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QJEEM24Phaa7b: JEE Main 2024 Physics - Class 12 JEEM24Phaa7b Solution: If Rydberg's constant is R , the longest wavelength of…

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

Step-by-Step Verified Solution

Longest wavelength corresponds to transition between $n = 3$ and $n = 4$

$\begin{aligned} \frac{1}{λ} = {RZ}^{2} (\frac{1}{3^{2}} - \frac{1}{4^{2}}) = {RZ}^{2} (\frac{1}{9} - \frac{1}{16}) \\ = \frac{7 {RZ}^{2}}{9 \times 16} \\ \Rightarrow λ = \frac{144}{7 R} for Z = 1 ∴ α = 144 \end{aligned}$

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