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)
2. Let's turn lead into gold. Read this.

   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.