In Paschen series, wavelength of first line is ' λ₁ ' and for… | MHT CET 2025 (26 Apr, Shift 1)

Q13MHT CET 2025 · 26 APR · SHIFT 1Medium

Hydrogen Spectrum & Spectral Series

In Paschen series, wavelength of first line is ' $\lambda_1$ ' and for Brackett series, wavelength of first line is ' $\lambda_2$ ' then ratio $\frac{\lambda_1}{\lambda_2}$ is

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Answer: (c)

Paschen first line ( $4 \to 3$ ): $\frac{1}{\lambda_1} = R\left(\frac{1}{9} - \frac{1}{16}\right) = \frac{7R}{144}$ .
Brackett first line ( $5 \to 4$ ): $\frac{1}{\lambda_2} = R\left(\frac{1}{16} - \frac{1}{25}\right) = \frac{9R}{400}$ .
$\frac{\lambda_1}{\lambda_2} = \frac{144}{7} \times \frac{9}{400} = \frac{1296}{2800} = \frac{81}{175}$ .
So the answer is (c) $\frac{81}{175}$ .

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