The ionisation energy of `He^(+)` is `19.6 xx 10^(-18)"J atom"^(-1)`. Calculate the energy of first stationary state of `Li^(2+)`.

Explanation

Ionisation energy of hydrogen like species = Ionisation energy of `H xx Z^(2)`
I.E. of `He^(+)` = I.E. of `H xx 4`, I.E. of `H = (19.6 xx 10^(-18))/(4)` ….(1)
I.E. of `Li^(2+)` = I.E. of `H xx 9`, I.E. of `H = ("I.E. of " Li^(2+))/(9)` ….(2)
equating (1) and (2) `("I.E. of "Li^(2+))/(9) = (19.6 xx 10^(-18))/(4)`
I.E. of `Li^(2+) = (19.6 xx 10^(-18) xx 9)/(4)`
The energy of first stationary state of `Li^(2+)`
`= (-19.6 xx 10^(-18) xx 9)/(4) = -4.41 xx 10^(-17) " J atom"^(-1)`