1) the mean life time for d is around 1 second and for p its billions of years so thats a pretty simple answer.
a) You can consider the S-factor in both reactions and compare these to find that the probability of reaction is lower for one or the other. Alternatively you can consider how slow the p-p reaction is and consider this a limiting factor.
How does the mean lifetime of a deuteron (d) in the core of the Sun compare with the mean lifetime of a proton (p) in the core of the Sun?
A) Considering the cross-sections for the two reaction steps, why does one of these two steps determines the overall rate of reaction.
B) Equating the rates of the two reaction steps, and expressing them in terms of the particle number densities and reaction cross-sections, what determines the ratio of the density of deuterons to the density of protons in the Sun's core?
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