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Question:

The ratio of the shortest wavelength of two spectral series of hydrogen spectrum is found to be about 9. The spectral series is:

Lyman and Paschen

Paschen and Pfund

Brackett and Pfund

Balmer and Brackett

Solution:

The correct option is B Lyman and Paschen
1/λ₂ = RH(1/n₁² - 1/n₂²)Z²
1/λ₁ = RH(1/m₁² - 1/m₂²)Z²
as for shortest wavelengths both n₂ and m₂ are ∞
λ₁/λ₂ = 9
1 = m₁²/n₁²
Now if m₁=3 and n₁=1 it will justify the statement hence Lyman and Paschen (2) is correct.