Problem 1: At very high temperatures (as in the very early universe), the proton and the neutron can be thought of as two different states of the same particle, called the “nucleon". (The reactions that convert a proton to a neutron or vice versa require the absorption of an electron or a positron or a neutrino, but all of these particles tend to be very abundant at sufficiently high temperatures.) Since the neutron's mass is higher than the proton's by 2.3 x 10-30kg, its energy is higher by this amount times c2. Suppose, then, that at some very early time, the nucleons were in thermal equilibrium with the rest of the universe at 1011K. What fraction of the nucleons at that time were protons, and what fraction were neutrons?

Problem 1: At very high temperatures (as in the very early universe), the proton and the neutron can be thought of as two different states of the same particle, called the “nucleon". (The reactions that convert a proton to a neutron or vice versa require the absorption of an electron or a positron or a neutrino, but all of these particles tend to be very abundant at sufficiently high temperatures.) Since the neutron's mass is higher than the proton's by 2.3 x 10-30kg, its energy is higher by this amount times c2. Suppose, then, that at some very early time, the nucleons were in thermal equilibrium with the rest of the universe at 1011K. What fraction of the nucleons at that time were protons, and what fraction were neutrons?