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

Asked in NEET 2023 · Spectral series and wavelengths

(1) 2λ
(2) 4λ
(3) 9λ
(4) 16λ

Answer: (2) 4λ

Step-by-step solution

The shortest wavelength in a series is the series limit, n₁→∞: 1/λ=R/(n₂²).

Balmer (n₂=2): λ=4/R.

Brackett (n₂=4): λ'=(16)/R.

λ'=4λ.

Why the other options are wrong

(1) Uses the ratio of the lower levels, 4/2, instead of the ratio of their squares, (16)/4.
(3) No single slip gives 9λ; 9λ=(36)/R would be the limit of a series ending on n=6.
(4) (16)/R is sixteen times the Lyman limit 1/R, not the Balmer limit 4/R.

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