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QJEEM22Ph3c8d: JEE Main 2022 Physics - Class 12 JEEM22Ph3c8d Solution: x x + 4 is the ratio of energies of photons produced due to…

$\frac{x}{x + 4}$ 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 ____________.

Step-by-Step Verified Solution

$E_{n} = - \frac{13.6}{n^{2}} e V$

$\frac{\frac{1}{2^{2}} - \frac{1}{3^{2}}}{\frac{1}{2^{2}}} = \frac{x}{x + 4}$

$\Rightarrow \frac{9 - 4}{9 \times 4 \times \frac{1}{4}} = \frac{x}{x + 4} = \frac{5}{9}$

$x = 5$