Question

How much energy does a hydrogen atom, treated as a point mass, have to give up to fall from the level with n=3 to the lowest energy level? Assume it is confined to a one-dimensional square well of width 1.0 nm.

Answer 1

Mass of the hydrogen atom m = 1.6727*10-27 kg
Planks constant h = 6.62*10-34
Width of square well L = 1.0 nm = 10-9 m
Energy level of a particle enclosed in one dimensional Infinite square well will be
En = n2h2/(8mL2)
Energy at the lowest level will be for n = 1
E1 = 12*(6.62*10-34)2/ ((8*1.6727*10-27 *( 10-9)2)
E1 = 1.6727*10-27 Joule
Energy at the level 5 will be for n = 3
E5 = 9*E1
= 9*1.6727*10-27
E3 = 15.05*10-27 Joules
So energy give up to fall from the level with 3 to the lowest energy level will be
E = E3 - E1
E = (15.05 - 1.6727) *10-27 Joule
E = 13.3810-27 Joule
E = 1.38*10-26 Joules