The ratio of the wavelengths of the light absorbed by a Hydrogen atom when it undergoes n = 2 → n = 3 and n = 4 → n = 6 transitions, respectively, is
1/36
1/16
1/9
1/4
1/4
For hydrogen,
En = −RH / n2
Absorbed photon energy:
ΔE = RH (1/n12 − 1/n22)
Thus,
2 → 3 : ΔE1 = RH × 5/36
4 → 6 : ΔE2 = RH × 5/144
Since λ ∝ 1/ΔE
λ1 / λ2 = ΔE2 / ΔE1 = 1/4
Hence option (4) is the correct answer.