Calcultte the enrgy required for the process ,
` He^+ (g) rarr He^(2+) (g) + e`
The ionization energy for the H-atom in the grounds state is ` 2. 18 xx 10 ^(-18) J "atom"^(-1)`.

Explanation

For H-like particles, `E_(n) = - (2pi^(2) m Z^(2) e^(4))/(n^(2) h^(2))`
For H-atom, I.E. `= E_(oo) - E_(1) = 0 - (-(2pi^(2) me^(4))/(1^(2) xx h^(2))) = (2pi^(2) me^(4))/(h^(2)) = 2.18 xx 10^9-18) J "atom"^(-1)` (Given)
For the given process,
Energy required `= E_(oo) - E_(1) = 0 = (-(2pi^(2) m xx 2^(2) xx e^(4))/(1^(2) xx h^(2))) = 4 xx (2pi^(2) me^(4))/(h^(2)) = 4 xx 2.18 xx 10^(-18) J`
`= 8.72 xx 10^(-18) J`