Q 12-12-039JEE MainJEE Main 2024 (1 Feb, Shift 2)Easy
A particular hydrogen-like ion emits radiation of frequency $3\times10^{15}\ \text{Hz}$ when it makes a transition from $n = 2$ to $n = 1$. The frequency of radiation emitted in the transition from $n = 3$ to $n = 1$ is $\dfrac{x}{9}\times10^{15}\ \text{Hz}$, when $x = $ ______.
Numerical value type. Enter your answer.
Answer: 32
$f \propto \left(\dfrac{1}{n_1^2} - \dfrac{1}{n_2^2}\right)$:
$$\frac{f_{31}}{f_{21}} = \frac{1 - 1/9}{1 - 1/4} = \frac{8/9}{3/4} = \frac{32}{27}$$
$$f_{31} = 3\times10^{15}\times\frac{32}{27} = \frac{32}{9}\times10^{15}\ \text{Hz} \Rightarrow x = 32$$
Solution by Sreeraj P, M.Sc Physics