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(B) The wavelength of the last line of the Balmer series is given by the Rydberg formula:$\frac{1}{\lambda_{B}} = R \left( \frac{1}{2^{2}} - \frac{1}{

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$4$

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(B) The wavelength of the last line of the Balmer series is given by the Rydberg formula:$\frac{1}{\lambda_{B}} = R \left( \frac{1}{2^{2}} - \frac{1}{\infty^{2}} \right) = \frac{R}{4}$$\lambda_{B} = \frac{4}{R}$The wavelength of the last line of the Lyman series is given by:$\frac{1}{\lambda_{L}} = R \left( \frac{1}{1^{2}} - \frac{1}{\infty^{2}} \right) = R$$\lambda_{L} = \frac{1}{R}$Taking the ratio of the two wavelengths:$\frac{\lambda_{B}}{\lambda_{L}} = \frac{4/R}{1/R} = 4$Thus,the ratio is $4$.

The ratio of wavelengths of the last line of the Balmer series and the last line of the Lyman series is

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