Electron in hydrogen atom first jumps from third excited state to second excited state and then from second excited to the first excited state. The ratio of the wavelengths ₁: ₂ emitted in the two cases is

Step-by-step solution

Here, for wavelength ₁n₁=4 and n₂=3 and for ₂, n₁=3 and n₂=2 We have h c =-13.6 [ 1 n₂^2 - 1 n₁^2 ] So, for ₁ aligned h c ₁ & =-13.6 [ 1 (4)^2 - 1 (3)^2 ] h c ₁ & =13.6 [ 7 144 ] aligned Similarly, for ₂ aligned h c ₂ & =-13.6 [ 1 (3)^2 - 1 (2)^2 ] h c ₂ & =13.6 [ 5 36 ] aligned Hence, from Eqs. (i) and (ii), we get ₁ ₂ = 20 7