Question

The energy of an atom (or ion) in its ground state is −54.4 eV. It may be

Options

•  hydrogen

• deuterium

• He⁺

• Li⁺⁺

Answer 1

He⁺

The total energy of a hydrogen-like ion, having Z protons in its nucleus, is given by

`E = - (13.6Z^2)/(n^2)eV`

Here, n = Principal quantum number

For ground state,
n = 1
∴ Total energy, E = - `13.6 Z^2 eV`

For hydrogen,
Z = 1
∴ Total energy, E = - 13.6 eV

For deuterium,
Z = 1
∴ Total energy, E = - 13.6 eV

For He⁺,
Z = 2
 ∴ Total energy, E = - 13.6×2² = - 54.4 eV

For Li⁺⁺,
Z = 3
∴ Total energy, E = - 13.6×3² = - 122.4 eV

Hence, the ion having an energy of −54.4 eV in its ground state may be He⁺.