The wavelength of a spectral line emitted by hydrogen atom in the Lyman series is $\frac{16}{15 R} \mathrm{~cm}$. What is the value of $n_2 ? \quad(R=$ Rydberg constant)

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Aicharya · Accepted Answer

For Lyman series, $\begin{aligned} \frac{1}{\lambda} & =R\left[\frac{1}{1^2}-\frac{1}{n_2^2}ight] \ \frac{15 R}{16} & =R\left[\frac{1}{1^2}-\frac{1}{n_2^2}ight] \ \frac{15 R}{16 R} & =\left[\frac{n_2^2-1}{n_2^2}ight] \ \frac{15}{16} & =\frac{n_2^2-1}{n_2^2} \ 15 n_2^2 & =16 n_2^2-16 \ n_2^2 & =16 \ n_2 & =4\end{aligned}$

The wavelength of a spectral line emitted by hydrogen atom in the Lyman series is $\frac{16}{15 R}…

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