JEE Main 2024 — Physics Modern Physics

2024integermedium

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

Official previous-year question

Held on 1 Feb 2024 · Verified 6 Jul 2026.

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Solution

For Hydrogen like atom, energy emitted is $E=-13.6{Z}^{2}(\frac{1}{{n}_{i}^{2}}-\frac{1}{{n}_{f}^{2}})$

$\Rightarrow E=C(\frac{1}{{n}_{f}^{2}}-\frac{1}{{n}_{i}^{2}})$

$\Rightarrow h\nu =C[\frac{1}{{n}_{f}^{2}}-\frac{1}{{n}_{i}^{2}}]$

Therefore, the ratio $\frac{{v}_{1}}{{v}_{2}}=\frac{{[\frac{1}{{n}_{f}^{2}}-\frac{1}{{n}_{i}^{2}}]}_{2-1}}{{[\frac{1}{{n}_{f}^{2}}-\frac{1}{{n}_{i}^{2}}]}_{3-1}}$

$=\frac{[\frac{1}{1}-\frac{1}{4}]}{[\frac{1}{1}-\frac{1}{9}]}=\frac{\frac{3}{4}}{\frac{8}{9}}$

$=\frac{3}{4}\times \frac{9}{8}$

$\Rightarrow \frac{{v}_{1}}{{v}_{2}}=\frac{27}{32}$

$\Rightarrow {v}_{2}=\frac{32}{27}{v}_{1}=\frac{32}{27}\times 3\times {10}^{15}\mathrm{Hz}=\frac{32}{9}\times {10}^{15}\mathrm{Hz}$

Hence, $x=32$ .

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Solution

For Hydrogen like atom, energy emitted is $E=-13.6{Z}^{2}(\frac{1}{{n}_{i}^{2}}-\frac{1}{{n}_{f}^{2}})$

$\Rightarrow E=C(\frac{1}{{n}_{f}^{2}}-\frac{1}{{n}_{i}^{2}})$

$\Rightarrow h\nu =C[\frac{1}{{n}_{f}^{2}}-\frac{1}{{n}_{i}^{2}}]$

Therefore, the ratio $\frac{{v}_{1}}{{v}_{2}}=\frac{{[\frac{1}{{n}_{f}^{2}}-\frac{1}{{n}_{i}^{2}}]}_{2-1}}{{[\frac{1}{{n}_{f}^{2}}-\frac{1}{{n}_{i}^{2}}]}_{3-1}}$

$=\frac{[\frac{1}{1}-\frac{1}{4}]}{[\frac{1}{1}-\frac{1}{9}]}=\frac{\frac{3}{4}}{\frac{8}{9}}$

$=\frac{3}{4}\times \frac{9}{8}$

$\Rightarrow \frac{{v}_{1}}{{v}_{2}}=\frac{27}{32}$

$\Rightarrow {v}_{2}=\frac{32}{27}{v}_{1}=\frac{32}{27}\times 3\times {10}^{15}\mathrm{Hz}=\frac{32}{9}\times {10}^{15}\mathrm{Hz}$

Hence, $x=32$ .

JEE Main 2024 — Physics Modern Physics

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JEE Main 2024 — Physics Modern Physics

Did you get this right?

Solution

Your note

JEE Main Modern Physics in other years

More JEE Main Modern Physics questions

Other Physics topics for JEE Main

Mechanics

Electromagnetism

Optics

Thermodynamics

Waves & Oscillations

Keep practicing Modern Physics