The atomic hydrogen emits a line spectrum consisting of different series. The ratio of frequencies of the first line in Lyman and Balmer series is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 27 : 5 \)
For hydrogen, the frequency of a line is proportional to \( 1/\lambda \), given by the Rydberg formula.
\( \displaystyle \nu \propto \frac{1}{\lambda} = R\left(\frac{1}{n_1^{2}} - \frac{1}{n_2^{2}}\right) \)
The first line of the Lyman series is \( n = 2 \rightarrow 1 \) and the first line of the Balmer series is \( n = 3 \rightarrow 2 \).
\( \displaystyle \nu_{L} \propto 1 - \frac{1}{4} = \frac{3}{4} \qquad \nu_{B} \propto \frac{1}{4} - \frac{1}{9} = \frac{5}{36} \)
\( \displaystyle \frac{\nu_{L}}{\nu_{B}} = \frac{3/4}{5/36} = \frac{27}{5} \)
Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), and it also appears to be out of the CUET 2026 syllabus.
NCERT (Pre-rationalised edition, 2022-23):
Spectral Series – “… Balmer found a simple empirical formula for the observed wavelengths
\( \displaystyle \frac{1}{\lambda} = R\left(\frac{1}{2^2} - \frac{1}{n^2}\right) \qquad (12.5) \)
where λ is the wavelength, R is a constant called the Rydberg constant, and n may have integral values 3, 4, 5, etc.”
Spectral Series – “… Other series of spectra for hydrogen were subsequently discovered. These are known, after their discoverers, as Lyman, Paschen, Brackett, and Pfund series. These are represented by the formulae:
Lyman series:
\( \displaystyle \frac{1}{\lambda} = R\left(\frac{1}{1^2} - \frac{1}{n^2}\right) \qquad n = 2,3,4\ldots \qquad (12.6) \)”