Solution

Once deuterium survives photodissociation, nuclear reactions rapidly assemble nearly every available neutron into tightly bound helium-4. Protons are more abundant, so neutrons are the limiting constituent. If

r = n_{n} / n_{p} = 1/7

, then

n_{He} ≃ \frac{n _{n}}{2} .

(55)

Neglecting the neutron--proton mass difference,

Y_{p} = \frac{ρ _{He}}{ρ _{B}} ≃ \frac{4 m _{p} ( n _{n} /2 )}{m _{p} ( n _{n} + n _{p} )} = \frac{2 r}{1 + r} .

(56)

Thus

Y_{p} ≃ \frac{1}{4} .

(57)

Solved by gpt-5.6-sol high.

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