The ratio of minimum wavelengths of Lyman and | vedclass

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(B) The minimum wavelength of a spectral series corresponds to the transition from $n_{i}=\infty$ to the final orbit $n_{f}$.For the Lyman series,$n_{

Vedclass · Accepted Answer

$0.25$

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(B) The minimum wavelength of a spectral series corresponds to the transition from $n_{i}=\infty$ to the final orbit $n_{f}$.For the Lyman series,$n_{f}=1$:$\frac{1}{(\lambda_{\min})_{L}} = R \left[ \frac{1}{1^2} - \frac{1}{\infty^2} \right] = R$$\Rightarrow (\lambda_{\min})_{L} = \frac{1}{R}$  --- $(i)$For the Balmer series,$n_{f}=2$:$\frac{1}{(\lambda_{\min})_{B}} = R \left[ \frac{1}{2^2} - \frac{1}{\infty^2} \right] = \frac{R}{4}$$\Rightarrow (\lambda_{\min})_{B} = \frac{4}{R}$  --- (ii)Dividing equation $(i)$ by (ii):$\frac{(\lambda_{\min})_{L}}{(\lambda_{\min})_{B}} = \frac{1/R}{4/R} = \frac{1}{4} = 0.25$

The ratio of minimum wavelengths of Lyman and Balmer series will be

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