Q 12-12-070JEE MainJEE Main 2023 (11 Apr, Shift 1)Medium
A monochromatic light is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. The frequency of incident light is $x\times10^{15}\ \text{Hz}$. The value of $x$ is ______. (Given $h=4.25\times10^{-15}\ \text{eV s}$)
Numerical value type. Enter your answer.
Answer: 3
Six lines means $\dfrac{n(n-1)}{2}=6\Rightarrow n=4$. The atoms were excited from $n=1$ to $n=4$:
$$E=13.6\left(1-\frac1{16}\right)=12.75\ \text{eV},\qquad\nu=\frac{12.75}{4.25\times10^{-15}}=3\times10^{15}\ \text{Hz}$$
Solution by Sreeraj P, M.Sc Physics