Calculate the energy required for the process `He ^(+) (g) to He ^(2+) (g) + e ^(-)` The ionisation energy for the H-atom in the ground state is `2. 18 xx 10 ^(-18) J "atom" ^(-1).`

Explanation

For H species
`E _(n ) = ( - 2 pi ^(2) m Z ^(2) e ^(4))/( n ^(2) h ^(2))`
For H-atom
`IE = E _(n) - E _(1) = 0 - (- ( 2 pi ^(2) m e ^(4))/( 1 xx h ^(2)))`
`IE = ( 2 pi ^(2) m e ^(4))/( h ^(2))`
Given `IE = 2. 18 xx 10 ^(-18) J "atom"^(-1)`
Energy required `= E _(n) - E _(1) = 0 - (- ( 2 pi ^(2) me ^(4) (2) ^(2))/(1 ^(2) xx h^(2))) = ( 4 xx 2 pi ^(2) m e^(2))/( h ^(2)) = 4 xx 2. 18 xx 10 ^(-18) J.`
`=8.72 xx 10 ^(-18) J`