A star converts all its hydrogen into helium, achieving 100\% helium. It then converts the helium into carbon via the reaction ^4_2\text{He} + ^4_2\text{He} + ^4_2\text{He} \xrightarrow{\quad} ^{12}_6\text{C} + 7.27\text{ MeV} The mass of the star is 5.0 \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 ?

Calculate the binding energy per nucleus for ^{87}_{38}\text{Sr}.

What are magic numbers ? Discuss the shell structure of a nucleus. How is this model able to explain various properties of nuclei ? Discuss the limitations of this model.