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

Explanation

The energy of an electron residing in the nth-orbit of hydrogen-like atom/ion is `E_(n)=-(2pi^(2)mZ^(2)e^(4))/(n^(2)h^(2))`
Ionisation enthalpy for H-atom=`E_(oo)-E_(1)`
`=0-[-(2pi^(2)me^(4)xx1^(2))/(1^(2)xxh^(2))]`
or, `(2pi^(2)me^(4))/(h^(2))=2.18xx10^(-18)" "[becauseIE=2.18xx10^(-18)" (given)"]`
Again, ionisation enthalpy of `He^(+)` ion=`E_(oo)-E_(1)`
`=0-[-(2pi^(2)me^(4)xx2^(2))/(1^(2)xxh^(2))]" "[because Z=2]`
`=4xx(2pi^(2)me^(4))/(h^(2))=4xx2.18xx10^(-18)J=8.72xx10^(-18)J`
`therefore`Energy required for the process`=8.72xx10^(-18)J`.