditionally designated the abundances of hydrogen, helium, and all other elements by the letters X, Y, and Z.
In one of the more bizarre quirks of language usage, Z became known among workers in the structure of stars as the abundance of ``metals.'' Since in most stars, the bulk of the contribution to Z comes from carbon, oxygen, and nitrogen, this is a rather severe misnomer. It arises from a time when it was thought that the bulk of Z was not due to these lighter elements but from iron and its nearby congeners. We shall say more about this when we discuss the history of abundance determinations in stars. For the present, it is useful to use the symbol Z to describe the chemical evolution of stellar systems.
Initially, we may suppose that Z is nearly zero--all of the matter is either hydrogen or helium. As stars evolve and die, in most cases they manage to return some of their mass to the interstellar medium. Because of the processes called nucleosynthesis--the manufacture of nuclei--the returned material has a larger Z than that which formed the star in the first place. Stars may manufacture nuclei rapidly in gigantic explosions, or by slow cooking, but the net result is this slow increase in the average Z for the stellar system. Even in the most mature systems, Z is not very large. In the case of the SAD, Z is about 0.02, so only 2 per cent of the original hydrogen and helium (mass) has been converted into heavy elements (or ``metals'').
In the terrestrial planets, Z is much larger than in stars--more than 0.99. Consequently we needed to talk about entirely different mixtures. Only with the Jovian planets do we reach values of Z that are significantly below 0.99.
The Z-values of spiral and elliptical galaxies follow two quite different patterns. In the spirals, Z is largest where the gas content is least. This effect may be seen both from one galaxy to another, and within a spiral. Z is low in the gas-rich arms and higher in the bulges, where there is relatively little gas. In elliptical systems it is the mass that seems to govern the value of Z. Massive systems have high Z, while dwarf ellipticals have typically lower values.
It is still useful to think of the sun as a typical star. It has a typical mass. Indeed, most stellar masses are contained within 1/10 and 10 times the solar mass. Some stars can have intrinsic brightnesses that are many orders of magnitude greater than that of the sun, but these objects are relatively rare.
We can tell the distances to the stars by a variety of methods. A basic method uses triangulation--observing a nearby star against the background of distant stars. If you hold your finger up at arms length, and alternately open and close your left and right eye, you will see the finger appear to move with respect to objects behind it. This method is used for stellar distances, but instead of a baseline from one eye to another, stars are observed from different points of the earth's orbit. This is illustrated in figure 3-3.
Figure: 3-3. Stellar Parallax. A relatively
nearby star appears to move
with respect to background stars when it is viewed from different
parts of the earth's orbit.
The angle 
subtended by the
radius of the earth's orbit, as seen from the star,
is defined to be the parallax
of the star. When
is measured in seconds of arc, then
the distance to the star is said to be 
in parsecs.
Most stars are slowly converting hydrogen into helium, and during this process, there is a close dependence of the star's surface temperature and its energy output or luminosity. This relationship is most easily represented with what is called a Herzsprung-Russell (HR) diagram, after the astronomers who first noted it. We show an HR diagram in figure 3-4.
Figure 3-4: Herzsprung-Russell (HR) Diagram. The surface temperature of the stars is plotted along the x-axis, but increasing to the left. The y-axis is the ratio of the intrinsic stellar brightness or luminosity to that of the sun.
Most stars fall along the main sequence which stretches from the upper left to lower right. Hotter stars fall the left while cooler ones are on the right. The brighter stars are called giants, and the fainter ones dwarfs. Since the colors of stars indicate their surface temperatures, we may say the main sequence extends from the blue giants to the red dwarfs.
With very few exceptions, we think the surface composition of main sequence stars is the same as the material from which the star was formed. Thus, in the case of the sun, its composition would be the best indication of the composition of the primordial solar nebula. We determine the composition of material at the surfaces of the sun and stars by analytical spectroscopy. This involves the use of an instrument called a spectroscope, which splits the starlight into its constituent colors, or wavelengths. The resulting spectra contain the imprint of the atoms in the material in the stellar atmospheres. We shall have more to say about spectroscopic methods in a subsequent chapter.
In addition to main sequence objects, we also show the location of red giants and white dwarfs. As stars use up their hydrogen, they swell up and become red giants. In later stages of evolution, the stars may explode, or follow complicated tracks that eventually take them back across the main sequence and down to the region of the white dwarfs.
We think a relatively small percentage of stars are single. Perhaps 70% are in double or multiple systems. Beyond these multiple systems, triples, quadruples, etc., are star clusters. There are two very different kinds of star clusters in galaxies. In the planes of spirals, there are clusters of relatively young stars that have formed from contracting clouds of gas. These clusters contain from some tens to a thousand or so stars.
In our Galaxy, such clusters are found along the Milky Way, which is really the plane of our system seen from the location of the sun. These clusters of young stars were called galactic clusters because of their location in the galactic plane. Two bright galactic clusters known as the Hyades and the Plieades. They are both in the constellation of Tarus, and readily visible in the winter sky.
Figure: 3-5.
The Globular Cluster M15. It is located in the direction
of the constellation Pegasus, and is some 15 kiloparsecs away from us.
M15 is located well away from the plane of the Galaxy, in the region
astronomers call the halo. The blow-up shows the
central regions of the cluster. It is resolved into individual
stars for the first time by the Hubble Space Telescope.
There is an entirely different kind of cluster associated with both spiral and elliptical galaxies. These fascinating objects are called globular clusters. They are nearly spherical and contain as many as 105 closely-packed stars. A typical globular cluster is shown in figure 3-5. The globular clusters form a spherical halo about our Galaxy, falling within the volumes left unoccupied by the largely flattened system.
The globular clusters are old systems, relative to the hotter stars that can be found in spiral arms, and their Z-values are typically lower. The German-American astronomer Walter Baade (1893-1960) discovered that important properties of stars with low Z were significantly different from those with solar and higher Z's. He called the latter stars Population I and the former Population II. Some Population II stars are found in the plane of the Galaxy. These ``general field'' objects are not in globular clusters, although perhaps they once were.
Go out on some moonless summer night and look up at the Milky Way. You can find it by locating the ``Northern Cross'' in the constellation of Cygnus. You may have to drive out in the country to get away from the city lights! The axis of the cross lies nearly along the Milky Way. One side of the summer triangle, the bright stars Deneb, Altair, and Vega, also falls in the Milky Way. The Deneb-Altair side is in the Milky Way, with Vega just to the east.
The band of the Milky Way forms a great circle. It continues south, and returns to the northern sky among winter constellations, where it is less spectacular than in the summer sky. This beautiful band of light is seen when we look along the plane of the Galaxy, as we have already noted. The remarkable Galileo pointed out that this band of diffuse light was due to myriad unresolved stars.
It was only in the present century that astronomers realized the significant role of interstellar dust in dimming starlight in the plane of the Galaxy. Naively, one might expect the Milky Way to be significantly brighter in the direction to the Galactic Center. But as late as the early decades of the 1900's astronomers thought the sun was near the center of a flattened system of stars, because they could detect no concentration of brightness that would indicate a center in any specific direction. We now know that the dimming of starlight is so effective that we just can't see far enough to tell which direction is toward the Galactic center.
Modern astronomical techniques involve observations at wavelengths that were not possible until the latter half of the 20th century. Some of these wavelengths are quite unaffected by dust, so we can ``see'' right through the Galactic center to material on the opposite side. Astronomers began to map out clouds of neutral hydrogen gas in the years immediately following World War II. They used the new radio telescopes, which made use of the radar techniques perfected during the war. Some decades later, still newer methods made it possible to observe lines from interstellar molecules. With these observations, the intimate relationship between dust, gas, and the formation of new stars became apparent.
In the arms of the Galaxy, there are roughly equal masses of stars and gas. The overall fraction of mass that is dust cannot be very large. We know this because dust must be metal, rock, or ice, and these materials have a high value of Z. While the SAD isn't really universal, we can at least use it to estimate what the interstellar Z might be. We have already noted that Z is 0.02 in the SAD. Estimates of the fraction of the total dust to gas ratio are about 1% or somewhat less.
Most of the gas in the plane of the Galaxy is in molecular clouds. There are several thousand giant molecular clouds, or GMC's, and their masses are comparable to those of the globular clusters, up to some 105 solar masses.
It is in these objects that star formation is taking place. In agreement with our notion of the SAD, most of this gas is molecular hydrogen, H2, but in the denser regions of these clouds very complicated molecules occur. These molecules are shielded from the general stellar ultraviolet radiation field by dust. The molecules would be dissociated by the ultraviolet photons without this protection, so the dust is necessary for these clouds to form. Interestingly, the interstellar dust is thought to originate in evolved stars. Thus, there is an interesting chicken-and- egg question regarding these giant clouds and the associated dust.
One theory is that the dust is formed by stars in the general field--not in clusters. The dust then clumps, for reasons that are not understood, and within these clumps molecular clouds can form. Once the molecules form, the clouds can grow, and eventually reach densities where new stars can be formed.
Gas in the GMC's is generally cold gas, but there are also regions in the plane of the Galaxy where the gas is mostly ionized. Astronomers now call these hot clouds H II (H-two) regions. Neutral hydrogen gas is often called H I, so one might speak of either H I or H II regions, depending on whether the gas was predominantly neutral or ionized.
H II regions typically surround hot, young stars, whose ultraviolet photons are capable of maintaining the hydrogen gas in an ionized state. There are also H II regions in our Galaxy where the gas is ionized as a result of shock waves generated by exploding stars. These H II regions show spectra of helium and heavier elements, and it is possible to derive abundances from them. For many years there was little evidence that these abundances were significantly different from the SAD. Recent work however has revealed significant departures from this standard.
It is possible to observe H II regions in some distant galaxies where it would be impossible to determine abundances from individual stars. Much of our knowledge of abundances in distant systems has been derived from these emission regions rather than from stars.
We explored a heiarchy of cosmic systems, starting with the largest structures containing clusters of galaxies. Much of the visible matter in our universe is not in stars at all, but a very hot, diffuse, gas found in clusters of galaxies. We found it convenient to add another category of composition to the crude divisions of metal, rock, and ice, namely, that of the SAD. The SAD contains elements capable of forming the first three materials, but it is 98% hydrogen and helium by mass. By definition, the sun should have the SAD composition.
Galaxies contain globular and galactic clusters. The former are old systems; the latter are young, and in some cases are still forming stars. Young stars are formed in giant molecular clouds, where interstellar dust shields the molecules from ultraviolet radiation from the hottest stars. We may crudely describe the composition of stars and gas using the parameter Z, which is 0.02 in the SAD. As galaxies evolve, we think their compositions change from values of Z nearly zero to those that may be as much as 0.2. In elliptical galaxies, Z is correlated with the mass of the systems, while in spirals, it is most closely related to the gas fraction. Spiral systems that have used up their gas have high Z.
Astronomers know what stars are made of by studying their light with an instrument called a spectrograph.
A spectrograph is used to break up light into its constituent colors, or wavelengths. Figure 4-1 shows the components of a prismatic spectrograph, where a prism is used to separate the wavelengths. Gratings are now more commonly used in astronomical spectrographs. If the light is visible, we may refer to its colors, with the shortest wavelengths being violet, and the longer ones red. Visible light is a small fraction of the electromagnetic spectrum, and astronomers now study such radiation from the short-wavelength gamma rays to radio waves.
Figure: 4-1 A Simple Prism Spectrograph. A slit is at the left, and rays are shown converging on it from a light source to the left that is not shown. The rays are rendered parallel by the first lens, and passed through the prism, where the colors are separated. We show only two colors, red (R) and blue (B) for simplicity. The different rays are focused by the second lens on a detector, the flat surface to the right.
A convenient unit for the discussion of stellar spectra is the angstrom unit, 10-8 cm. The symbol Åis commonly used to mean angstrom units. Visible light stretches from about 4 000 to 6 500Å. Modern instrumentation, including satellites make it possible for stellar astronomers to analyze light from gamma-rays to 10 000 Åand beyond.
When light interacts with atoms or atomic ions, it can cause the electrons to occupy higher energy states. When this happens, the photon vanishes, and its energy is taken up by the atom. We say the atom is ``excited.'' This process is called absorption.
The inverse of absorption is emission. Here, the excited atom creates a photon with an energy just equal to the difference in the energies of the excited and deexcited atomic states. Molecules can undergo transitions of this kind just as atoms or atomic ions.
It was known even in the nineteenth century that each chemical substance absorbs and emits photons of only certain special wavelengths, and these wavelengths can be used to identify the materials. The atoms ``write their names'' in the light which they emit or absorb.
When light from the hot interior of stars passes through the overlying cooler layers, atoms and ions absorb some of the photons. This leaves the departing radiation with characteristic wavelengths where some of the energy is missing. Spectroscopists call these absorption lines (figure 4-2). By carefully measuring the wavelengths of these lines, it is possible to tell which chemical elements are present in a stellar atmosphere. Moreover, the relative abundances of the elements may be determined from the strengths of the lines.
The job is not easy, because the lines from one atom may overlap those from another. Nevertheless, by the mid 1960's some 65 chemical elements had been identified in the solar spectrum, and crude abundances had been made for about two-thirds of them. These abundances approximated that of the SAD, but were too uncertain for use in theories of the origin of the elements. Fortunately, a different route was available to cosmochemists, and by 1960 the modern theory of the origin of the chemical elements had been laid.
Chemical abundances may be determined from stellar spectra, but very little information is contained in these spectra on the relative isotopic content. Each chemical element has a number of isotopes that are distinguished from one another by the number of neutrons in the nucleus. Because the electronic structure of atoms is determined primarily by the nuclear charge, the number of protons, isotopes have very nearly the same patterns of spectral lines.
Not all isotopes are stable. There is an optimum mix of protons and neutrons that an atomic nucleus can live with. If there are too many or too few neutrons, the nucleus will spontaneously change. What typically happens in these changes depends upon whether there are too many or two few neutrons. If there are too many neutrons, a neutron will change into a proton. What happens is that one of the excess neutrons will emit an electron. The neutron had no charge to begin with, while the electron has a negative charge. The newly created proton has exactly the same charge as the created electron, but with a positive sign, and in this way nature preserves the net electrical charge.
Nuclear transformations of this kind were known from the early days
of radioactivity, even though they were not completely understood. The
electrons that are created when the neutrons turn into protons leave the
atom altogether. Early investigations of these escaping electrons referred
to them as a kind of ``radiation,'' and the particles that came off were
called beta-rays (
-rays). Beta-rays are nothing more than ordinary
electrons created by nuclei with too many neutrons for them to be stable.
Physicists often call the process -decay.
If there are not enough neutrons in a nucleus for it to be stable,
a similar process takes place, but this time a proton will turn into a
neutron by emitting a positive electron or a positron. The process
is still called -decay, and if it is necessary to make clear which
process is meant, we can refer to beta-plus or beta-minus emission.
Whenever beta emission takes place, neutrinos are also emitted. We
shall say more about them later.
Like charges repel one another. In the nucleus, strong attractive
forces overcome this repulsion until the number of protons exceeds the
number 83, of the element bismuth. All known nuclei with more protons
than 83 are unstable, although some, like thorium (90 protons) and
uranium (92 protons) last a long time. The common isotopes of thorium
and uranium will spontaneously emit the nucleus of a helium atom.
These helium nuclei were called alpha-rays (
-rays) in the early
history of radioactivity.
A third kind of ``ray'' emitted by radioactive nuclei is known as the gamma-ray
(
-ray). Gamma rays are just highly energetic photons. All three
kinds of radiation were known by 1900. Heavy nuclei may also break apart,
or fission, the process that was involved with the first atomic
bomb.
The word ``decay'' is used generally to describe these radioactive
emissions, so one may speak of 
-, 
-, or
-decay. Since gammas are really photons, it is perhaps more
common to speak of gamma emission than -decay, but
the latter term is also used.
The kinds of radioactivity that we have mentioned limit the number of stable nuclei to about 265. But this is a considerably larger number than the 83 chemical elements from hydrogen through bismuth. It therefore turns out that there is a lot more information in the chemical composition of material if the isotopic abundances as well as the elemental abundances are available.
In Chapter I we mentioned that the history of cosmic materials were written in their abundance patterns. The book in which this information is written is, so to speak, more informative when we have information on the isotopes. The current ideas of the origin of the chemical elements were formulated when accurate isotopic abundances became available in the early 1950's.
William Harkins (1873-1951) was a chemist at the University of Chicago when he published a seminal paper on the abundances of the chemical elements in 1917. This study was primarily concerned with the structure of atomic nuclei, but Harkins's reasoning was remarkably astute. He argued that an important clue to the stability of nuclei was their abundance in nature. Moreover, he was among the early workers to emphasize the importance of meteorites as a source of the most relevant abundances.
Isotopes played no significant role in Harkins's study, although they had been known for a few years prior his 1917 paper. He mentions the word in it only once. His work focused on the elements, or the atomic number, for which the symbol Z is usually employed. Thus Z = 1 for hydrogen, 2 for helium, and so on. Note that this is a different meaning for the symbol Z than that used in the last chapter.
Figure 4-3:
Meteoritic Abundances from a table published by Harkins in 1917 for
stony meteorites.
The major regularity that Harkins emphasized is that the abundance of elements with even atomic numbers is characteristically higher than the abundance of neighboring elements with odd Z's. Figure 4-3 was plotted from data in his paper, and shows the outstanding abundances of oxygen (Z = 8), silicon (Z = 14), and iron (Z = 26). While we would not accept these numbers quantitatively today, their qualitative relationships are important. Harkins noted that when two even elements were particularly abundant, as magnesium and silicon, that the odd-Z element between them was somewhat more abundant than the odd-Z elements nearby. Harkins used this notion to argue that the chemical elements might have originated by a build up from the lightest to the heaviest. We essentially believe this today. Figure 4-4 is a modern plot of the SAD.
Figure 4-4: The SAD. The values are from a paper of Edward Anders and Nicholas Grevesse published in 1989.
By the mid-1920's the mass spectrograph had been invented by Aston (1877-1945). This instrument makes it possible to measure atomic masses with great accuracy. In addition to elemental abundances, with the help of this instrument, investigators could obtain isotopic abundances as well.
Now until the end of the 1960's it was thought that the relative abundances of isotopes of an element were generally the same in meteorites or crustal rocks of the earth. Early work on what was then called the ``cosmical abundances'' concentrated on elemental compositions. If relative isotopic abundances were needed, they were usually taken from terrestrial sources. Today's student of cosmochemistry may find this difficult to believe. Much effort is now devoted to isotopic variations within and among meteorites. Nevertheless, this constancy was taken for granted in 1950.
Several compilations of what we now
call the SAD had been attempted in the years since Harkins's paper.
We must pass them by here, and note the celebrated abundance study of
Hans Suess (1909-
) and Harold Clayton Urey (1893-1981),
which was published in 1956.
Within a year of the appearance of this work, the foundations of our
modern theory of the origin of the chemical elements had been laid.
Interestingly,
the key ideas were developed independently by the Canadian nuclear
astrophysicist A. G. W. Cameron, and a team of four British and American
workers. E. M., and G. R. Burbidge, William A. Fowler, and Fred Hoyle
published a paper that is familiarly known to astronomers as 
,after the initials of the authors.
The founders of the theory first spoke of nucleogenesis, the origin of the elements. This term has fallen out of usage, possibly because it suggests a common event. We now describe the synthesis of the nuclei, mostly in stars, but also near the time of the birth of the universe. We have already encountered the term nucleosynthesis.
We shall follow , and show the distribution of abundances
as a function of what physicists call the mass number, A,
simply the number of protons and neutrons in the nucleus. The data used
to make figure 4-5 is from the modern compilation cited above,
but the
basic features were present in the older work. Let us summarize
the salient features of this plot.
Figure 4-5: Abundances vs. Mass Number
It was the task of the founders of the theory of nucleosynthesis to explain these features. Their explanation rested heavily on the properties and structure of atomic nuclei, to which we now turn.
By the early 1930's all of the pieces of the puzzle of atoms had fallen into place. The behavior of the electrons, even in complicated atoms was understood, at least in principle, and physicists turned their attention to atomic nuclei.
Since the work of Bohr and Rutherford, people knew that the nucleus was a tiny point like mass in the center of atoms. Most of the volume of atoms is taken up by the electrons, which occupy the various shells that we discussed in Chapter I.
After the discovery of the neutron in 1932 it was reasonably straightforward to come up with ``models'' of the atomic nucleus consisting of protons and neutrons. Physicists use the word nucleon to mean either a proton or a neutron. There is a deeper meaning to the use of a single word for a proton or a neutron, in terms of the quark model of elementary particles, but we need not concern ourselves with that here.
Many nuclear masses became accurately known in the decade or so following the first use of the mass spectrograph by Aston (ca. 1920). It then became possible to account for isotopes of various elements in terms of these nucleons as building blocks. Even before the discovery of the neutron, people thought about the nucleus as a mixture of protons and electrons. Proton-electron pairs served much the same function in this early thought as neutrons do today.
It was known that the masses of nuclei were not exactly equal to the masses of the constituent protons and neutrons. Einstein had made it possible to understand these differences. Nuclear masses are less than the combined masses of the number of protons and neutrons of which they are composed. Masses of free protons and free neutrons were known. If you summed the masses of two protons and two neutrons the result was greater than the mass of a helium nucleus. Einstein's famous equation E = mc2 could account for this discrepancy if one assumed that the difference between the mass of the four nucleons and the helium nucleus went into the energy with which the nucleus is bound.
It was even possible to determine the relative binding of the nucleons in different atomic nuclei, and in this way get some insight into the relative stability of the different nuclei. If one uses the mass discrepancy as a measure of the total binding of a nucleus, then the most tightly bound nuclei occur on the iron peak, providing an immediate explanation of that particular high point at iron on the abundance plot (Figure 4-4).
The redoubtable Harkins was one of the early workers to look at the relative binding energies of the different atomic nuclei. He was also a trailblazer in the use of meteoritic abundances as more representative of the bulk earth, and perhaps the ``cosmos.''
The modern theory of the electronic structure of atoms was worked out in the decade from about 1925 to 1935. The overall physical principles that made this possible are known as quantum mechanics. Quantum mechanics and Einstein's relativity were revolutionary concepts. For nearly two hundred years, physics was dominated by the principles laid down by Isac Newton. Now, in the first several decades of the twentieth century, physicists learned to think about phenomena in totally different ways.
The quantum theory is only necessary if we need to understand nature at the atomic or molecular level. Relativity, on the other hand, must be used if velocities approach the speed of light or when gravitational fields are particularly strong. The part of Einstein's theory that neglects gravitation is called the special theory of relativity. It was incorporated into the ideas of quantum mechanics by the British physicist Paul Dirac (1902-1984) in 1928. Dirac's work was the last piece of the puzzle of atomic structure. With it, physicists could say that the principles of atomic structure were understood completely. Even though all properties of all atoms could not be worked out on the basis of this theory, it was possible to suppose that only mathematical techniques, and not physical principles were lacking.
Another name for quantum mechanics is wave mechanics. This comes from the fact that small particles may act like waves, but also from a famous equation that describes them called the wave equation. The wave equation is also called the Schrödinger equation, after Erwin Schrödinger (1887-1961) who first used it to explain the structure of atoms. Schrödinger and Werner Heisenberg (1901-1976) are generally credited as founding quantum mechanics. Dirac refined it in significant ways.
Dirac's theory made it possible to understand a ubiquitous phenomena of small particles known as spin. It may help to think of an electron as a little ball of charge that spins on an axis, something like the earth. This is hardly an accurate picture of an electron in an atom, but it is of heuristic value. Most scientists who are not specialists in particle physics probably think of spin in this way, so there is no harm in our doing it.
Spin had been postulated, but not rigorously accounted for before the Dirac Equation. With it, and the nonrelativistic quantum mechanics, the nature of the atomic shells and subshells that account for the Periodic Table were rigorously understood. Atoms were simply aggregates of charged negative particles bound to a point like nucleus of positive charge, all obeying the laws of quantum mechanics.
It turns out that most of the important properties of the shell structure of atoms follow just from the fact that they too are spherical in shape. It isn't easy to explain this without talking about he mathematical functions that describe the atom, so you may have to take my word for it that the fact that you can get only 2 electrons in an s-subshell, 6 in a p, 10 in a d, etc. arises from the fact that the atoms are spherical.
If it weren't for the property of electrons known as spin, these numbers would be half as large as they are, that is 1 for s subshells, and 3 for p's, etc. Among other things, spin doubles the number of electrons that you can pack closely to one another. It isn't possible to get more than 2, 6, 10, etc. in these subshells because of a law known as the exclusion principle. It is an important physical principle, and it is not possible to understand atomic or nuclear structure without it.
We must now take up several ideas that bothered scientists and philosophers alike in the early days. If we try to apply our every day experience to the quantum domain, we are often led to paradoxes. One of the greatest of these was the ability of particles that obeyed the laws of quantum mechanics to behave like either waves or particles. People asked, ``How could this be?'' ``Is an electron a wave or a particle?''
Scientists eventually decided that was just the way things worked, and there wasn't much point in asking if an electron was a wave or a particle. One popularizer of science coined the term ``wavicle,'' to try to palliate this problem. It is interesting that this no longer seems to bother people so much. For a while, one read about ``wave-particle duality,'' but even that notion no longer seems necessary today.
Since atoms and nuclei obey quantum phenomena, we have to get an idea of how the quantum laws modify our intuitive notions of how systems ought to behave. To do this, we can scale up the sizes of atoms or nuclei until we can have some picture of them. We think of atoms as little balls of negative charge orbiting tiny centers of positive charge called nuclei. And we think of nuclei as spherical collections of nucleons, where the size of the nuclei depends on the number of nucleons in them.
Once we have a physical picture of a system like an atom or a nucleus, we need to ask how it would behave if it obeyed Newton's laws. Newton's laws are incorporated into the single equation F = ma, force is mass times acceleration. If the world obeyed these laws and only these laws, we would call it Newtonian. An important aspect of a Newtonian world is that it would be completely deterministic. The future of a Newtonian universe is entirely determined by the conditions at any one instant.
Newtonian determinism poses the philosophical problem of understanding how there can be such a thing as free will. Free will is not important for the sun and stars. As far as we know, it is only important for beings capable of thought processes. Do we have the freedom to change our behavior? This is a humanistic, psychological, moral, and perhaps religious question, but it is one about which basic physics has something to add. In a Newtonian universe, there is no basis for free will. It turns out the quantum theory changes this in a fundamental way. In order to understand how this can be, we need to explore an idea that has no meaning in a Newtonian world.
The quantum theory enabled physicists to calculate the properties of small physical systems--molecules, atoms, and nuclei. The basic ideas of Newton were retained, but modified in subtle and sometimes very substantial ways. Quantum phenomena still involve the basic observable properties of matter, mass, length and time, and then quantities that derive from them, such as velocity, momentum (mass times velocity), and energy (kinetic and potential).
The way these properties are determined with the quantum theory is quite different from Newtonian procedures. There is a new concept that is relevant for all matter in the quantum domain that has no analogue in classical or Newtonian physics. The reader must focus on these special differences, and try to learn the important ones by heart.
For every particle of matter, be it an electron or a nucleon, there is a finite probability that it can be anywhere in the universe. This may seem a little strange, but it is a natural consequence of the quantum theory. For bodies of finite size, like a pencil, a person, or an automobile, it doesn't help us to explore this notion. Suppose you are sitting at a desk, looking at a pencil. You look up, and I tell you there is a finite probability the pencil isn't where you think it is, but it may be a foot to the right. ``Fine,'' you say. ``Somebody pushed it while I wasn't looking.'' But the reason it might be someplace else is not (necessarily) that somebody pushed it there. There is just something deep in nature that will allow things to jump around. Probably you'd be skeptical. If the pencil wasn't rolling, you would surely be skeptical.
On the other hand, suppose we are not talking about a pencil, but an electron, whose position had just been measured by some technique we need not elaborate. The electron was found to have coordinates, (x, y, z) at time t. And let's assume too, that the velocity of the electron had also been measured, and was zero, as accurately as we could determine it. Now I say there is a finite probability the electron will not be at the position (x, y, z) the next time you measure it, but 10-7 centimeters away.
There is an important difference between the case of the electron and that of the pencil. If you discounted the possibility of the pencil jumping from one place to another, you wouldn't get into any difficulties. But for the electron, if you didn't take this possibility seriously, you wouldn't be able to understand the way mater works at very small scales.
If we just measured an electron at (x, y, z) with velocity near zero, then the probability that it will be 10 centimeters to the right is small, but not zero. The probability that it would be 1 meter to the right would be smaller still, but again, not zero. The fact that the probability never gets to be zero is a property of the number system, and the mathematics used by quantum mechanics. For any small number you name, I can give you back a smaller number, just by dividing your number by two (say). Therefore, we can always find a smaller number than any given one, without having to use zero.
We can say that the probability is effectively zero, that is, very small, for positions where we don't expect a particle to be. We can actually calculate the probability that an electron we just measured on earth will be on Mars when we next measure it. But don't worry. The answer would be smaller than any number you could imagine.
Physicists describe the probability that a particle has some
position with the help of a mathematical
function. We may take this function to be a mathematical recipe
for deriving one number from three different numbers. Given three
coordinates, say x, y, and z, quantum mechanics provides a recipe
for deriving a number that physicists usually designate by the Greek
letter 
. They call this number the wave function, and
they may write it 
to indicate that when the three coordinates
are given, a value for may be obtained.
Schrödinger provided the recipe for getting from the
values of x, y, and z. This function typically oscillates like
a wave, and that is why it is called the wave function.
Suppose the wave function describes a particle, such as an electron
or a proton. Then it turns out that if we square it, or multiply it
by itself, we get another number that is proportional to the probability
that the particle is near the position given by the three coordinates
x, y, and z.
In this book, we won't go through the mathematics to get from the famous equation Schrödinger gave for it. But we will
present graphs that show oscillating functions that are proportional
to this wave function. Often, we will focus on only one coordinate.
For example, in cases with spherical symmetry, it is convenient to
think of the wave function as being only dependent on the radial
coordinate r.
Sometimes, is called the probability semi-amplitude.
When you see a graph of the wave function, think of its square as
telling you where the particle can be.
One of the properties of quantum particles that has no classical analogue was elaborated by Heisenberg, and is known as his uncertainty principle.
An aspect of Heisenberg's fundamental concept concerns the domain in space where the wave function has some appreciable value. Again, suppose the wave function describes a particle. If its wave function is relatively large for some region of space, it means we are most likely to find the particle in this volume. Heisenberg's principle tells us that if this volume is very small, the corresponding momentum (mass times velocity) of the particle may be very large. The smaller the volume, the larger the momentum that is allowed by the quantum theory.
Now the energy of a particle is proportional to the square of its momentum. Double the momentum and the energy increases by a factor of four. So the uncertainty principle tells us that if a particle is confined to a very small volume, its energy is also allowed to be very large.
The exact relation between the kinetic energy of a particle and its momentum also involves the mass. If we denote the momentum by the symbol p, and the mass by m, the kinetic energy E is p2/2m. Thus for a given value of p, the energy is lower for a massive particle, like a proton, than for a less massive one, such as an electron.
Suppose the momentum uncertainty is fixed by the size of a relevant volume, such as that of a nucleus. Then the allowed energy of an electron would be about 2000 times that of a proton, because the mass of the electron is about 2000-times less than that of a proton, and we have to divide by the mass to get the allowed energy.
As soon as the quantum theory was accepted, and the size of nuclei became known, physicists realized there was a problem with their old model of the nucleus. In this old model, all of the heavy nucleons were protons, but there were also electrons inside the nucleus to offset some of the positive charge. The number of electrons needed was exactly the same as the number of neutrons (N) that we now know go to make up the various nuclides. However, neutrons were not discovered until 1932, so the only possibility was to assume the proton charge was canceled by electrons.
The Heisenberg uncertainty principle explains why electrons can't exist in nuclei. The size of the nucleus means their wave functions would be finite (the electrons would be found) only in a very small volume. The possible momenta of the electrons would be large, and the energies large indeed, because of the division by mass explained above. The energies of protons and neutrons that are confined to the nucleus are much smaller, because of their larger masses.
Even before the discovery of the neutron, physicists had an idea of the energies of nucleons in the nucleus. They were about right for protons confined to a small volume, but not large enough for electrons.
Attempts were made to understand the structure of nuclei using the tools that had proved successful with atoms. The nuclei were far smaller, having radii of the order of 10-13 cm rather than 10-8, which is characteristic of atoms. Also, the nucleons were considerably more massive. No one really knew the shape of the nuclei, but it could be assumed they were spherical, and with a few reservations, we accept this notion today.
Spherical nuclei then should show similar shell structure to
atoms. There ought to be something similar to the periodic table.
However there were no indications of periods based on numbers like
2, 6, 10, 14, etc., or combinations of these particular numbers,
which is the situation with atoms. The main regularities had been
pointed out by Harkins: nuclei with an even number of protons were
more stable than those with an odd number, and there seemed to be a
preference for nuclei to be built of combinations of
-particles, or the nuclei of helium atoms.
Faced with the absence of properties that would be expected from spherical symmetry, physicists turned to other nuclear properties. There was one definite way that nuclei differed from atoms. The size of nuclei seemed to depend directly on the number of nucleons. It was as though there were a fixed volume for each nucleon, and the volume of the nucleus was very closely equal to the combined volume of the nucleons.
One has to be a little careful when talking about the sizes of atoms and nuclei. Both are strongly subject to quantum laws, which means that we often must picture them as fuzzy clouds rather than billiard balls. However, one can define distances over which the densities in the clouds fall to one half, or one tenth, and then use these as measures of the radii.
The sizes of atoms are very different in this respect. Atomic radii do get a little larger for heavier elements in a given column of the periodic table, but not a lot. If you consider radii in one period, the radii typically decrease!
Basically, it looks like the atom is ``squeezable,'' while the nuclei are not. Liquids are nearly incompressible, so people have tried to make models of nuclei as a kind of liquid. Even today, the liquid drop model is of considerable use. Of course, solids are also incompressible, but it turned out to be simpler to model the nucleus as a kind of spherical, nearly incompressible fluid.
One very great puzzle is why the nucleus holds together. It is
composed of protons jammed closely together, and like charges repel.
We now know that when protons and neutrons get close together, they
are subject to a special attractive force that overcomes this electrical
repulsion--until too many protons get in the nucleus. This is why there
is a limit to the mass of stable nuclei. Neutrons can do the trick
for a while, but if enough protons get in, eventually the nucleus
must make some adjustment. The protons in the nucleus may
emit positrons, or in some cases -particles may be emitted.
The strong nuclear force is understood in principle, although not in detail, even today. This very strong attraction of the protons and neutrons occurs because of the exchange of particles known as pions. An analogy that can be used to see why exchange forces give rise to attractions is to imagine people standing close to one another and passing a heavy ball from one to another. To make the analogy work, you have to imagine that one person grabs the ball from the other, and someone else grabs the ball from that person. If this process continues, you can see that the group will be drawn close together.
For our purposes, it is sufficient to think of these forces as creating a kind of ``well'' in which the nucleons are held, just the way that gravity would hold a bunch of marbles enclosed in a tube. The strength of the force with which the nucleons are held can be represented by the depth of the well (or tube). Physicists call such a well a ``potential well,'' because it is useful in describing the notion of potential energy. This concept is well defined in both classical as well as quantum physics. We shall have to deal with it at various places in this book in order to understand why nature works the way it does.
Figure 4-6: Potential Wells for Nucleons. The figure shows three theoretical approximations to potential wells of an atomic nucleus. The simplest (dashed) potential assumes no force on a bound neutron or proton until it reaches a certain constant distance from the center, at which point, the force increases very rapidly. This potential is called, for obvious reasons, the square well. Another simple approximation is to assume nucleons are bound by stiff springs. Such potentials (dot-dash) are called harmonic oscillator potentials. The solid curve shows a more realistic, but still simplified model of a nuclear potential.
Physicists speak to two different kinds of energy, kinetic and potential. Imagine a ball rolling down the well, as shown in figure 4-6 (solid or dot-dash). On the way down into the well, the ball rolls slowly. It is said then to have a relatively small kinetic energy. As it approaches the bottom of the well, it rolls faster, so it has a higher kinetic energy, but when it gets to the bottom, it can gain no further energy. As long as the ball has some distance to roll before reaching the bottom of the well, we say it has potential to gain more energy. In general, we say it has potential energy.
When the ball is up high in the well, its energy is mostly potential and relatively little kinetic. It is possible to express these two energies mathematically so that in the process of rolling down into the well, the kinetic and potential energies sum to the same number. The sum of these two forms of energy is constant, and this is a very important requirement for any physical process. Energy is said to be ``conserved'' or be held constant. This is a basic principle of physics, of course, the conservation of energy. Unless energy is supplied to some system from the outside, or lost, the total energy must be constant.
The term strong nuclear force has a
technical meaning. It turns out that there is also a weak force
associated with nucleons. The weak force is responsible for the fact
that the free neutron has a half-life of only 10.3 minutes. It is also
responsible for the -plus and -minus decay that limits
the number of stable isotopes of any element. We will discuss this
force a bit later. For the present, we want to make use of the concept
of a potential well.
An electron, in the neighborhood of a nucleus is also in a kind of potential well. This is because the nucleus pulls on the electron, just as gravity would pull on a ball in the well of our figure 4-6. All of this makes perfect sense for balls and wells, without any appeal to the quantum theory.
If we put in the quantum theory, a new wrinkle develops. There are only special places in the well that the ball can be. Since the distance down in the well corresponds to a specific amount of kinetic energy, we can say that only special amounts of kinetic energy are allowed. The fact that only certain special energies are allowed is one of the major differences between particles that obey the laws of quantum mechanics and those that obey classical mechanics.
Some insight into this special behavior may be gained by thinking of the particle in the well as a wave rather than a particle. Just what sort of a wave? Well, we have to think of the amplitude of the wave, as a sort of probability of finding the particle somewhere. Let us plot the wave, so it has a maximum amplitude at the center of the well. This is shown in figure 4-7.
Figure 4-7: Waves in a Potential Well. The amplitude of the wave is the distance above (or below) the horizontal line that defines the energy of the particle, in this case, a proton. The waves must fit in the well in such a way that there is very little amplitude outside of the well. Whether this happens or not depends on the energy of the wave. The energy shown (left) leads to a satisfactory (quantized) energy. But for an energy slightly more or less than that shown, the amplitude would grow rapidly within the region ``inside'' the well. Such energies are considered impossible--they are not allowed by the theory. The figure on the right shows a wave corresponding to an energy only one part in 500 greater than that on the left, but the solution to the wave equation (the amplitude) shows that energy is not physically realizable in the given potential well.
The wavelength of a quantum mechanical particle is determined by its kinetic energy. The higher the energy of the particle, the smaller the wavelength.
To apply these ideas to the well, we must reverse our starting point from that of the ball rolling down into the well, and imagine a particle that starts at the bottom with a minimum of kinetic energy. How would the ball get down in the well with a minimum of energy? It would have to lose energy for this to happen. With a real ball and a well that might have the shape of a bowl, the ball would lose energy by friction, and as we all know, would eventually come to rest at the bottom of the bowl.
A nucleon entering a well from the top would also have to lose energy
to get to the bottom of the well. Usually this would happen by having
the nucleus lose energy by emitting a -ray. It turns
out that the rules of quantum mechanics will not allow zero kinetic energy
for a particle if it is constrained by anything like a well. So there
is always some minimum energy, and that amount turns out to correspond
to a wave that has one node (or zero of the amplitude) at each end of the well.
Actually, as we have shown, the amplitude of the wave doesn't die exactly at the edge of the well. What this means is that there is a tiny probability that the quantum mechanical particle will penetrate the wall of the well. The deeper the well, the lower this probability is, but it is never exactly zero. This tiny persistence of the wave is of considerable importance near the top of the well, as we shall see later on. Let us store this idea at the back of our minds, and we shall use it later on.
What now happens if you add energy to the quantum mechanical particle? What happens is that the wavelength shortens. But if the particle is to be capable of accepting the offered energy, its new wavelength must be such that the total wave has a very small amplitude at the walls of the well. This is shown in figure 4-7 (left). We also show a case where the amplitude is not small at the side of the well. That energy would not be possible.
So if the particle is to absorb energy, it must be a very specific amount between two allowed levels. Then the particle will make the proverbial quantum jump the energy value allowed.
These relationships were found by Erwin Schrödinger as he explored the consequences of his famous wave equation. He did this first for the simplest atom, hydrogen, for which the approximate answers were already known. There was an earlier theory, due to the Danish physicist Niels Bohr (1885-1962). It got the energies for hydrogen about right, but couldn't do helium, or any of the more complicated atoms.
Schrödinger's theory not only got the energies for hydrogen right, it explained in a very straightforward way why the periodic table has the form it does. The notions of s, p, d, etc. electrons fell out of Schrödinger's theory. The original theory didn't have spin, but once that was added, all the pieces of the puzzle fell into place.
Could the same thing be done with atomic nuclei?
The strong nuclear force overcomes the coulomb repulsion of protons and binds the nuclei. It acts over a very short distance, but within its domain, it is the strongest force known in nature. Only when a very large number of protons get in the nucleus does the electrical repulsion begin to become important, and by the time the number of protons Z = 83 is reached at bismuth, there are no more stable nuclei. Figure 4-8 is a chart of the isotopes (or nuclides), where the number of protons, Z, is plotted on the y-axis and the number of neutrons, N, on the x-axis. Stable isotopes are represented by filled (red) squares. The open (green) squares represent long-lived isotopes.
Figure 4-8: Nuclide Chart. Number of Protons (Z) vs. Number of Neutrons (N). Stable isotopes are filled (red) squares, while open (green) squares are for long-lived isotopes. The magic numbers are shown as dashed lines. Nuclides can be magic in either Z or N. Notice that there tend to be more stable or long-lived nuclides when Z or N is magic.
The strip that is outlined by the filled squares is called the valley of beta-stability by nuclear physicists. There are nuclides, or isotopes, away from this region, but they have short half-lives. They undergo radioactive decay.
Consider
cut at some fixed value of A = N + Z. The cut runs diagonally, from
upper left to lower right, as shown in figure 4-8.
Nuclides (upper left) with greater Z than those
in the valley have too many protons for stability. They will decay
emitting a positron-a -plus decay. Nuclides (lower right)
with smaller
Z than those in the valley have too few protons. They will emit
(negative) electrons, converting one of the neutrons in the nucleus
to a proton. Two such cuts are shown in figures 4-9.
Figure 4-9:
Cuts at constant A across the valley of beta stability.
Separate curves are shown for even A. Ordinates are a
measure of the departure of the nuclides from the sums of the
masses of the constituent particles.
This region where the stable nuclides are found is a true valley in the following sense. Consider the masses of the nuclides along any cut such as those in figure 4-9. Since A = Z + N is constant, they all have the same number of nucleons, and so all should have roughly the same masses. But the masses are not exactly the same. As you move along the cut, the masses of the nuclides reach a minimum where the stable nuclei lie. And this is why the nuclides are stable. The mass differences along the cuts are a measure of the relative binding energy of the nucleons, by Einstein's E = mc2. The least massive nuclei are the most tightly bound.
When the mass number A is even, there are two possible combinations of neutron (N) and proton (Z) numbers that will give the same A. In one case, both Z and N will be even, and in the other, both will be odd. The cases where both numbers of nucleons are odd leads to much less stability, and than when both are even, so there are two curves at the top of figure 4-9.
It is interesting that chemical abundances played very little
role in the development of the shell model of atoms. The structure of the
Periodic Table was developed from the masses of the chemical elements,
and their chemical properties. The chemist Harkins introduced the
relevance of abundances into thinking about the atomic structure. But
he was really thinking about nuclei. The nature of isotopes
was just beginning to be understood at the time of his early work.
Nevertheless, he saw that those elements whose nuclei could be thought
of as composed of -particles were more abundant than their
neighbors.
From the beginning of our understanding of the nature of the atomic nucleus, cosmical abundances were a valuable guide.
The Nobel Laureate Hans Bethe (1906-) has said that nuclear physics ``as we know it'' dates from 1932, the year of the discovery of the neutron. In the decade of the '30's, various experiments were being done on isotopes to discover why some were more stable than others. It soon turned out that nuclei with special numbers of nucleons had a special stability. These numbers are 2, 8, 20, 28, 50, and 82, and it doesn't matter whether these are numbers of protons or neutrons. Either way, you get a nucleus that is particularly tightly bound. This property is almost always reflected in the relative abundances of the nuclei.
Figure 4-10:
Isotopic Abundances of Strontium and Cerium.
Figure 4-10 shows isotopic abundances for strontium and cerium. In both cases there are several stable isotopes. The more abundant isotopes in both cases have favored numbers of neutrons: 88Sr has 50 neutrons, while 140Ce has 82 neutrons.
In the 1930's physicists tried to understand why such numbers were special. Another Nobel Prize winning physicist, Eugene Wigner (1902--), called these numbers ``magic,'' and the name has been adopted. I have always thought this quite fascinating, because Wigner was a kind of wizard, who snowed even his peers with his mathematical insights. Yet even he could not understand why these numbers were special, so he called them magic.
The magic numbers manifest themselves in a variety of ways in addition to abundances. For example, the number of stable isotopes of with magic numbers of stable protons or neutrons is typically large. Tin, for example, has 10 stable isotopes, the most of any element. Tin has a magic number Z= 50 of protons. A similar thing holds for neutrons. There are typically 3 or 4 stable isotopes with a given even number of neutrons. But for N = 50 there are 6 (counting the long-lived Rb-87), and for N = 82 there are 7 stable isotopes.
In nuclear physics, the magic numbers are 2, 8, 20, 28, 50, 82, and for neutrons, 126. (No stable nuclei are known with 126 protons.) It is interesting that there are also magic numbers in atoms, associated with the number of electrons in a shell. If we plot the amount of energy necessary to remove an electron from a neutral atom as a function of Z, the number of electrons, we get obvious peaks at the positions of helium and the other noble gases. This is shown in figure 9-11.
Figure 9-11:
Ionization Potentials of Neutral Atoms. We can see that
atoms with 2, 10, 18, 36, 54, and 86 electrons are particularly
stable. These are the noble gases.
The nuclear magic numbers are different from the atomic numbers Z of the noble gases. Moreover, there is nothing that is special about abundances of the noble gases. Indeed, they are often called ``rare gases'' because they are relatively rare in the earth's atmosphere. In the SAD, their abundances fit right in with their even-Z neighbors, as may be seen in figure 4-4.
Physicists thought of the strong nuclear force in terms of a potential well, using classical analogy just as we did in a previous section.
But if atomic nuclei could be described by potential wells, then there ought to be shell structure, like that of the atom. This puzzle remained until the late 1940's when the solution was found nearly simultaneously by Maria Mayer (1906-1972) and Hans Jensen (1907-1973). They were awarded the Nobel Prize for their work in 1963.
It is most relevant that both Mayer and Jensen were occupied with abundances of the elements and their isotopes.
Mayer's work was done at the University of Chicago. Her husband was a highly respected physical chemist, and was a Professor of Chemistry at Chicago. Maria, in a paradigm example of unfairness to women, was a paid no salary, nor was she given the professorial title she deserved. Her talents were well recognized by those with the ability to see them, and she had worked with Nobel Laureates and their peers in the 1940's and 50's. The time was not right. Not only were professorial positions very difficult for women to obtain in the man's world of American Universities, but there were also ``anti-nepotism'' rules that prevented husband and wife from simultaneously holding professorships.
Maria Mayer's story is a fascinating one from many points of view. Her father was a professor at the University of Göttingen, and her youth corresponded to a golden age of physics when the ideas of Einstein were still new, and modern quantum mechanics was being born. She knew and sometimes worked with the future Nobel Prize winners, virtuosos like Heisenberg, Born, and Dirac--the glorious ones of physics. We must leave her personal story for another time.
Mayer started her Nobel Prize work while working with
Edward Teller (1908-
), the father of the hydrogen bomb, and
dark eminence of theoretical physics of our time. They were
working on a theory of the origin of the elements in what we
now call the Big Bang, and Mayer assembled an abundance table
that the theory needed to explain. In so doing, she became
fascinated with the magic numbers, and went on to develop the
nuclear shell model that explained them.
At nearly this same time, Hans Jensen was a professor of physics at the University of Heidelberg. He was contacted by Hans Suess--the same Suess who had worked with Urey on the SAD. It is no accident that the geochemist Suess was deeply involved in the solution of the magic numbers. Like Harkins before him, he has devoted a long and distinguished career to the relation between cosmic abundances and atomic nuclei. Suess convinced Jensen there was something really fundamental in these magic numbers, and Jensen finally cracked the puzzle.
One might easily argue that Suess deserved to share in the Nobel prize with Jensen. He was a coauthor of the paper submitted by Jensen on the shell model. However, this was not the decision of the Nobel Committee. Suess was, after all, a chemist, and this prize was for physics.
What Jensen and Mayer discovered was that the spin of nucleons was much more important than that of atoms. For atoms, to a first approximation, spin only doubles the available number of particles that can fit into a shell. For atoms, the energy of the shell is changed a little, but not a great deal. Physicists spoke of the interaction between an electron's spin and its orbit, and called the resulting energy differences ``fine structure.''
You can use a classical picture to get some insight into what is happening. If the electron is a spinning ball of charge, then it will generate a magnetic field. If the electron is in orbit about the nucleus, then the charged nucleus generates its own magnetic field, as seen from the electron. These two magnetic fields interact energetically. While it is not quantitatively the same, the energy difference may be pictured as that arising from a magnet (the electron) that is aligned parallel or antiparallel to an external field (caused by the apparently orbiting nucleus).
Figure 9-12: Spin-Orbit Interaction. If a magnet is aligned with a magnetic field as in (a), it has a lower energy state than if it is aligned against the field, as in (b). You have to do work to twist it from position (a) to (b). A spinning charge can generate its own field (c). Nucleons behave like spinning charges, and the fields they generate interact with the general fields resulting from the orbital motion of the nucleons in the nuclear potential wells.
For nuclei, the effect of spin-orbit interaction is much bigger, but there wasn't any real clue to this. According to an account by Bethe, Wigner didn't even believe it at first. Eventually, measurements were made that showed this was indeed the case. When the spin-orbit terms were included in the nucleon energies, the magic numbers appeared from the theory. Mayer and Jensen wrote a book together describing their new theory, and in it they showed how to get the magic numbers from a very simple model of the nuclear potential.
Physicists found important clues to the theory of nuclear structure from the abundances of the chemical elements, and especially their isotopes. This is immediately relevant to our study of the history of matter. If abundances are relevant for the structure of nuclei, then clearly nuclear processes have left their imprint on cosmical abundances.
Maria Mayer and Hans Jensen were able to clarify the shell structure of the nucleus after they became aware that certain magic numbers of nucleons led to special stability of nuclides. These magic numbers first became apparent from studies of isotopic abundances of the elements. Just as Harkins found that nuclei with even values of the number of protons Z were more abundant in nature than their odd-Z neighbors, nuclei with magic numbers of protons or neutrons were more abundant than nearby non-magic nuclides.
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