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.

JEE Main · 2026 · 24 Jan 2026 · Shift 1 · Modern Physics

Two electrons are moving in orbits of two hydrogen like atoms with speeds

3 \times 1 0^{5} m / s

and

2.5 \times 1 0^{5} m / s

respectively. If the radii of these orbits are nearly same then the possible order of energy states are ______ respectively.

(A)6 and 5✓ Correct
(B)9 and 8
(C)8 and 10
(D)10 and 12

Answer: (A)

Solution

For a hydrogen-like atom the orbital speed is

v \propto \frac{Z}{n}

and the radius is

r \propto \frac{n ^{2}}{Z}

, which combine to

r \propto \frac{n}{v}

. Equal radii therefore require

\frac{n _{1}}{v _{1}} = \frac{n _{2}}{v _{2}}

, so

\frac{n _{1}}{n _{2}} = \frac{v _{1}}{v _{2}} = \frac{3 \times 1 0 ^{5}}{2.5 \times 1 0 ^{5}} = \frac{6}{5}

. The possible orders of the energy states are

6

and

5

respectively.

JEE Main · 2026 · 24 Jan 2026 · Shift 1 · Single correct option

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