Nuclear Physics — UPSC Physics Optional CSE 2010 Paper II

A star converts all its hydrogen to helium, achieving 100% helium. It then converts the helium to carbon via the reaction {}^{4}_{2}\mathrm{He}+{}^{4}_{2}\mathrm{He}+{}^{4}_{2}\mathrm{He}\rightarrow{}^{12}_{6}\mathrm{C}+7\cdot27\mathrm{MeV} The mass of the star is 5.0\times10^{32}\,\mathrm{kg} and it generates energy at the rate of 5\times10^{30}\,\mathrm{W}. How long will it take to convert all Helium to carbon at this rate?