Two electrons are moving in orbits of two hydrogen like atoms with speeds 3 × 10 5 m / s and 2.5 × 10 5 m / s respectively. If the radii of these orbits are nearly same then the possible order of energy states are \ \ \ \ respectively.

Physics · Atomic Physics

JEE Main 2026 — 24 January, Morning Shift — Question 30

Two electrons are moving in orbits of two hydrogen like atoms with speeds $3 \times 10^{5} \mathrm{~m} / \mathrm{s}$ and $2.5 \times 10^{5} \mathrm{~m} / \mathrm{s}$ respectively. If the radii of these orbits are nearly same then the possible order of energy states are $\_\_\_\_$ respectively.

Option A:
6 and 5
Correct
Option B:
9 and 8
Option C:
8 and 10
Option D:
10 and 12

Answer: A

Step-by-step solution

$V \propto \frac{Z}{n}$ $r \propto \frac{\mathrm{n}^{2}}{\mathrm{Z}}$ Thus ; $r \propto \frac{\mathrm{n}}{\mathrm{V}}$ Radii are same then $\frac{\mathrm{n}_{1}}{\mathrm{~V}_{1}}=\frac{\mathrm{n}_{2}}{\mathrm{~V}_{2}}$ $\frac{\mathrm{n}_{1}}{\mathrm{n}_{2}}=\frac{3 \times 10^{5}}{2.5 \times 10^{5}}=\frac{6}{5}$ Possible order is 6 and 5

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 24 January, Morning Shift
Subject: Physics
Chapter: Atomic Physics
Topic: Rutherford's and Bohr's Model of Atom