Question 458: Atoms & Nuclei

Question

The shortest wavelength for Lyman series is 912 $$\mathop A\limits^o $$. The longest wavelength in Paschen series is

Accepted Answer

Shortest wavelength in Lyman series is given by
$$\begin{aligned}
\frac{1}{\lambda_L} & =R\left[\frac{1}{1^2}-\frac{1}{\infty}ight]=R \
	herefore \lambda_L & =\frac{1}{R}
\end{aligned}$$
The longest wavelength in Paschen series is given by
$$\begin{aligned}
\frac{1}{\lambda_p} & =\mathrm{R}\left[\frac{1}{(3)^2}-\frac{1}{(4)^2}ight] \
& =\mathrm{R}\left[\frac{1}{9}-\frac{1}{16}ight]=\mathrm{R} \cdot \frac{7}{144} \
\lambda_{\mathrm{p}} & =\frac{144}{7 \mathrm{R}} \
	herefore \quad \frac{\lambda_p}{\lambda_L} & =\frac{144}{7 \mathrm{R}} \cdot \mathrm{R}=\frac{144}{7} \
	herefore \quad \lambda_{\mathrm{p}} & =\frac{144}{7 \mathrm{R}} \cdot \lambda_L=\frac{144}{7} 	imes 912=18760 \mathop A\limits^o
\end{aligned}$$

Answer

1216 $$\mathop A\limits^o $$

Answer

3646 $$\mathop A\limits^o $$

Answer

18760 $$\mathop A\limits^o $$

Answer

8208 $$\mathop A\limits^o $$

Atoms & Nuclei

The shortest wavelength for Lyman series is 912 $\mathop A\limits^o $. The longest wavelength in Paschen series is

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