If λ 1 and λ 2 are the wavelengths of the third member of Lyman and… | JEE Main 2021 (26 Feb, Shift 1)

Q44JEE Main 2021 · 26 FEB · SHIFT 1Medium

Hydrogen Spectrum & Spectral Series

If $\lambda$ 1 and $\lambda$ 2 are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of $\lambda$ 1: $\lambda$ 2 is:

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Answer: (a)

Lyman third member ( $4 \to 1$ ): $\frac{1}{\lambda_1} = R\left(1-\frac{1}{16}\right) = \frac{15R}{16}$
Paschen first member ( $4 \to 3$ ): $\frac{1}{\lambda_2} = R\left(\frac{1}{9}-\frac{1}{16}\right) = \frac{7R}{144}$
$\frac{\lambda_1}{\lambda_2} = \frac{7/144}{15/16} = \frac{112}{2160} = \frac{7}{135}$
So the answer is (a) 7 : 135.

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