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Home›Chapters›Atomic Structure PYQs›Transitions, Photon Emission & Excitation›Question 19

JEE Main 2024 (1 Feb, Shift 2) · Transitions, Photon Emission & Excitation

Transitions, Photon Emission & Excitation question from JEE Main 2024 (1 Feb, Shift 2)

Q19JEE Main 2024 · 1 FEB · SHIFT 2Medium

Transitions, Photon Emission & Excitation

A particular hydrogen-like ion emits the radiation of frequency $3 \times 10^{15}\text{ Hz}$ when it makes transition from $n = 2$ to $n = 1$ . The frequency of radiation emitted in transition from $n = 3$ to $n = 1$ is $\frac{x}{9} \times 10^{15}\text{ Hz}$ , when $x =$ ________.

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

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Answer: 32

$\nu \propto \left(\frac{1}{n_f^2} - \frac{1}{n_i^2}\right)$ : $\nu_{21} \propto \frac{3}{4}$ , $\nu_{31} \propto \frac{8}{9}$
$\nu_{31} = 3 \times 10^{15} \times \frac{8/9}{3/4} = 3 \times 10^{15} \times \frac{32}{27} = \frac{32}{9} \times 10^{15}$ Hz
So $x = 32$ .

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