Question

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

(a) hydrogen
(b) deuterium
(c) He⁺
(d) Li⁺⁺

Answer 1

(c) He⁺

The total energy of a hydrogen-like ion, having Z protons in its nucleus, is given by
$E=-\frac{13.6Z^2}{n^2}$ eV

Here, n = Principal quantum number

For ground state,
n = 1
∴ Total energy, E = $-$ 13.6 Z² 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⁺.