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The evolving Universe
The evolving Universe

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1.8 Primordial nucleosynthesis

Time: 100 s to 1000 s

Temperature: 109 K to 3 × 108 K

Energy: 300 keV to 100 keV

As the temperature continued to decrease, protons and neutrons were able to combine to make light nuclei. This marked the beginning of the period referred to as the era of primordial nucleosynthesis (which literally means 'making nuclei'). The first such reaction to become energetically favoured was that of a single proton and neutron combining to produce a deuterium nucleus, with the excess energy carried away by a gamma-ray photon:

Question 15

What is deuterium?

Answer

Deuterium is an isotope of hydrogen. Whereas normal hydrogen nuclei consist simply of a proton, deuterium nuclei (sometimes called 'heavy hydrogen') contain a proton and a neutron.

At high temperatures (greater than 109 K), there are a lot of high-energy photons so this reaction is favoured to go from right to left. As a result, deuterium nuclei were rapidly broken down. However, as the temperature fell below 109 K when the Universe was about 100 s old, deuterium production was favoured. Virtually all of the remaining free neutrons in the Universe were rapidly bound up in deuterium nuclei, and from then on other light nuclei formed. One of the reactions that occurred was:

Question 16

What is the nucleus represented by ?

Answer

This represents a nucleus of another isotope of hydrogen (called tritium), which contains two neutrons and one proton.

This shows that two deuterium nuclei react together to form a nucleus of tritium with the ejection of a proton. The tritium nucleus immediately reacts with another deuterium nucleus to form a nucleus of helium-4 with the emission of a neutron. The proton and neutron produced in the two reactions above can combine to form another deuterium nucleus, so the net result of this set of reactions is that two deuterium nuclei are converted into a single nucleus of helium-4.

Other more massive nuclei were also made as follows:

This shows that deuterium nuclei react with protons to make nuclei of helium-3. These can then either react with other helium-3 nuclei to make helium-4 plus more protons or with nuclei of helium-4 to make beryllium-7. Nuclei of beryllium-7 are unstable and immediately capture an electron to form lithium-7 with the emission of an electron neutrino. Lithium-7 nuclei can react further with a proton to create nuclei of beryllium-8, but these too are unstable and immediately split apart into a pair of helium-4 nuclei. The end products of the four reactions are nuclei of helium-3, helium-4 and lithium-7, with the vast majority ending up as helium-4.

Question 17

The reactions in Equation 8 are the same as those that comprise the later stages of the proton-proton chain that occurs in the Sun. Why did the first stage of the proton-proton chain not occur to any great extent in the early Universe?

Answer

The first stage of the proton-proton chain relies on the weak interaction and takes, on average, 1010 years to occur for any individual pair of protons. In the early Universe at this epoch, there was just not enough time for this reaction to occur to any great extent over the period considered here.

Nuclei with a mass number greater than seven did not survive in the early Universe. This is because there are no stable nuclei with a mass number of eight — notice from above that the beryllium nuclei decay spontaneously, leading ultimately to more helium-4. The reactions that by-pass this bottleneck take much longer than the few minutes that were available for nucleosynthesis at this time. (Remember, we're now talking about a time-span of around 15 minutes when the Universe had an age of between 100 and 1000 s.) Before more advanced reactions could occur, the Universe cooled too much to provide the energy necessary to initiate them.

The ratio of protons to neutrons had, by this time, reached about seven protons for every one neutron. Because the neutrons were bound up in nuclei, they no longer decayed, and the ratio remained essentially fixed from here on. The vast majority of the neutrons ended up in nuclei of helium-4. Only very tiny fractions were left in deuterium, helium-3 and lithium-7 nuclei, since the reactions to produce them were far more likely to continue and produce helium-4 than they were to halt at these intermediate products.

By the time the Universe had cooled to a temperature of about 3 × 108 K after 1000 s, the particles had insufficient energy to undergo any more reactions. The era of primordial nucleosynthesis was at an end, and the proportion of the various light elements was fixed. The rates of reaction to form helium and the other light elements have been calculated, and the abundances predicted may be compared with the abundances of these nuclei that are observed in the Universe today. There is close agreement between theory and observation.

The close agreement between the theoretically predicted abundances of the light elements and the observed abundances in the Universe today is the third major piece of evidence, alongside the cosmic microwave background and the Hubble expansion, in favour of the hot big bang model for the origin of the Universe.

At an age of 1000 s, the Universe reached a state where its matter constituents were essentially as they are today. There are about 109 photons for every baryon (proton and neutron), and about seven protons and electrons for every one neutron. Neutrinos and antineutrinos continue to travel through the Universe unhindered by virtually anything they encounter.

Worked example 2

Assume that the Universe contains one neutron for every seven protons, and that all the neutrons are today bound up in nuclei of helium-4. (a) What are the relative numbers of hydrogen and helium nuclei in the Universe? (b) What are the relative percentages, by mass, of hydrogen and helium in the Universe?

Answer

(a) One way to calculate the answer is as follows. Imagine that you have a box containing 14 protons and two neutrons — the 7:1 ratio mentioned in the question. If a nucleus of helium-4 is made from two protons and two neutrons, there will be 12 protons remaining in the box, each of which can be considered as a hydrogen nucleus. Therefore there are 12 hydrogen nuclei for every one helium-4 nucleus in the Universe.

(b) Taking the mass of a helium-4 nucleus to be four units, and that of a hydrogen nucleus to be one unit, the relative masses of the helium-4 and hydrogen in the box are 4 and 12, respectively. The fraction of the mass in the box due to helium-4 is therefore 4/(4 + 12) = 0.25 or 25%, and that due to hydrogen is 12/(4 + 12) = 0.75 or 75%. (In fact the actual mass fraction of helium-4 that is predicted to have come out of the Big Bang is between about 22% and 24%.)