Let the total number of neutrons be Nn, the number of protons be Np, and N = Nn + Np. Let the fractions be Xi = Ni/N. (a) If the probability of a particle having energy E is proportional to the Boltzmann factor, exp(-E/kT), show that Xn/Xp exp(-1.3 MeV/kT). (b) For what temperature was the ratio of protons to neutrons in the universe 6.7? (c) What is the kinetic energy associated with this temperature? Is there anything noteworthy about this temperature?

Question

Let the total number of neutrons be Nn, the number of protons be Np, and N = Nn + Np. Let the fractions be Xi = Ni/N. (a) If the probability of a particle having energy E is proportional to the Boltzmann factor, exp(-E/kT), show that Xn/Xp exp(-1.3 MeV/kT). (b) For what temperature was the ratio of protons to neutrons in the universe 6.7? (c) What is the kinetic energy associated with this temperature? Is there anything noteworthy about this temperature?

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