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Match List-I (Spectral Series) with List-II (corresponding wave number expressions).

List-I (Series) A. Balmer series B. Lyman series C. Brackett series D. Pfund series

List-II (Wave number in cm⁻¹) I. R(1/1² - 1/n²) II. R(1/4² - 1/n²) III. R(1/5² - 1/n²) IV. R(1/2² - 1/n²)

Choose the correct answer from the options given below:

A

A-I, B-IV, C-III, D-II

B

A-II, B-III, C-IV, D-I

C

A-IV, B-I, C-II, D-III

D

A-III, B-II, C-I, D-IV

Step-by-Step Solution

The wave number of spectral lines in the hydrogen spectrum is given by the Rydberg formula: νˉ=RH(1n12−1n22)\bar{\nu} = R_H (\frac{1}{n_1^2} - \frac{1}{n_2^2}). Each series corresponds to a specific ground state (n1n_1):

  1. Lyman series (B): Transitions to n1=1n_1 = 1. Matches formula I: R(1/12−1/n2)R(1/1^2 - 1/n^2).
  2. Balmer series (A): Transitions to n1=2n_1 = 2. Matches formula IV: R(1/22−1/n2)R(1/2^2 - 1/n^2).
  3. Brackett series (C): Transitions to n1=4n_1 = 4. Matches formula II: R(1/42−1/n2)R(1/4^2 - 1/n^2).
  4. Pfund series (D): Transitions to n1=5n_1 = 5. Matches formula III: R(1/52−1/n2)R(1/5^2 - 1/n^2).

Therefore, the correct matching is A-IV, B-I, C-II, D-III .

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