Question

In the hydrogen atom, what is the electric potential energy of the electron when it is found in the n = 3 state? Hint: refer to the derivation of the total energy for energy proportions.

Answer 1

For an electron revolving in a circular orbit of radius, r around a nucleus with Z positive charge,

PE = -Ze²/r

KE = Ze²/2r

Hence:

E_total = (-Ze²/r) + (Ze²/2r) = -Ze²/2r

and

Since Z = 1 for hydrogen above equation can be further simplified to:

E_n = -13.6/n² eV

so, potential energy is double of total energy with negative sign

E_n = -2x13.6/n² eV

so, for n = 3

E3 = - 2x13.6/3^2 eV = -3.02 eV.............................ANS