3.1.2: Thinking About Atomic Origins

The current model of the universe begins with a period of very rapid expansion, from what was essentially a dimensionless point, a process known as inflation. As you might well imagine there is some debate over exactly what was going on during the first 10^-43 seconds (known as the Planck time) after the universe’s origin. Surprisingly, there is a remarkable level of agreement on what has happened since then.⁵³ This is because there is lots of observable evidence that makes it relatively easy to compare hypotheses, accepting some and ruling out others. Initially remarkably hot (about 10²³ K), over time the temperature (local energy levels) of the universe dropped to those that are reachable in modern particle accelerators, so we have actual experimental evidence of how matter behaves under these conditions. At 1 picosecond after the Big Bang, there were no atoms, protons, or neutrons, because the temperature was simply too high. There were only elementary particles such as photons, quarks, and leptons (electrons are leptons) - particles that appear to have no substructure. By the time the universe was ~0.000001 seconds old (a microsecond or 1 x 10^–6 second), the temperature had dropped sufficiently to allow quarks and gluons to form stable structures, and protons and neutrons appeared. A few minutes later the temperature dropped to about 1,000,000,000 K (1 x 10⁹ K), which is low enough for some protons and neutrons to stick together and stay together without flying apart again. That is, the kinetic energy of the particles colliding with them was less than the forces (the weak and strong nuclear forces) holding the protons, neutrons, and nuclei together. At this point the density of particles in the universe was about that of our air.

By the time the universe was a few minutes old it contained mostly hydrogen (¹H¹ = one proton, no neutrons) and deuterium (²H¹ = one proton and one neutron) nuclei, with some helium (³He² and ⁴He² = two protons and either one or two neutrons, respectively), and a few lithium (⁷Li³ = three protons and four neutrons).⁵⁴ These nuclei are all formed by nuclear fusion reactions such as

¹p⁺ + ¹n⁰ → ²H⁺ + gamma radiation and ²H⁺ + ²H⁺ → ³He²⁺ + ¹n⁰.

These fusion reactions take place in a temperature range where the nuclei have enough kinetic energy to overcome the electrostatic repulsion associated with the positively charged protons but less than that needed to disrupt the nuclei once formed. After a few minutes the temperature of the universe fell below ~10,000,000 (10⁷) K. At these temperatures, the kinetic energy of protons and nuclei was no longer sufficient to overcome the electrostatic repulsion between their positive charges. The end result was that there was a short window of time following the Big Bang when a certain small set of nuclei (including ¹H⁺, ²H⁺, ³He²⁺, ⁴He²⁺, and ⁷Li³⁺) could be formed. After ~400,000 years the temperature of the universe had dropped sufficiently for electrons to begin to associate in a stable manner with these nuclei and the first atoms (as opposed to bare nuclei) were formed. This early universe was made up of mostly (> 95%) hydrogen atoms with a small percentage each of deuterium, helium, and lithium, which is chemically not very interesting.

The primary evidence upon which these conclusions are based comes in the form of the cosmic microwave background radiation (CMBR), which is the faint glow of radiation that permeates the universe. The CMBR is almost perfectly uniform which means that no matter where you look in the sky the intensity of the CMBR is (essentially) the same. To explain the CMBR, scientists assume that the unimaginably hot and dense early universe consisted almost entirely of a plasma of hydrogen nuclei that produced vast amounts of electromagnetic radiation, meaning that the early universe glowed. The CMBR is what is left of this radiation, it is a relic of that early universe. As the universe expanded it cooled but those photons continued to whiz around. Now that they have to fill a much larger universe individual photons have less energy, although the total energy remains the same! The current background temperature of the universe is ~2.27 K, which corresponds to a radiation wavelength of ~1.9 mm (radiation in the microwave region); hence the name cosmic microwave background radiation.

After a billion years or so things began to heat up again literally (albeit locally). As in any randomly generated object the matter in the universe was not distributed in a perfectly uniform manner and as time passed this unevenness became more pronounced as the atoms began to be gravitationally attracted to each other. The more massive the initial aggregates the more matter was attracted to them. As the clumps of (primarily) hydrogen became denser the atoms banged into each other and these systems, protostars, began to heat up. At the same time the gravitational attraction resulting from the overall mass of the system caused the matter to condense into an even smaller volume and draw in more (mostly) hydrogen. As this matter condensed its temperature increased, as gravitational potential energy was converted into kinetic energy. At a temperature of ~10,000,000 (10⁷) K the atoms (which had lost their electrons again because of the higher temperature) began to undergo nuclear fusion. At this point we would probably call such an aggregate of matter a star. This process of hydrogen fusion produced a range of new types of nuclei. Hydrogen fusion, or hydrogen burning as it is sometimes called, is exemplified by reactions such as the formation of helium nuclei:

4 ¹H⁺ → ⁴He²⁺ + 2e⁺ + energy.

When four protons are fused together they produce one helium-4 nucleus, containing two protons and two neutrons, plus two positrons (e⁺ - the antiparticle of the electron), and a great deal of energy. As the number of particles decreases (4 ¹H⁺ into 1 ⁴He^2+,), the volume decreases. Gravity produces an increase in the density of the star (fewer particles in a smaller volume). The star’s core, where fusion is occurring, gets smaller and smaller. The core does not usually collapse totally into a black hole, because the particles have a huge amount of kinetic energy, which keeps them in motion and moving on average away from one another.⁵⁵

As the star’s inner temperature reaches ~10⁸ K there is enough kinetic energy available to drive other fusion reactions. For example three helium nuclei could fuse to form a carbon nuclei:

3 ⁴He²⁺ → ¹²C⁶⁺ + lots of energy (note again, the result is fewer atoms).

If the star is massive enough, a further collapse of its core would increase temperatures so that carbon nuclei could fuse, leading to a wide range of new types of nuclei, including those of elements up to iron (⁵⁶Fe²⁶⁺) and nickel (⁵⁸Ni²⁸⁺), as well as many of the most common elements found in living systems, such as nitrogen (Ni⁷), oxygen (O⁸), sodium (Na¹¹), magnesium (Mg¹²), phosphorus (P¹⁵), sulfur (S¹⁶), chlorine (Cl¹⁷), potassium (K¹⁹), calcium (Ca²⁰), manganese (Mn²⁵), cobalt (Co²⁷), copper (Cu²⁹), and zinc (Zn³⁰).

In some instances these nuclear reactions cause a rapid and catastrophic contraction of the star’s core followed by a vast explosion called a supernova. Supernovae can be observed today, often by amateur astronomers, in part because seeing one is a matter of luck. They are characterized by a sudden burst of electromagnetic radiation, as the supernova expels most of its matter into interstellar dust clouds. The huge energies involved in such stellar explosions are required to produce the naturally occurring elements heavier than iron and nickel, up to and including Uranium (Ur⁸²⁺). The material from a supernova is ejected out into the interstellar regions, only to reform into new stars and planets and so begin the process all over. So the song is correct, many of the atoms in our bodies were produced by nuclear fusion reactions in the cores of stars that, at one point or another, must have blown up; we are literally stardust, except for the hydrogen formed before there were stars!

References

⁵³ http://www.astro.ucla.edu/~wright/BBhistory.html

^​54 In this nomenclature (described more on the web), the first superscript number is the number of proton and neutrons, while the second superscript number is the number of protons; both numbers are always integers. The letter is the symbol of the element, e.g. He for helium or Li for lithium.

⁵⁵ Nuclear fusion releases huge amounts of energy (some of the mass is transformed into energy). On Earth, controllable nuclear fusion has long been a potential target in the search for new energy sources, but so far the energy required to bring about the initial fusion has not been replaced when the fusion occurs – i.e., nuclear fusion reactors have yet to break even. Uncontrolled nuclear fusion takes place in hydrogen bombs – clearly not a viable option for a useful energy source at the moment. Nuclear fusion does however take place in stars, and is self-sustaining. The reason you can see and feel the energy from the Sun is that is it undergoing nuclear fusion reactions, which supply us with almost all the energy that is used on Earth today.