Arrange the range of frequencies of the following series of hydrogen…

The correct answer is Option (4) → (D), (C), (A), (B)

The frequencies of the lines of a series ending on level \( n_1 \) are given by the Rydberg formula:

    \( \displaystyle \nu = Rc\left(\frac{1}{n_1^{2}} - \frac{1}{n_2^{2}}\right), \quad n_2 \gt n_1 \)

The highest frequency of a series (its series limit) is \( Rc/n_1^{2} \), so a series ending on a higher level \( n_1 \) lies at lower frequencies.

    \( \text{Lyman: } n_1 = 1 \text{ (ultraviolet)} \)
    \( \text{Balmer: } n_1 = 2 \text{ (visible)} \)
    \( \text{Paschen: } n_1 = 3 \text{ (infrared)} \)
    \( \text{Brackett: } n_1 = 4 \text{ (infrared)} \)

So in ascending order of frequency: Brackett, Paschen, Balmer, Lyman, that is D, C, A, B.

Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), but it is still in the CUET 2026 syllabus, so do not skip it.

NCERT (Pre-rationalised edition, 2022-23):
Spectral Series – “… In 1885, the first such series was observed by a Swedish school teacher Johann Jakob Balmer (1825–1898) in the visible region of the hydrogen spectrum. This series is called Balmer series (Fig. 12.6).”

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:

    \( \displaystyle \frac{1}{\lambda} = R\left(\frac{1}{1^2} - \frac{1}{n^2}\right) \qquad n = 2,3,4\ldots \qquad (12.6) \)

Paschen series:

    \( \displaystyle \frac{1}{\lambda} = R\left(\frac{1}{3^2} - \frac{1}{n^2}\right) \qquad n = 4,5,6\ldots \qquad (12.7) \)

Brackett series:

    \( \displaystyle \frac{1}{\lambda} = R\left(\frac{1}{4^2} - \frac{1}{n^2}\right) \qquad n = 5,6,7\ldots \qquad (12.8) \)

Pfund series:

    \( \displaystyle \frac{1}{\lambda} = R\left(\frac{1}{5^2} - \frac{1}{n^2}\right) \qquad n = 6,7,8\ldots \qquad (12.9) \)

The Lyman series is in the ultraviolet, and the Paschen and Brackett series are in the infrared region.”