Atoms & Nuclei

JEE Main level, single correct, medium

87 of 239

Question 87 of 239

In a hydrogen like atom electron makes transition from an energy level with quantum number n\text{n} to another with quantum number (n−1)\left(\text{n}-1\right). If n \gt\gt1\text{n \gt \gt 1}, the frequency of radiation emitted is proportional to :

Show answer and solution

Answer: (B) 1n3\dfrac{1}{{\text{n}}^{3}}

ΔE=hν\Delta \text{E}=\text{h}\nu
ν=ΔEh=k[1(n−1)2−1n2]=k2nn2(n−1)2\nu =\dfrac{\Delta \text{E}}{\text{h}}=\text{k}\left[\dfrac{1}{{\left(\text{n}-1\right)}^{2}}-\dfrac{1}{{\text{n}}^{2}}\right]=\dfrac{\text{k}2\text{n}}{{\text{n}}^{2}{\left(\text{n}-1\right)}^{2}}

≈2kn3∝1n3\approx \dfrac{2\text{k}}{{\text{n}}^{3}}\propto \dfrac{1}{{\text{n}}^{3}}

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.
See it move: Atoms: Rutherford, Bohr and X-rays simulationDrag the sliders and watch the numbers in this question change.Revise Modern Physics firstFormula sheet, solved examples and the traps students fall into.

More Physics practice

JEE Main Physics practice question on Atoms & Nuclei (Bohr's Atomic Model), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.