Q 12-12-087JEE MainJEE Main 2022 (25 Jul, Shift 2)Medium
$\dfrac{x}{x+4}$ is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) third permitted energy level to the second level and (ii) the highest permitted energy level to the second permitted level. The value of $x$ will be ______.
Numerical value type. Enter your answer.
Answer: 5
$E_{3\to2} = 13.6\left(\dfrac14 - \dfrac19\right) = 13.6\times\dfrac{5}{36}$ and $E_{\infty\to2} = 13.6\times\dfrac14$.
$$\frac{E_{3\to2}}{E_{\infty\to2}} = \frac{5}{9} = \frac{x}{x+4}\ \Rightarrow\ 9x = 5x + 20\ \Rightarrow\ x = 5$$
Solution by Sreeraj P, M.Sc Physics