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TFM
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Homework Statement
At very high temperatures (as in the 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 × 10−30 kg, 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 1011 K. What fraction of the nucleons at that time were protons, and what fraction were neutrons?
Homework Equations
[tex] \frac{P(s_2)}{P(s_1)} = \frac{e^-E(s_1)/k_BT}{e^-E(s_2)/k_BT} [/tex]
The Attempt at a Solution
I have done most of this question.
I have said (s_1) is the neutron, and (s_2) = the proton
S_1 = 2.3 * 10^{-30}C^2 = 2.07*10^{-13}
S_2 = 0
I have inserted these values, as well as T = 10^11, into the above equation and have got:
[tex] \frac{P(s_2)}{P(s_1)} = \frac{1}{0.98} = 1.015 [/tex]
I have now arranged it to say:
P(protons) = 1.015 P(Neutrons)
from this, how can I calculate the fraction of the nucleons that were protons, and what fraction were neutrons?
Many Thanks,
TFM