Consider the energy of an electron in its orbit. The electron has a charge of -e, while the nucleus has a charge of +Ze, where Z is the atomic number of the element. The energy is then given by:

E = U + K = -kZe²/r + mv²/2

The electron is experiencing uniform circular motion, with the only force on it being the attractive force between the negative electron and the positive nucleus. Thus:

kZe²/r² = mv²/r

Therefore mv² = kZe²/r

Plugging this back into the energy equation gives:

E = -kZe²/r + kZe²/2r = -kZe²/2r

We have already shown that the radius is given by:

r = n²h²/4p²mkZe²

Plugging this into the energy equation gives the total energy of the nth level:

E = -2p²mk²Z²e⁴/n²h²

This can be written in a more compact form:

E_n = (-13.6 eV) Z²/n²

So, Bohr's assumption that the momentum of the electron is quantized leads directly to the result that the electron energy is quantized.