$3.$ The Sun is powered $($in part$)$ by a nuclear fusion reaction called the p$-$p chain in which,

through a series of processes, four protons $($in the form of hydrogen nuclei$)$ are fused together

into a helium nucleus. The process produces accompanying emission of two positrons, a bunch

of neutrinos, and rays $($photons$).$ Most of the energy emerges from the surface of the star in

the form of radiation $($photons$).$

$($a$)$ From the masses of the proton and the helium nucleus and the total luminosity of the Sun,

make an estimate of the number of kilograms of hydrogen that the Sun converts into helium per

second.

$($b$)$ Assuming that most of the mass of the Sun is in the form of hydrogen, and that the Sun

has access of all of its nuclear fuel, about how many years will the Sun burn for before it runs

out of hydrogen and adjusts its structure?