The ratio of momentum of the photons of the 1^ st and 2^ nd line of Balmer series of Hydrogen atoms is / . The possible values of and are:-

Step-by-step solution

The momentum of a photon is given by p = h . From Rydberg's formula, the wave number is 1 = R ( 1 n₁^2 - 1 n₂^2 ) . For the first line of the Balmer series, the transition is from n₂ = 3 to n₁ = 2 . p₁ = h ₁ = hR ( 1 2^2 - 1 3^2 ) = hR ( 1 4 - 1 9 ) = 5hR 36 For the second line of the Balmer series, the transition is from n₂ = 4 to n₁ = 2 . p₂ = h ₂ = hR ( 1 2^2 - 1 4^2 ) = hR ( 1 4 - 1 16 ) = 3hR 16 The ratio of the momenta is: p₁ p₂ = 5hR 36 3hR 16 = 5 36 16 3 = 20 27 Comparing with , the possible values are = 20