x/x+4 is the ratio of energies of photons produced due to transition… | JEE Main 2022 (25 Jul, Shift 2)

Q41JEE Main 2022 · 25 JUL · SHIFT 2Medium

Transitions, Photon Emission & Excitation

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

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 5

$E \propto \left(\frac{1}{n_f^2} - \frac{1}{n_i^2}\right)$
(i) $3\to2$ : $\frac{1}{4} - \frac{1}{9} = \frac{5}{36}$ ; (ii) $\infty\to2$ : $\frac{1}{4} = \frac{9}{36}$
Ratio $= \frac{5}{9} = \frac{x}{x+4}$
So $x = 5$ .

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