If lambda_1 and lambda_2 are the wavelengths | vedclass

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(D) Using Rydberg's formula,$\frac{1}{\lambda} = R \left[ \frac{1}{n_1^2} - \frac{1}{n_2^2} \right]$.For the first line of the Lyman series,$n_1 = 1$

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$108: 7$

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(D) Using Rydberg's formula,$\frac{1}{\lambda} = R \left[ \frac{1}{n_1^2} - \frac{1}{n_2^2} ight]$.For the first line of the Lyman series,$n_1 = 1$ and $n_2 = 2$:$\frac{1}{\lambda_1} = R \left[ \frac{1}{1^2} - \frac{1}{2^2} ight] = R \left[ 1 - \frac{1}{4} ight] = \frac{3R}{4}$.For the first line of the Paschen series,$n_1 = 3$ and $n_2 = 4$:$\frac{1}{\lambda_2} = R \left[ \frac{1}{3^2} - \frac{1}{4^2} ight] = R \left[ \frac{1}{9} - \frac{1}{16} ight] = R \left[ \frac{16 - 9}{144} ight] = \frac{7R}{144}$.Now,calculating the ratio $\frac{\lambda_2}{\lambda_1}$:$\frac{\lambda_2}{\lambda_1} = \frac{1}{\lambda_1} 	imes \lambda_2 = \left( \frac{3R}{4} ight) 	imes \left( \frac{144}{7R} ight) = \frac{3 	imes 36}{7} = \frac{108}{7}$.Thus,$\lambda_2 : \lambda_1 = 108 : 7$.

If $\lambda_1$ and $\lambda_2$ are the wavelengths of the first line of the Lyman and Paschen series respectively,then $\lambda_2 : \lambda_1$ is

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