# 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?

### Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Science