Problem $5$: The Sun is mainly composed at $73\mathrm{.}5\%$ by hydrogen and at $24\mathrm{.}9\%$ by helium $($mass percentage$).$ Its total mass is $M_S=1\mathrm{.}99*{10}^{30}kg.$ Its energy comes in majority from the following nuclear fusion reactions:

${?}_1^{1}H+{?}_1^{1}Hlongrightarro{w}_1^{2}H+e^{+}+$

$u,$

${?}_1^{1}H+{?}_1^{2}Hlongrightarro{w}_2^{3}He+,$

${?}_2^{3}He+{?}_2^{3}Helongrightarro{w}_2^{4}He+{?}_1^{1}H+{?}_1^{1}H.$

These three reactions can be condensed in one:

$4_1^{1}Hlongrightarro{w}_2^{4}He+2e^{+}+2$

$u.$

$($a$)$ How many hydrogen nuclei are inside the Sun $($suppose all the hydrogen nuclei are ${?}^{1}H$ isotope$).$

$($b$)$ Using its Q energy given in lecture, what is the total energy produced by the Sun from now until its end of life $-$ when all the hydrogen fuel will disappear.

$($c$)$ Knowing the Sun can still live $5$ billion years more $(5$ Gy: $5$ giga$-$years$),$ what is the energy per second $($power$)$ produced by the Sun? Compare it with the typical energy released by one hydrogen bomb of $1$ megaton.