# 11.7 Evolution of the early universe  (Page 2/10)

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To describe the conditions of the early universe quantitatively, recall the relationship between the average thermal energy of particle ( E ) in a system of interacting particles and equilibrium temperature ( T ) of that system:

$E={k}_{B}T,$

where ${k}_{\text{B}}$ is Boltzmann’s constant. In the hot conditions of the early universe, particle energies were unimaginably large.

## Strategy

The average thermal energy of a particle in a system of interacting particles depends on the equilibrium temperature of that system [link] . We are given this approximate temperature in the above timeline.

## Solution

Cosmologists think the temperature of the universe just after the Big Bang was approximately $T=1{0}^{32}\text{K}.$ Therefore, the average thermal energy of a particle would have been

## Significance

This energy is many orders of magnitude larger than particle energies produced by human-made particle accelerators. Currently, these accelerators operate at energies less than $1{0}^{4}\phantom{\rule{0.2em}{0ex}}\text{GeV}.$

Check Your Understanding Compare the abundance of helium by mass 10,000 years after the Big Bang and now.

Nucleons form at energies approximately equal to the rest mass of a proton, or 1000 MeV. The temperature corresponding to this energy is therefore

$T=\frac{1000\phantom{\rule{0.2em}{0ex}}\text{MeV}}{8.62\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{11}\phantom{\rule{0.2em}{0ex}}\text{MeV}·{\text{K}}^{-1}}=1.2\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{13}\phantom{\rule{0.2em}{0ex}}\text{K}\text{.}$

Temperatures of this value or higher existed within the first second of the early universe. A similar analysis can be done for atoms. Atoms form at an energy equal to the ionization energy of ground-state hydrogen (13 eV). The effective temperature for atom formation is therefore

$T=\frac{13\phantom{\rule{0.2em}{0ex}}\text{eV}}{8.62\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{5}\phantom{\rule{0.2em}{0ex}}\text{eV}·{\text{K}}^{-1}}=1.6\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{5}\phantom{\rule{0.2em}{0ex}}\text{K}\text{.}$

This occurs well after the four fundamental forces have separated, including forces necessary to bind the protons and neutrons in the nucleus (strong nuclear force), and bind electrons to the nucleus (electromagnetic force).

## Nucleosynthesis of light elements

The relative abundances of the light elements hydrogen, helium, lithium, and beryllium in the universe provide key evidence for the Big Bang. The data suggest that much of the helium in the universe is primordial. For instance, it turns out that that 25% of the matter in the universe is helium, which is too high an abundance and cannot be explained based on the production of helium in stars.

How much of the elements in the universe were created in the Big Bang? If you run the clock backward, the universe becomes more and more compressed, and hotter and hotter. Eventually, temperatures are reached that permit nucleosynthesis    , the period of formation of nuclei, similar to what occurs at the core of the Sun. Big Bang nucleosynthesis is believed to have occurred within a few hundred seconds of the Big Bang.

How did Big Bang nucleosynthesis occur? At first, protons and neutrons combined to form deuterons, ${}^{2}\text{H}$ . The deuteron captured a neutron to form triton, ${}^{3}\text{H}$ —the nucleus of the radioactive hydrogen called tritium. Deuterons also captured protons to make helium ${}^{3}\text{He}$ . When ${}^{3}\text{H}$ captures a proton or ${}^{3}\text{He}$ captures a neutron, helium ${}^{4}\text{He}$ results. At this stage in the Big Bang, the ratio of protons to neutrons was about 7:1. Thus, the process of conversion to ${}^{4}\text{He}$ used up almost all neutrons. The process lasted about 3 minutes and almost $25\text{%}$ of all the matter turned into ${}^{4}\text{He}$ , along with small percentages of ${}^{2}\text{H}$ , ${}^{3}\text{H}$ , and ${}^{3}\text{He}$ . Tiny amounts of ${}^{7}\text{Li}$ and ${}^{7}\text{Be}$ were also formed. The expansion during this time cooled the universe enough that the nuclear reactions stopped. The abundances of the light nuclei ${}^{2}\text{H}$ , ${}^{4}\text{He}$ , and ${}^{7}\text{Li}$ created after the Big Bang are very dependent on the matter density.

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