UPSC Physics Optional PYQs (CSE & IFoS)PYQs

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

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 ?

Predict from the single particle shell model, the shell configuration, ground state spin and parity for the following nuclei : {}^7_3\text{Li}, \quad {}^{13}_7\text{N}, \quad {}^{17}_8\text{O}, \quad {}^{27}_{13}\text{Al}