Question

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${}^{-1}$.

Answer 1

The ionization enthalpy is the amount of energy required to remove an electron from ground state to infinity. The energy of electron in the ground state is $-2.18\times {10}^{-18}J$.
The energy of electron at infity is zero.

The energy required to remove electron is $0-(-21.8\times {10}^{-18}J)=2.18\times {10}^{-18}J$.

To remove 1 mole of electrons, the amount of energy required is $2.18\times {10}^{-18}\times 6.023\times {10}^{23}=13.130\times {10}^{5}J/mol$. This is the ionization enthalpy of hydrogen.