# Astrophysics: Number of pp-reactions occuring in the Sun

1. Nov 5, 2013

### kirstlen

1. The problem statement, all variables and given/known data
Calculate the number of proton-proton reactions that occur in the Sun each second. For simplicity consider only the energy generation produced by the PPI chain. Consider that the Sun produces its energy in a steady state from the pp chain.

2. Relevant equations
4H$\rightarrow$He+2e$^{+}$+2$\nu_{e}$+2$\gamma$
$\frac{N_{ix}}{\Delta t}$ = n$_{i}$σv <-- this equation was given in class as the reactions per time.

3. The attempt at a solution
I'm pretty sure you need to use the equation that was given in class however I'm not sure. The textbook gives that σ $\propto$ 1/E so would it help to find the energy produced in the PPI chain to find σ? As for n$_{i}$ and v I'm not sure what those are or how to find them.

2. Nov 5, 2013

### Staff: Mentor

What you wrote is the sum of multiple reactions, not a single reaction, so it does not have a well-defined cross-section.

You need some data about the sun. One option is the microscopic way - find temperature, density, cross-sections and so on, and calculate the rate. I don't think you are supposed to do that, however. There is also the macroscopic way, where "steady state" comes into play: how much energy does the sun lose due to radiation? What is the energy released per pp-reaction (including follow-up reactions, but excluding neutrinos)?

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