Question

A singly ionized helium atom is in the ground state. It absorbs energy and makes a transition to the n = 3 excited state. The ion returns to the ground state by emitting two photons. What are their wavelengths of a lower and higher energy photon?

Answer 1

1/λ₁ =Z²R[(1/n²) – (1/m²)] =2²•1.1•10⁷[(1/1²) –(1/3²)]
λ₁=2.56•10⁻⁸ m
1/λ₂ =Z²R[(1/n²) – (1/m²)] =2²•1.1•10⁷[(1/2²) –(1/3²)]
λ₂ =1.63•10⁻⁷ m