2:11 6 of 8 Nuclear Done Turn over Page 6 Question B3 SPA5302 (2020) a) Explain the Geiger-Nuttal rule for a-decay, illustrating your answer with a graph. [6 marks] b) Sketch the potential for a-decay, assuming it can be modelled as a pre-formed particle inside the daughter nucleus. On this sketch, illustrate a typical tunnelling wave-function, which has an energy Q which is less than the potential for RR.) [12 marks] Assuming that the potential between m², where m = m₁m₂/(m + m2) is c) Consider two nuclei which might undergo fusion. nuclei 1 and 2 is a coulomb potential, and that Q the reduced mass here and in the definition of G above, and is the relative velocity of the nuclei before fusion, show that EG 2m2 where Ec=2m² (αZ₁₂)² where a = e²/4 colic 1/137 is the fine structure constant. Two protons collide with a relative kinetic energy of 1 keV. Calculate the probability of barrier penetration. SPA5302 (2020) Question B4 [7 marks] Page 7 E 2:11 Nuclear √2m² where EG=2mc²(#aŹŹ₁)* hc1/137 is the fine structure constant. Done 7 of 8 with a relative kinetic energy of 1 keV. Calculate the probability of barrier [7 marks] SPA5302 (2020) Question B4 Page 7 a) Sketch a graph of the present day abundances of the elements. List the key features of your graph. [5 marks] b) During Big Bang Nucleosynthesis neutrinos freeze out at t 1s, and Helium production begins around 300s. Give a discussion of the physical processes during this time, and show that the mass fraction of 'He to Hydrogen is approximately 1/4. (You may use the following facts: The temperature of the Universe scales with time as T(t) ~ 101 K (15) 1/2 The number density of a non-relativistic particle of mass m in equilibrium scales as n xx [8 marks] c) Explain what is meant by r-process and s-process, and the astrophysical environments in which they take place. Explain, with the aid of a diagram, their importance in the formation of the elements [5 marks] d) Estimate the upper mass of a neutron star in solar mass units. Explain your reasoning, and comment on your answer. (You may assume that the escape velocity for an object mass M and radius R is v = √2GM/R.) Page 8 End of Paper - An Appendix of 1 page follows [7 marks] Turn over SPA5302 (2020)