JEE MAIN - Physics (2024 - 27th January Evening Shift - No. 30)
If Rydberg's constant is $$R$$, the longest wavelength of radiation in Paschen series will be $$\frac{\alpha}{7 R}$$, where $$\alpha=$$ ________.
Answer
144
Explanation
Longest wavelength corresponds to transition between $$\mathrm{n}=3$$ and $$\mathrm{n}=4$$
$$\begin{aligned} & \frac{1}{\lambda}=\mathrm{RZ}^2\left(\frac{1}{3^2}-\frac{1}{4^2}\right)=\mathrm{RZ}^2\left(\frac{1}{9}-\frac{1}{16}\right) \\ & =\frac{7 \mathrm{RZ}^2}{9 \times 16} \\ & \Rightarrow \lambda=\frac{144}{7 \mathrm{R}} \text { for } \mathrm{Z}=1 \quad \therefore \alpha=144 \end{aligned}$$
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