# A hydrogen atom in its excited state emits radiations of wavelengths $1218\AA$ and $974.3\AA$ when it finally comes to the ground state. Identify the energy levels from where transitions occur. Given Rydberg constant $\inline R=1.1\times 10^{7}\; m^{-1}$. Also specify the spectral series to which these lines belong.

$\lambda _{1}=1218\; \AA$

$\lambda _{2}=974.3\; \AA$

Rydberg const, $\inline R=1.1\times 10^{7}\; m^{-1}$

$\frac{1}{1218\times 10^{-10}}=1.1\times 10^{7}\left ( \frac{1}{1^2}-\frac{1}{n^{2}} \right )$

$n^{2}=\frac{1}{0.2536}$

$n^{2}=3.9429$               $\therefore n=1.98\cong 2$

given $\lambda _{2}=974.3\; \AA$

$\frac{1}{974.3\times 10^{-10}}=1.1\times 10^{^{-1}}\left ( \frac{1}{1^{2}}-\frac{1}{n^{2}} \right )$

$n^{2}=\frac{1}{0.0669}$

$n^{2}=14.9411$

$\therefore n=3.86\cong 4$

These lines belong to layman series

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