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Q.
If $\lambda_{1}$ and $\lambda_{2}$ are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of $\lambda_{1}: \lambda_{2}$ is :
$\frac{1}{\lambda_{1}}= R \left[\frac{1}{1^{2}}-\frac{1}{4^{2}}\right]$
$\frac{1}{\lambda_{2}}= R \left[\frac{1}{3^{2}}-\frac{1}{4^{2}}\right]$
$\frac{\lambda_{1}}{\lambda_{2}}=\frac{\left[\frac{1}{9}-\frac{1}{16}\right]}{\left[1-\frac{1}{16}\right]}=\frac{7}{9 \times 15}$
$\frac{\lambda_{1}}{\lambda_{2}}=\frac{7}{135}$