Match List-I with List-II
| List-I | List-II | ||
| Series | Values of \( n_1 \) and \( n_2 \) in Bohr's formula | ||
| (A) | Lyman | (I) | \( n_1 = 4,\ n_2 \ge 5 \) |
| (B) | Balmer | (II) | \( n_1 = 3,\ n_2 \ge 4 \) |
| (C) | Paschen | (III) | \( n_1 = 2,\ n_2 \ge 3 \) |
| (D) | Brackett | (IV) | \( n_1 = 1,\ n_2 \ge 2 \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
In Bohr's formula for the hydrogen spectrum, \( n_1 \) is the lower level on which the electron lands and \( n_2 \) the higher level from which it falls.
\( \displaystyle \frac{1}{\lambda} = R\left(\frac{1}{n_1^{2}} - \frac{1}{n_2^{2}}\right), \qquad n_2 \gt n_1 \)
Each series is named by its lower level, \( n_1 = 1, 2, 3, 4 \) in the order Lyman, Balmer, Paschen, Brackett.
(A) Lyman — this matches (IV) \( n_1 = 1,\ n_2 \ge 2 \). The lines end on the ground state and lie in the ultraviolet.
(B) Balmer — this matches (III) \( n_1 = 2,\ n_2 \ge 3 \). The lines end on the first excited state; this is the visible series.
(C) Paschen — this matches (II) \( n_1 = 3,\ n_2 \ge 4 \). The lines end on \( n = 3 \) and lie in the infrared.
(D) Brackett — this matches (I) \( n_1 = 4,\ n_2 \ge 5 \). The lines end on \( n = 4 \), further in the 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):
Summary – “… 6. The atomic hydrogen emits a line spectrum consisting of various series. The frequency of any line in a series can be expressed as a difference of two terms;
Lyman series:
\( \displaystyle \nu = Rc\left(\frac{1}{1^2} - \frac{1}{n^2}\right);\quad n = 2, 3, 4, \ldots \)
Balmer series:
\( \displaystyle \nu = Rc\left(\frac{1}{2^2} - \frac{1}{n^2}\right);\quad n = 3, 4, 5, \ldots \)
Paschen series:
\( \displaystyle \nu = Rc\left(\frac{1}{3^2} - \frac{1}{n^2}\right);\quad n = 4, 5, 6, \ldots \)
Brackett series:
\( \displaystyle \nu = Rc\left(\frac{1}{4^2} - \frac{1}{n^2}\right);\quad n = 5, 6, 7, \ldots \)”