The correct sequence A, B, C, D, E with reference to atomic spectral series is:
(A) Lyman series \( \displaystyle\frac{1}{\lambda} = R\left(\frac{1}{A^{2}} - \frac{1}{n^{2}}\right) \)
(B) Balmer series \( \displaystyle\frac{1}{\lambda} = R\left(\frac{1}{B^{2}} - \frac{1}{n^{2}}\right) \)
(C) Pfund series \( \displaystyle\frac{1}{\lambda} = R\left(\frac{1}{C^{2}} - \frac{1}{n^{2}}\right) \)
(D) Brackett series \( \displaystyle\frac{1}{\lambda} = R\left(\frac{1}{D^{2}} - \frac{1}{n^{2}}\right) \)
(E) Paschen series \( \displaystyle\frac{1}{\lambda} = R\left(\frac{1}{E^{2}} - \frac{1}{n^{2}}\right) \)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (B), (E), (D), (C)
In the Rydberg formula \( \frac{1}{\lambda} = R\left(\frac{1}{n_f^{2}} - \frac{1}{n^{2}}\right) \) the number in the first bracket is the lower level \( n_f \) to which the electron falls, and each spectral series has its own value: 1 for Lyman, 2 for Balmer, 3 for Paschen, 4 for Brackett and 5 for Pfund. The letters A to E stand for these numbers, so the correct sequence lists the series in order of \( n_f = 1, 2, 3, 4, 5 \).
\( n_f = 1 \): Lyman series, so \( A = 1 \)
\( n_f = 2 \): Balmer series, so \( B = 2 \)
\( n_f = 3 \): Paschen series, so \( E = 3 \)
\( n_f = 4 \): Brackett series, so \( D = 4 \)
\( n_f = 5 \): Pfund series, so \( C = 5 \)
So the sequence is (A), (B), (E), (D), (C).
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 λ 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:
\( \displaystyle \frac{1}{\lambda} = R\left(\frac{1}{4^2} - \frac{1}{n^2}\right) \qquad n = 5,6,7\ldots \qquad (12.8) \)
Pfund series:
\( \displaystyle \frac{1}{\lambda} = R\left(\frac{1}{5^2} - \frac{1}{n^2}\right) \qquad n = 6,7,8\ldots \qquad (12.9) \)”