Astrophysics: Number of pp-reactions occuring in the Sun

[kirstlen]

Homework Statement

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.

Homework Equations

4H\rightarrowHe+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.

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.

 

[mfb]

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)?