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  4. The wavelength of the first line of Lyman series is λ. The wavelength of the first line in Paschen series is

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Q. The wavelength of the first line of Lyman series is $\lambda$. The wavelength of the first line in Paschen series is ______

Gujarat CETGujarat CET 2019

Solution:

$\frac{1}{\lambda_{1}}=R\left(\frac{1}{1^{2}}-\frac{1}{2^{2}}\right)$
$\frac{1}{\lambda_{1}}=R\left(\frac{1}{3^{2}}-\frac{1}{4^{2}}\right)$
$\frac{\lambda_{1}}{\lambda}=\frac{\frac{3}{4}}{\frac{7}{16 \times 9}}$
$\lambda_{1}=\frac{3}{4} \times \frac{16 \times 9}{7} \lambda$
$\lambda_{1}=\frac{108}{7} \lambda$