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Q.

In the hydrogen spectrum, λ be the wavelength of first transition line of Lyman series. The wavelength difference will be “aλ” between the wavelength of 3rd transition line of Paschen series and that of 2nd transition line of Balmer series where a = _______.

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answer is 5.

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Detailed Solution

$\begin{aligned} \frac{1}{λ} = R_{H} (\frac{1}{1^{2}} - \frac{1}{2^{2}}) \\ λ = \frac{4}{3 R} \\ \frac{1}{λ_{3}} = R_{H} (\frac{1}{3^{2}} - \frac{1}{6^{2}}) \\ λ_{3} = \frac{12}{R_{H}} \\ \frac{1}{λ_{2}} = R_{H} (\frac{1}{2^{2}} - \frac{1}{4^{2}}) \\ λ_{2} = \frac{16}{3 R} \\ ∴ λ_{3} - λ_{2} = \frac{20 R}{3} = 5 (\frac{4 R}{3}) \\ a = 5 \end{aligned}$

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