Atomic Physics Question 4
Question 4 - 2024 (27 Jan Shift 2)
If Rydberg’s constant is $\mathrm{R}$, the longest wavelength of radiation in Paschen series will be $\frac{\alpha}{7 R}$, where $\alpha=$
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Answer: (144)
Solution:
Longest wavelength corresponds to transition between $\mathrm{n}=3$ and $\mathrm{n}=4$
$\frac{1}{\lambda}=\mathrm{RZ}^{2}\left(\frac{1}{3^{2}}-\frac{1}{4^{2}}\right)=\mathrm{RZ}^{2}\left(\frac{1}{9}-\frac{1}{16}\right)$
$=\frac{7 \mathrm{RZ}^{2}}{9 \times 16}$
$\Rightarrow \lambda=\frac{144}{7 \mathrm{R}}$ for $\mathrm{Z}=1 \quad \therefore \alpha=144$
