Explanation:

Ionisation energy is the energy required to remove an electron from an atom or a molecule.

Ionisation energy of hydrogen atom = 13.6 eV

Ionisation energy of helium atom can be calculated as follows:

First ionisation energy of helium = energy required to remove one electron from helium atom

He (Z=2) → He+ (Z=3) + e-

The electronic configuration of helium is 1s². Both the electrons are in the 1s orbital. The first electron will be removed from the 1s orbital. Since the 1s orbital can accommodate only two electrons, the removal of the first electron will leave the helium atom with a completely filled 1s orbital. This configuration is very stable and the removal of the second electron will require much more energy than the first electron. Hence, we can consider the ionisation of the first electron only.

The energy required to remove an electron from the 1s orbital of the helium atom will be less than that required to remove an electron from the 1s orbital of the hydrogen atom because the effective nuclear charge experienced by the electron in the 1s orbital of helium is higher than that experienced by the electron in the 1s orbital of hydrogen. However, the exact value of the first ionisation energy of helium cannot be equal to half of the ionisation energy of hydrogen because the electrons in the helium atom experience repulsion from each other due to their like charges. This electron-electron repulsion causes the energy required to remove an electron from helium to be slightly higher than what we would expect based on the effective nuclear charge alone.

The experimental value of the first ionisation energy of helium is 24.6 eV. Therefore, the correct option is (d) 54.4 eV, which is twice the ionisation energy of helium.