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(A) The shortest wavelength $(\lambda)$ for a spectral series is given by the Rydberg formula: $\frac{1}{\lambda} = R_H 	imes Z^2 	imes (\frac{1}{n_

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Lyman and Paschen

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(A) The shortest wavelength $(\lambda)$ for a spectral series is given by the Rydberg formula: $\frac{1}{\lambda} = R_H 	imes Z^2 	imes (\frac{1}{n_1^2} - \frac{1}{n_2^2})$.For the shortest wavelength,$n_2 = \infty$,so $\frac{1}{\lambda} = \frac{R_H}{n_1^2}$.Thus,$\lambda = \frac{n_1^2}{R_H}$.The ratio of the shortest wavelengths of two series with lower energy levels $n_1$ and $n_2$ is $\frac{\lambda_2}{\lambda_1} = \frac{n_2^2}{n_1^2} = 9$.This implies $\frac{n_2}{n_1} = 3$.For the Lyman series,$n_1 = 1$. For the Paschen series,$n_2 = 3$.Therefore,the ratio is $\frac{3^2}{1^2} = 9$. The series are Lyman and Paschen.

The ratio of the shortest wavelength of two spectral series of the hydrogen spectrum is found to be about $9$. The spectral series are

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