Q 12-12-098JEE MainJEE Main 2021 (26 Feb, Shift 1)Medium
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:
Answer: (A) $7 : 135$
Third Lyman line: $n = 4 \to 1$, $\dfrac{1}{\lambda_1} = R\left(1 - \dfrac{1}{16}\right) = \dfrac{15R}{16}$.
First Paschen line: $n = 4 \to 3$, $\dfrac{1}{\lambda_2} = R\left(\dfrac{1}{9} - \dfrac{1}{16}\right) = \dfrac{7R}{144}$.
$$\frac{\lambda_1}{\lambda_2} = \frac{7/144}{15/16} = \frac{7}{135}$$
Solution by Sreeraj P, M.Sc Physics