The chemical elements have not always existed. Their nuclei can not have a huge age, for if they did, the radioactive nuclei would have already vanished. They could be twice as old as the Earth, for instance, but not ten times as old.
Radioactivity has the fascinating property called "half-life". Each radioactive nucleus is characterized by its own half-life. Given an initial number of such nuclei, half of them will change to some other nucleus in a time equal to the half-life. The nuclei themselves do not remember their age. Whatever their age, half will decay to another element within the next half-life, leaving half remaining. After two half-lives, 1/4 remain, only 1/8 after three half-lives, and so forth.
Figure 1. The "aging" of radioactive isotope ratios.
For example, half of an initial number of uranium nuclei having atomic mass 235, the uranium isotope that was used to make the atomic bomb and nuclear reactors, will decay to the element lead in 0.7 billion years, its half-life. After so much history, that uranium isotope is today 140 times less numerous in nature than the more common isotope of uranium having mass 238. When the Earth and planets and Sun were born 4.5 billion years ago, the 235 isotope was only three times less abundant than the 238 isotope. But every 0.7 billion years half of it transmuted to lead, so that after the 4.5 billion year age of the Earth, their number had decreased to only 1/140th of the 238 uranium. In such ways one knows the age of the Earth.
If the uranium had been created longer ago than actually was the case, we would today have even less of it. But because a substantial amount remains, the nuclei must not be much older than twice Earth's age. Had they been much older, the uranium would have to have been even more abundant initially, so that the element to which it decays, lead, would today be much more abundant than it is demonstrated to be. Figure 1 illustrates this relationship between the two isotopes of uranium and the daughter lead isotopes to which they transmute. These arguments are powerful and persuasive. At least a dozen other nuclei also remain in significant numbers, and by comparing them one can determine that the nuclei began coming into existence about 12 billion years ago and were produced continuously from that time until the present.
There seems to exist only one plausible means by which new elements can continuously be born, as required by the radioactivity. That place is within the stars.
Figure 2. An illustration of the pressure support of a star against gravity.
What is a star? Using the Sun and the laws of physics as a guide, stars are known to be giant balls of gas that are held together by their own weight. Each parcel of a star is attracted to all of the remainder of that star by the force of gravity, just as the Earth's gaseous atmosphere is attracted by gravity to the bulk of the Earth, thereby holding it in place just above our heads. To hold up the weight of the overlying gas, the pressure must get larger at increasing depths within a star, just as pressure increases with depth below the top of the atmosphere, or as water pressure increases deeper in a lake. Figure 2 shows how that increasing pressure can just exactly balance the overlying weight, which also increases at greater depth. The star hovers in balance, in equilibrium between these opposing forces.
Increasing pressure deeper within is achieved by increasing temperature of the solar gases. Because the sun is hotter within, heat flows outward, for it is one of the fundamental laws that heat flows from hot toward cold. The outflowing heat makes the surface also hot, and that causes the star to shine. By why does it not cool off? How can the sun have continued to shine for its 4.5 billion year life?
For stars to remain hot even while they lose heat at staggering rates, they must utilize a source of energy within. Some "coal furnace" keeps pouring out the heat at the center, which allows it to flow toward the colder surface and off into space as light. This continues for a very long time without the star cooling off. The Sun radiates 400 billion billion Megawatts of visible heat energy (light), enough energy in one second to vaporize the Earth's oceans if it were concentrated into those oceans. The Sun's central furnace is actually a nuclear reactor. The laws of nuclear physics confirm that at the fierce temperatures of the stellar centers, the gas particles, which are none other than the nuclei of the atoms, collide with enough speed to cause nuclear reactions to occur. Nuclear reactions liberate great energy, generating mankind's hope that the power needed for civilization could be extracted in fusion reactors by fusing tiny amounts of nuclei from the oceans. This heating at the solar center sets up another balance, a heat balance. The centers of the stars exist at just the right temperature to cause their reactors to run at the needed rates. Experiments in nuclear physics have made it possible to calculate the rate at which the nuclear reactors generate nuclear power. Perhaps it fascinates to realize that we all live from nuclear power--the Sun's!
It is a property of fusion reactors that new, heavier nuclei are fused from the initial lighter ones. This fusion generates the heat, as in nuclear reactors on Earth. But, unavoidably, new chemical elements are brought thereby into being. Study of the light emitted by the hot gases at the surfaces of stars shows that they began their lives as hydrogen and helium, the two lightest elements, and that the nuclear reactors slowly fuse the heavier elements from those initial building blocks. The solar center transforms as much hydrogen as exists in Lake Michigan into helium in every second! But so great is the Sun's supply that it will continue this process for another five billion years, roughly the present age of the Earth. This reveals how it is that the stars can be a continuous source of new heavy elements, including the radioactive ones whose lifetimes are so limited.
Astronomers not only see stars, they see stars being born from dark clouds of cold gas that hover in the spaces between the stars. Gravity collects that cold gas into dense balls that get hot and turn on. Several new stars are born yearly in the Milky Way. This means that all stars do not have the same birthday. Like people, some are born every year. As a consequence, the stars we see in the sky are of differing ages. Some are old; some are young. A similar spread can be seen in a photograph of all of the people at an Atlanta Braves baseball game. Not only could an alien studying such a photo reason that not all people are the same age, he could even discern that some phases of human life are fast. For example, there are so few small humans with a missing upper front tooth that the life of each human must not long dwell in that condition. Astronomers use that very idea to map out the evolution of the life of a star. Doing so is a careful amalgamation of astronomical observations of many stars with computerized calculations of the fate of hot balls of gas held together by gravity. Those computer models of stars have no choice but to evolve, because the nuclear reactions change the atomic weight of the gas particles in the central regions. As particles fuse into fewer, heavier, particles, the star must lose pressure, whereupon it must shrink. This slow contraction of the center to a denser gaseous state is accompanied by an increase in its temperature. The compression of gas in the cylinder of a diesel engine so heats it that its fuel ignites. It occurs similarly in computer models of the stars. When one nuclear fuel is exhausted, the compression so heats the remaining gas that it ignites a new fuel at higher temperature. This continues until all forms of nuclear fuel are spent.
When all nuclear fuel is spent, the core of the star quickly collapses and bounces, causing violent ejection of most of the overlying matter. Astronomers see only about one of these per century in the Milky Way. They are called "supernovae". Each ejects so many new heavy elements, including that suite of radioactive nuclei that are so diagnostic of natural history, that over one hundred million centuries all of the heavy elements contained in all of the stars and in all of the planetary systems within the entire Milky Way galaxy can have been assembled by fusion from initial hydrogen and helium. Many short-lived radioactive nuclei are now extinct but can nonetheless be seen to have existed when the solar system was forming. They leave within solid minerals, after they decay, an anomalously high number of atoms of the daughter nuclear isotope to which the now extinct radioactivity decayed. These telltale markers assert that when the solar system formed, the interstellar gases from which it collected contained radioactivity having half-lives much shorter than that of uranium. Even shorter half-lives can be seen by gamma-ray astronomers and space telescopes, such as NASA's Compton Gamma Ray Observatory. Their faster decay rates produce gamma rays more rapidly than can the slowly decaying long living radioactive nuclei. These observations have proven the long held belief that the chemical elements were overwhelmingly created in the supernova explosions that occurred prior to the birth of the sun. Supernova ejecta is profoundly radioactive.
Figure 3. The relative natural abundances of isotopes of intermediate atomic weight..
Figure 3 shows the numbers of naturally occurring atoms of the metals between atomic weights 45 and 65. They are dominated, like a mountain, by four abundant isotopes of iron. This is the sort of abundance data that the theory of nucleosynthesis must consider. The scientific method has achieved a great triumph here, from the first argument half a century ago that iron is the natural product of the evolution of the stellar core, to the recent proof by detected gamma rays from supernovae that the iron isotopes were ejected as isotopes of radioactive nickel and cobalt, and in just the ratios found within a common hammer!
Figure 4. Stars in the Hertzsprung-Russell
To glimpse all of this, astronomers first had to understand what a star is. That required meaningful photographs of their population. Stars are not all born with the same mass as the Sun, though it is a very common star. Increasingly massive stars are born both more luminous and more blue in color. That trend is called "the main sequence". Their greater mass causes higher central temperature to achieve enough pressure to support the increased overlying weight. That higher temperature causes the nuclear reactions to proceed more rapidly, generating greater power than the Sun. The stars 30 times more massive than the Sun are a staggering 100,000 times more luminous owing to this 100,000 times more prolific nuclear reactor. This much greater power can be radiated from the surface only if it gets bluer. The blacksmith here in Williamsburg knows well that if the forge gets iron hotter than red-hot, it becomes yellow-hot, and hotter still it become blue-hot. This fundamental truth of thermal physics holds also for stars. And the hotter ones, the bluer ones, radiate heat much more prolifically. It has satisfied generations of astronomers that these basic laws of physics interpret the main sequence so convincingly. An illustration of the main sequence is in Figure 4.
But what of the evolution of the star from the main sequence to its final supernova explosion? That evolution occurs so rapidly that, like the toothless child, the condition does not long remain and the fraction of the population in that situation is small. But by studying tens of thousands of stars, astronomers find hundreds that are making the relatively fast transition toward their life's end. It would be hard to believe all this except that the faithful computer and the laws of physics produce numerical models of stars that do what the real stars are observed to do. As shown in Figure 5, the outer layers get redder and more luminous during the transition from main sequence to presupernova star. Getting more heat from a redder, cooler, star would be impossible except for the huge increase in its surface radiating area as the star expands in size. Computers confirm it: as the central core contracts and gets hotter, the outer envelope of the spherical gas ball expands and gets cooler, redder. These are the "red giants". They may live yet only another few million years, even though they were main sequence stars for hundreds of millions of years, or even several billion years like our Sun.
The life of a star is not so
unknowable after all. It can be discerned even though it happens so
slowly that we cannot watch it happen during our own lifetimes. It
depends on three things: careful observational data from telescopes
of all types; faithful application of the hard-won understanding of
the laws of physics; and intelligent modeling by numerical
construction on computers. And then--Voila! Not only can we glimpse
the lives of the heavenly bodies, but we see and comprehend the
creation of the chemical elements within their interiors and their
expulsion at the ends of their lives. From these we ourselves were
born. The calcium in our bones, the iron in our hemoglobin, all, all
but the initial hydrogen and helium, are thermonuclear debris from
exploding stars. Some of you may find unexplained satisfaction in
Donald D. Clayton