What is the energy (in J atom ^ -1 ) required for the following...

The given process $Li^{2+}(g) \rightarrow Li^{3+}(g) + e^-$ represents the ionization of the hydrogen-like ion $Li^{2+}$ from its ground state.

The ionization energy for a hydrogen-like species is given by the formula:
$IE = IE_{H} \times Z^2$

For $Li^{2+}$, the atomic number $Z = 3$.

Given the ionization energy of the hydrogen atom $IE_{H} = 2.18 \times 10^{-18}$ J atom$^{-1}$.

Substituting the values:
$IE = 2.18 \times 10^{-18} \times (3)^2$

$IE = 2.18 \times 10^{-18} \times 9$

$IE = 19.62 \times 10^{-18}$ J atom$^{-1}$

$IE = 1.962 \times 10^{-17}$ J atom$^{-1}$

Answer: $1.962 \times 10^{-17}$