Calculate the energy required for the process
` He^(+)(g) to He^(2+) (g) + e^(-)`
The ionization energy for the H atom in the ground state is `2.18xx10^(-18) J "atom" ^(-1)`

Explanation

For H -like species the the energy of the nth shell is given by
`E_(n)=-1/((4pi epsi_(0))^(2)) xx (2pi^2 me^4 Z^2)/(n^2 h^2)`
`=-(2.18 xx 10^(-18) xx Z^2)/(n^2) " J atom"^(-1)`
For `He^(+) (g)"ion, "Z=2`
`E_(n)=-(2.18 xx 10^(-18) xx (2)^2)/(n^2)=-(8.72 xx 10^(-18))/(n^2) " J atom"^(-1)`
`E_(1)=-(8.72 xx 10^(-18))/((1)^2)=-8.72 xx 10^(-18)" J atom"^(-1)`
`E_(oo)=0`
Hence, energy required for the process
`He^(+) (g) to He^(2+) (g) +e^(-)`
`triangleE=E_(oo)-E_(1)=0 -(8.72 xx 10^(-18))`
`=8.72 xx 10^(-18)" J atom"^(-1)`