Question

If ionisation potential for hydrogen atom is 13.6 eV, then ionisation potential for $He^+$ will be

• A. 54.4 eV
• B. 6.8 eV
• C. 13.6 eV
• D. 24.5 eV

Answer 1

Answer: (A)

54.4 eV

Answer 2

The correct option is(A): 54.4 eV.

For hydrogen atom Z = 1
$\therefore\, \, \, \, Ionisation\, energy, E_H=\frac{2\pi^2 me^4}{n_2 h_2}\, \, \, \, \, \, \, \, \, \, \, ...(i)$
For $He^+ ion, (He^+ = 1s^1)$
so, $(He^+ = H)$ ionisation energy
$\, \, \, \, \, \, \, \, \, \, \, E_{{He}^+}=\frac{2\pi^2 me^4 Z^2}{n^2 h^2}\, \, \, \, \, \, \, \, \, \, \, \, ...(ii)$
Eq (i)/Eq (ii), we get
$\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, E_{{He}^+}= E_H \times Z^2$
$\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = 13.6 \times 4$ = 54.4eV