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JEE Main 2019 · 10 Apr · Shift II

JEE Main 2019 Chemistry question on Atomic Structure

The ratio of the shortest wavelength of two spectral series of hydrogen spectrum is found to be about 9. The spectral series are
  1. A.
    Lyman and Paschen
  2. B.
    Brackett and Pfund
  3. C.
    Paschen and Pfund
  4. D.
    Balmer and Brackett
Show answer and solution

Correct option: A

Solution

The shortest wavelength in any spectral series corresponds to the series limit (n→∞), giving 1/λ = R·(1/n₁²). So λ_min ∝ n₁².

For Lyman series: n₁ = 1, so λ_min(Lyman) ∝ 1.
For Paschen series: n₁ = 3, so λ_min(Paschen) ∝ 9.

The ratio λ_min(Paschen)/λ_min(Lyman) = 9/1 = 9, which matches the given condition.

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