Question 323: Atoms & Nuclei

Question

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

Accepted Answer

Longest wavelength corresponds to transition between $$\mathrm{n}=3$$ and $$\mathrm{n}=4$$
$$\begin{aligned}
& \frac{1}{\lambda}=\mathrm{RZ}^2\left(\frac{1}{3^2}-\frac{1}{4^2}ight)=\mathrm{RZ}^2\left(\frac{1}{9}-\frac{1}{16}ight) \
& =\frac{7 \mathrm{RZ}^2}{9 	imes 16} \
& \Rightarrow \lambda=\frac{144}{7 \mathrm{R}} 	ext { for } \mathrm{Z}=1 \quad 	herefore \alpha=144
\end{aligned}$$

Atoms & Nuclei

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

Integer / Numeric Answer Type