Find the ratio of momentum of photons corresponding to the 1st and 2nd spectral lines of the Balmer series of hydrogen atom.

Momentum of a photon:

p = h/λ

Therefore:

p ∝ 1/λ

For Balmer series:

• 1st line: n = 3 → n = 2
• 2nd line: n = 4 → n = 2

Using Rydberg formula:

1/λ = R(1/2² − 1/n²)

For first line:

1/λ₁ = R(1/4 − 1/9) = 5R/36

For second line:

1/λ₂ = R(1/4 − 1/16) = 3R/16

Momentum ratio:

p₁/p₂ = (5/36)/(3/16)

= 20/27

Final Answer

20 : 27