[UPSC CSE 2024] Nuclear Physics (Q17, 15+5=20M)

(i) Write semi-empirical mass formula. Calculate the atomic number (Z) of most stable nucleus for given mass number (A) using the above formula. (Use the value of fitted coefficients for Coulomb energy a_3 = 0\cdot 711\text{ MeV} and that for asymmetry energy a_4 = 23\cdot 702\text{ MeV}). (ii) Calculate the Q-value of the following nuclear reaction : _4\text{Be}^9 + {}_2\text{He}^4 = {}_6\text{C}^{12} + {}_0\text{n}^1 Given : the mass of neutral atoms of \text{Be}, \text{He} and \text{C} are 9\cdot 015060, 4\cdot 003874 and 12\cdot 003815\text{ amu}, respectively. The mass of neutron is 1\cdot 008986\text{ amu}.