Q 12-12-078JEE MainJEE Main 2023 (8 Apr, Shift 2)Easy
The ratio of wavelength of spectral lines $\text{H}_\alpha$ and $\text{H}_\beta$ in the Balmer series is $\dfrac x{20}$. The value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 27
$\text{H}_\alpha$ ($3\to2$): $\dfrac14-\dfrac19=\dfrac5{36}$; $\text{H}_\beta$ ($4\to2$): $\dfrac14-\dfrac1{16}=\dfrac3{16}$.
$$\frac{\lambda_\alpha}{\lambda_\beta}=\frac{3/16}{5/36}=\frac{27}{20}$$
Solution by Sreeraj P, M.Sc Physics