The Physics
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Opus in profectus

# Nucleosynthesis

## Problems

### practice

1. Hydrogen fusion in the Sun is a multistep reaction, but the net result is that four hydrogen atoms fuse into one helium atom (plus a bunch of junk).

411H → 42He + 2(0+1e + 00γ + 00ν)

The mass of the Sun is 1.99 × 1030 kg, 91% of which is hydrogen. Its power output is 3.85 × 1026 W. Determine…

1. the mass of four hydrogen atoms
2. the mass defect when four hydrogen atoms fuse into one helium atom (in atomic mass units and megaelectronvolts)
3. the rate at which the Sun's mass is decreasing
4. the total mass destroyed if all the Sun's hydrogen were converted into helium
5. the expected lifetime of the Sun (assuming its power output will remain constant)

The dreams of medieval alchemists have nearly come true in the modern era of accelerators and nuclear reactions. For example, one can fuse two metallic atoms, a germanium‑74 (7432Ge) projectile with a tin‑124 (12450Sn) target. When the 7432Ge has a kinetic energy of 300 MeV, which corresponds to about 9% of the speed of light, a 19882Pb* nucleus is created in the nuclear fusion.

That initial 19882Pb* nucleus has a mass number equal to the sum of the Ge projectile's and the Sn target's mass numbers. The asterisk indicates that the nucleus — which is created "hot" with an excitation energy of about 50 MeV, corresponding to a temperature of more than 1010 K — is a compound nucleus, one that is not fully bound. It promptly evaporates several neutrons to cool down, and different Pb isotopes, called fusion-evaporation residues, are created in the process.

In the 19882Pb* example, the evaporation of four neutrons to produce 19482Pb accounts for about 60% of the evaporation residues. Within a few tens of minutes, beta decay transforms the 19482Pb into thallium‑194 (19481Tl). Then a second beta decay turns 19481Tl into mercury‑194 (19480Hg), a nucleus with a 520 year half life. The nuclear alchemist seeking Au has to wait quite some time for the next beta decay into 19479Au. Unfortunately, 19479Au is an unstable isotope, with a half life of only 38 hours.

The beta decay of 19479Au does create stable and even more precious platinum‑194 (19478Pt), but at typical beam intensities used in current SHE experiments, continuous irradiation of 12450Sn with 7432Ge would produce only 1 g of stable 19478Pt in about 100 million years. So nuclear alchemy is possible in principle, but it is definitely not a wise capital venture. However, experiments creating superheavy nuclei are much more rewarding in terms of scientific gain.

Oganessian and Rykaczewski, 2015

Now, write out the reactions in symbolic form.
3. Write something.
4. Write something.

### conceptual

1. Technetium is an artificially produced element that is used in nuclear medicine as a tracer. For each step in the process from production to use to eventual decay into a stable nucleus, write out the corresponding reaction in symbolic form.
1. Molybdenum 98 (9842Mo) is bombarded with neutrons so that one sticks to the nucleus. This is known as neutron capture.
2. The daughter nucleus of the previous reaction undergoes beta decay.
3. The daughter nucleus of the previous reaction is metastable and undergoes gamma decay. (The gamma ray from this decay is detected and used to create an image of an affected tissue.)
4. The daughter nucleus of the previous reaction undergoes beta decay to a stable nucleus.