[UPSC IFoS 2022] Schrodinger’s Wave equation and applications (Q133, 8M)

An electron is confined to an infinite well whose width L (= 100\text{ pm}) is roughly the size of an atom. (i) What are the energies of four least energetic quantum states? (ii) What energy must be imparted to the electron to raise it from a state with n = 12 to a higher energy state with n = 25?