The ionisation energy of H atom is `13.6 ` eV. What will be the ionisation energy of `He^(o+)` and `Li^(2+)` ions ?

Answer

`54.5 eV, 122.4 eV`

Explanation

Ionisation energy is the energy needed when an electron is removed from `n_1 = 1` to `n_2 = oo`. For H - atom,
`I.E. = (2pi^2 m e^4)/(n^2h^2)`
Since `n = 1`
`:. I.E. = (2pi^2 me^4)/(h^2) = 13.6 eV`
Ionisation energy of H like ion,
`I.E. = (2 pi^2 m e^4 Z^2)/(h^2)`
I.E. for `He^(+)` ion (Z = 2) = I.E. for `H - "atom" xx (2)^2`
`= 13.6 xx 4 = 54.4 eV`.
Similarly, `I.E.` for `Li^(2+)` ion (Z = 3) = I.E. For H-atom `xx (3)^2`
`= 13.6 xx 9 = 122.4eV`.