(2) 9/16 R
Since we are given that angular momentum = 3h/2π = n h/2π, hence n = 3
The radius, rn , of the nth allowed orbit, is given by rn ∝ n2/z
The wavelength, λ, of the emitted radiation, is
The three different ways, the atom can de–excute itself (from the state with n = 3) are
(i) n2 = 3 → n1 = 1; (ii) n2 = 3 → n1 = 2; and (iii) n2 = 2 → n1 = 1.
The corresponding wavelengths are
It follows that, out of the given values λ = 9/16 R, is the value , that the atom would not emit.