Spectroscopic studies have shown that the fusion reaction in the sun's core proceeds by a complicated mechanism. One proposed overall equation for the solar fusion reaction is

411H+2 0−1e→42He
which is also accompanied by the release of "massless" neutrinos and photons in addition to energy. Precise masses of the reactants and product are given below.

Species 11H 0−1e 42He
Mass (amu) 1.007825 0.000549 4.002603

The sun produces energy via nuclear fusion at the rate of 4×1026J/s . Based on the proposed overall fusion equation, how long will the sun shine in years before it exhausts its hydrogen fuel? (Assume that there are 365 days in the average year.)

I am not sure how to start this problem

1 answer

You can start by making the equation easier to read. In these situations it is easier to write the atomic number FIRST, then the symbol, then write the mass number SECOND so the equation would look like this.
4 1H1 + 2 -1e0 ==> 2He4 + heat + 0n0

4*mass 1H1 + 2*mass e - mass He = delta E in amu. Convert that to kg and use
delta E = delta M*c^2
That will give you the energy in joules per nuclear fusion.