If Rydberg's constant is R, the longest wavelength of radiation in Paschen series will be , where

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Solution

Q.
If Rydberg's constant is R, the longest wavelength of radiation in Paschen series will be $\frac{α}{7 R}$ , where $α$ = _______ . [2024]

Ans.
(144) Longest wavelength corresponds to transition between $n = 3$ and $n = 4$

$\frac{1}{λ} = R Z^{2} (\frac{1}{3^{2}} - \frac{1}{4^{2}}) = R Z^{2} (\frac{1}{9} - \frac{1}{16}) = \frac{7 R Z^{2}}{9 \times 16}$

$\Rightarrow λ = \frac{144}{7 R}$ for $Z = 1$

$∴ α = 144$

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