The Bohr moden does not apply when more than one electron orbit the nucleues because it does not account for the electrostatic force that the electron exert on one another.For instance , an electrically neutral lithium atom `(Li)` contains three electrons in orbit around a nucleus that includes three protons `(Z = 3)`, and Bohr's model can be used for the doubly charged positive ion of lithium `(Li^(2)^(+))` that results when two electrons are removed from the neutral atom, leaving only one electron to orbit the nucleus . Obtain the ionization energy that is needed to remove the remaining electron from `(Li^(2)^(+))`

Explanation

The lithium ion `Li^(2+)` contains three times the possitive nuclear charge as that of the hydrogen atom. Therefore , the orbiting electron is attracted more strongly to the nucleus in `Li^(2+)` than in the hydrogen atom. As a result , we expect that more energy is required to ionize `Li^(2+)` than the `13.6 e V` required for atomic hydrogen.
The Bohr energy levels for `Li^(2+)` are given by
`E_(0) = - (13.6 e V) (Z^(2))/(n^(2))`
With `Z = 3` and `n = 1`,
`E_(1) = - (13.6 e V) (3^(2))/(1^(2)) = - 122.4 e V`
To remove the electron from `Li^(2+), 122.4 e V` of energy must be supplied .So the ionization energy for `Li^(2+), 122.4 e V`.