If the wavelength of the first member of Lyman series of hydrogen is λ. The wavelength of the second member will be

Solution

Physics sir · 3 steps

Write the Rydberg formula for both lines and divide; R cancels and only the bracket terms remain.

1. Identify the transitions. Every Lyman line ends on n = 1. The first member is the jump 2 → 1, and the second member is the jump 3 → 1.

   1/λ = R(1/1²-1/2²) = 3R/4, 1/λ' = R(1/1²-1/3²) = 8R/9

2. Take the ratio. Wavelength is the reciprocal of these, so λ'/λ = (3R/4)/(8R/9) = 3/4 × 9/8 = 27/32.
3. So. λ' = 27/32λ, which is option (c). It is shorter than λ, as it should be, because the 3 → 1 jump releases more energy.

The idea to keep. For ratios of spectral wavelengths, write 1/λ for each line and divide. A bigger energy gap means a shorter wavelength, so always sanity-check whether your ratio is above or below 1.

Answer from the NTA final answer key. Solution by PrepWiser.