[UPSC CSE 2009] Schrodinger’s Wave equation and applications (Q202, 20M)

(i) Consider a positron in a box. If the energy released is 60 \text{ eV} when it jumps from the third excited state to the ground state, show that the width of the potential is nearly 0 \cdot 3 \text{ nm}. (ii) Prove that the most probable distance of an electron from the proton (in the hydrogen atom) is the Bohr radius of the hydrogen atom. Consider only the ground state.