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  • In hydrogen spectrum, the shortest wavelength in the Balmer series is . The shortest wavelength in the Bracket

In hydrogen spectrum, the shortest wavelength in the Balmer series is \lambda . The shortest wavelength in the Bracket series is :

Option: 1

2 \lambda


Option: 2

4 \lambda


Option: 3

9 \lambda


Option: 4

16 \lambda


Answers (1)

best_answer

For Balmer series

\begin{aligned} \frac{1}{\lambda_{\min }} & =\mathrm{R}\left(\frac{1}{(2)^2}-\frac{1}{\infty}\right)=\frac{\mathrm{R}}{4} \\ \Rightarrow \lambda_{\min } =\lambda & =\frac{4}{\mathrm{R}}\, \, \, \, \, \, ...(i) \end{aligned}

For Bracket series

\begin{aligned} & \frac{1}{\lambda_{\min }^{\prime}}=\mathrm{R}\left(\frac{1}{(4)^2}-\frac{1}{\infty}\right)=\frac{\mathrm{R}}{16} \\ & \Rightarrow \lambda_{\min }^{\prime}=\frac{16}{\mathrm{R}} \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, ...(ii)\\ & \Rightarrow \lambda_{\min }^{\prime}=4 \lambda \end{aligned}

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shivangi.bhatnagar

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