For hydrogen atom, ' $\lambda_1$ ' and ' $\lambda_2$ ' are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of ' $\lambda_1$ ' and ' $\lambda_2$ ' is $\frac{x}{32}$. The value of ' $x$ ' is

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Aicharya · Accepted Answer

$\frac{1}{\lambda_1}=\mathrm{R}\left[\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}\right]=\mathrm{R}\left[\frac{1}{1^2}-\frac{1}{3^2}\right]=\frac{8}{9} \mathrm{R}$
Similarly; $\frac{1}{\lambda_2}=R\left[\frac{1}{1^2}-\frac{1}{2^2}\right]=\frac{3}{4} R$ $\begin{aligned} & \therefore \quad \frac{\frac{1}{\lambda_1}}{\frac{1}{\lambda_2}}=\frac{\frac{8}{9} \mathrm{R}}{\frac{3}{4} R} \\ & \therefore \quad \frac{\lambda_1}{\lambda_2}=\frac{27}{32} \\ & \therefore \quad x=27 \end{aligned}$

For hydrogen atom, ' $\lambda_1$ ' and ' $\lambda_2$ ' are the wavelengths corresponding to the transitions…

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