In Balmer series, wavelength of the 2 nd line is ' λ₁ ' and for… | MHT CET 2023 (12 May, Shift 2)

Q31MHT CET 2023 · 12 MAY · SHIFT 2Medium

Hydrogen Spectrum & Spectral Series

In Balmer series, wavelength of the $2$ nd line is ' $\lambda_1$ ' and for Paschen series, wavelength of the $1$ st line is ' $\lambda_2$ ', then the ratio ' $\lambda_1$ ' to ' $\lambda_2$ ' is

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Answer: (c)

Balmer 2nd line ( $4 \to 2$ ): $\frac{1}{\lambda_1} = R\left(\frac{1}{4} - \frac{1}{16}\right) = \frac{3R}{16}$ , so $\lambda_1 = \frac{16}{3R}$ .
Paschen 1st line ( $4 \to 3$ ): $\frac{1}{\lambda_2} = \frac{7R}{144}$ , so $\lambda_2 = \frac{144}{7R}$ .
$\frac{\lambda_1}{\lambda_2} = \frac{16}{3} \times \frac{7}{144} = \frac{7}{27}$ .
So the answer is (c) $7 : 27$ .

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