Match the LIST-I with LIST-II (Symbols have their usual meaning)
| LIST-I Spectral series of Hydrogen | LIST-II Wave Number | ||
| A. | Lyman series | I. | \( \bar{\nu} = R\left[\displaystyle\frac{1}{1^{2}} - \frac{1}{n_{2}^{2}}\right] \) |
| B. | Paschen series | II. | \( \bar{\nu} = R\left[\displaystyle\frac{1}{2^{2}} - \frac{1}{n_{2}^{2}}\right] \) |
| C. | Balmer series | III. | \( \bar{\nu} = R\left[\displaystyle\frac{1}{3^{2}} - \frac{1}{n_{2}^{2}}\right] \) |
| D. | Brackett series | IV. | \( \bar{\nu} = R\left[\displaystyle\frac{1}{4^{2}} - \frac{1}{n_{2}^{2}}\right] \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A-I, B-III, C-II, D-IV
In the Rydberg formula \( \bar{\nu} = R\left(1/n_1^{2} - 1/n_2^{2}\right) \), each series is fixed by the lower level \( n_1 \) on which the electron lands.
(A) Lyman series — this matches (I) \( \bar{\nu} = R[1/1^{2} - 1/n_2^{2}] \). Transitions end on \( n_1 = 1 \) (ultraviolet).
(B) Paschen series — this matches (III) \( \bar{\nu} = R[1/3^{2} - 1/n_2^{2}] \). Transitions end on \( n_1 = 3 \) (infrared).
(C) Balmer series — this matches (II) \( \bar{\nu} = R[1/2^{2} - 1/n_2^{2}] \). Transitions end on \( n_1 = 2 \) (visible).
(D) Brackett series — this matches (IV) \( \bar{\nu} = R[1/4^{2} - 1/n_2^{2}] \). Transitions end on \( n_1 = 4 \) (infrared).
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 – “… 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 \( \lambda \) is the wavelength, R is a constant called the Rydberg constant, and n may have integral values 3, 4, 5, etc.”
Spectral Series – “… 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:
\( \displaystyle \frac{1}{\lambda} = R\left(\frac{1}{4^2} - \frac{1}{n^2}\right) \qquad n = 5,6,7\ldots \qquad (12.8) \)”