Energy of an electron in the ground state of the hydrogen atom is $-2.18 \times 10^{-18} \, J$. Calculate the ionization enthalpy of atomic hydrogen in terms of $J \, mol^{-1}$.

The energy of an electron in the ground state of the hydrogen atom is $-2.18 \times 10^{-18} \, J$.
The energy required to remove this electron to infinity (ionization) is the negative of the ground state energy,which is $2.18 \times 10^{-18} \, J$ per atom.
To calculate the ionization enthalpy in $J \, mol^{-1}$,we multiply the energy per atom by the Avogadro constant $(N_A = 6.022 \times 10^{23} \, mol^{-1})$:
$\text{Ionization enthalpy} = 2.18 \times 10^{-18} \, J \times 6.022 \times 10^{23} \, mol^{-1} = 1.312 \times 10^{6} \, J \, mol^{-1}$.