As per Bohr model , the minimum energy (in eV) required to remove an electron from the ground state of `Li^(2+) ion (Z=3)` is : A) 1.51 B) 13.6 C) 40.8 D) 122.4 - which one is correct?

Explanation

In a hydrogen atom, the force of attraction (in CGS system) between the nucleus having charge +e and electron of charge -e at a distance r is `e^2//r^2` .
Again, ground state energy of hydrogen atom,
`E_1=-(2pi^2me^4)/(h^2) =-13.6 eV`
In `Li^(2+) `ion , there is also one electron, the force of attraction between the nucleus having charge +Ze and electron having charge -e is `(Ze^2)/(r^2)` .
So, putting `Ze^2` in place of `e^2` in the expression for ground -state energy of hydrogen atom, the ground - state energy of `Li^(2+)` can be obtained . This energy is ,
`E_1^' =-(2pi ^2m(Ze^2)^2)/(h^2)=-(2pi^2me^4)/(h^2)*Z^2`
`=- 13.6xx3^2=-122.4 eV`
so, the answer D is correct.