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In hydrogen spectrum, the shortest wavelength in the Balmer series is   λ . The shortest wavelength in the Brackett series is :

Options

  1. A16 λ
  2. B2 λ
  3. C4 λ
  4. D9 λ

Correct answer

C. 4 λ

Step-by-step solution

Shortest wavelength means maximum energy in transition. Therefore for Balmer series transition would be n = ∞   to   n = 2 and for Brackett series transition would be from n = ∞   to   n = 4 . Now from Rydberg's formula, 1 λ B l 1 λ B r = R H 1 2 2 - 1 ∞ 2 R H 1 4 2 - 1 ∞ 2 ⇒ λ B r = 4 λ B l = 4 λ

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