The ionisation energy for the H-atom in the ground state is `xJ*"atom"^(-1)`. Show that the energy requried for the process, `He^(+)(g) to He^(2+)+e`, is `4x" "J*"atom"^(-1)`.

Explanation

The energy of the electron in the n-th orbit of H-like particle is,
`E_(n)=(2pi^(2)me^(4)Z^(2))/(n^(2)h^(2))=-Kxx(Z^(2))/(n^(2))`
[where `K=(2pi^(2)me^(4))/(h^(2))`=constant]
Now, `I.E_(H)=E_(prop)-E_(1)=0-(-Kxx(1^(2))/(1^(2)))=K`
`=xJ*"atom"^(-1)`
the energy requried for the given process is the ionisation energy of `He^(+)`.
Since `He^(+)` is hydrogen-like species so,
`I.E_(He^(+))=E_(alpha_E_(1)=0-(-Kxx(2^(2))/(1^(2)))" "[for" He^(+),z=2]`
`=4K=4xJ*"atom"^(-1)`.