[UPSC IFoS 2022] Schrodinger’s Wave equation and applications (Q134, 4+4=8M)

(i) Find the lowest energy of an electron confined in a three-dimensional cubic box of each side 1\text{ \AA}. (ii) Find the temperature at which the average energy of the molecule would be equal to the lowest energy of the electron. [Given : k = 1\cdot 38 \times 10^{-23}\text{ J/K}]