A particular hydrogen like ion emits radiation of frequency 2.92 ×… | JEE Main 2021 (26 Aug, Shift 1)

Q49JEE Main 2021 · 26 AUG · SHIFT 1Medium

Transitions, Photon Emission & Excitation

A particular hydrogen like ion emits radiation of frequency 2.92 $\times$ 1015 Hz when it makes transition from n = 3 to n = 1. The frequency in Hz of radiation emitted in transition from n = 2 to n = 1 will be:

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Answer: (d)

$\nu \propto \left(\frac{1}{n_f^2} - \frac{1}{n_i^2}\right)$ for the same ion.
$\nu_{31} \propto 1 - \frac{1}{9} = \frac{8}{9}$ , $\nu_{21} \propto 1 - \frac{1}{4} = \frac{3}{4}$
$\nu_{21} = 2.92 \times 10^{15} \times \frac{3/4}{8/9} = 2.92 \times 10^{15} \times \frac{27}{32}$
$\nu_{21} = 2.46 \times 10^{15}$ Hz, so the answer is (d).

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