Nuclear Physics — UPSC Physics Optional CSE 2007 Paper II

A star converts all its hydrogen to helium, achieving 100% helium composition. It then converts the helium to carbon via the reaction {}^{4}_{2}\text{He} + \text{He} \rightarrow {}^{12}_{6}\text{C} + 7.27\text{ MeV} The mass of the star is 5 \times 10^{32}\text{ kg} and it generates energy at the rate of 5 \times 10^{30}\text{ W}. How long will it take to convert all helium to carbon at this rate ?