Nuclear fusion reactions inside stars and reactors produce energy. One proposed reaction involves two protons (11H{}^1_1\text{H}11H) and one neutron (01n{}^1_0\text{n}01n) fusing to form a helium-3 nucleus (23He{}^3_2\text{He}23He):
2 11H+01n→23He 2 \ {}^1_1\text{H} + {}^1_0\text{n} \rightarrow {}^3_2\text{He} 2 11H+01n→23HeIn this reaction, 7.71 MeV7.71\text{ MeV}7.71 MeV of energy is released.
Only one of the particles in this reaction has a non-zero binding energy. Identify this particle, determine its binding energy per nucleon, and explain your reasoning.
Explain why extremely high temperatures are necessary for fusion reactions to occur between nuclei.
A high-energy gamma photon can spontaneously create a tau-antitau lepton pair (pair production). Calculate the maximum wavelength of a gamma photon for this pair production event.
(Mass of a tau lepton, mτ=3.17×10−27 kgm_{\tau} = 3.17 \times 10^{-27}\text{ kg}mτ=3.17×10−27 kg; Planck constant, h=6.63×10−34 J sh = 6.63 \times 10^{-34}\text{ J s}h=6.63×10−34 J s; speed of light, c=3.00×108 m s−1c = 3.00 \times 10^8\text{ m s}^{-1}c=3.00×108 m s−1)
