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In a hydrogen spectrum $λ$ be the wavelength of first transition line of Lyman series. The wavelength difference will be $^{"} a λ^{"}$ between the wavelength of 3^rdtransition line of Paschen series and that of 2^nd transition line Balmer Series where $a =_________$

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answer is 5.

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Detailed Solution

$\frac{1}{λ} = R (\frac{1}{1} - \frac{1}{4}) \Rightarrow λ = \frac{4}{3 R}$
3rd line of Paschen $\frac{1}{λ_{1}} = R (\frac{1}{3^{2}} - \frac{1}{6^{2}})$
2nd line of Balmer $\frac{1}{λ_{2}} = R (\frac{1}{2^{2}} - \frac{1}{4^{2}})$

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