If wavelength of the first line of the Paschen series of hydrogen atom is 720 nm, then the wavelength of the second line of this series is_____nm. (Nearest integer)

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answer is 492.

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Detailed Solution

$\frac{1}{λ} = R_{H} [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}]$
1st line of paschen series, $\frac{1}{λ_{1}} = R_{H} [\frac{1}{9} - \frac{1}{16}]$
2nd line of paschen series, $\frac{1}{λ_{2}} = R_{H} [\frac{1}{9} - \frac{1}{25}]$
$\frac{λ_{2}}{λ_{1}} = \frac{[\frac{1}{9} - \frac{1}{16}]}{[\frac{1}{9} - \frac{1}{25}]} \Rightarrow λ_{2} = 720 \times \frac{[\frac{7}{9 \times 16}]}{[\frac{16}{9 \times 25}]}$
= 492.19 nm

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