A proton confined in a onedimensional box emits a 40 MeV gam

A proton confined in a one-dimensional box emits a 4.0 MeV gamma-ray photon in a quantum jump from n = 2 to n = 1. What is the length of the box?

Solution

En = n^2h^2/(8mL^2)

energy difference b/w the states n=1 and n=2

dE = E2 - E1

= 3h^2/(8mL^2)

=> L = sqrt ( (3*(6.62*10^-34)^2)/(8*1.67*10^-27*4*1.60*10^-13)) = 1.24*10^-14 m = 12.4 fm