Question

The ionisation energy of hydrogen atom is 13.6 eV, the ionisation energy of a singly ionised helium atom would be

• A. 13.6 eV
• B. 27.2 eV
• C. 6.8 eV
• D. 54.4eV

Answer 1

The Correct Option is D

To determine the ionisation energy of a singly ionised helium atom (\( \text{He}^+ \)), we use the concept that the ionisation energy depends on the nuclear charge \( Z \) of the atom.

The general formula for the ionisation energy of hydrogen-like atoms (atoms with only one electron, such as \( \text{He}^+ \)) is given by:

E = 13.6 \times Z^2 \, \text{eV}

where

• E is the ionisation energy.
• 13.6 \, \text{eV} is the ionisation energy of a hydrogen atom.
• Z is the atomic number of the element.

Since helium (\( \text{He} \)) has an atomic number \( Z = 2 \), substitute \( Z = 2 \) into the formula:

E = 13.6 \times (2)^2 \, \text{eV} = 13.6 \times 4 \, \text{eV} = 54.4 \, \text{eV}

Thus, the ionisation energy of a singly ionised helium atom is 54.4 eV.

This calculated value matches the correct answer, 54.4 eV.