If ' λ₁ ' and ' λ₂ ' are the wavelengths of the first member of the… | MHT CET 2025 (19 Apr, Shift 1)

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Hydrogen Spectrum & Spectral Series

If ' $\lambda_1$ ' and ' $\lambda_2$ ' are the wavelengths of the first member of the Balmer and Paschen series, in hydrogen atom respectively, then the ratio of respective frequencies, $f_1/f_2$ , is

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Answer: (a)

$f \propto \frac{1}{\lambda} = R\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$ .
Balmer first line: $f_1 \propto \frac{1}{4} - \frac{1}{9} = \frac{5}{36}$ .
Paschen first line: $f_2 \propto \frac{1}{9} - \frac{1}{16} = \frac{7}{144}$ .
$\frac{f_1}{f_2} = \frac{5}{36} \times \frac{144}{7} = \frac{20}{7}$ .
So the answer is (a) $20 : 7$ .

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