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JEE Main 2026 (24 Jan, Shift 1) · Bohr Model: Orbits, Speed & Angular Momentum

Bohr Model: Orbits, Speed & Angular Momentum question from JEE Main 2026 (24 Jan, Shift 1)

Q18JEE Main 2026 · 24 JAN · SHIFT 1Medium

Bohr Model: Orbits, Speed & Angular Momentum

Two electrons are moving in orbits of two hydrogen like atoms with speeds 3×105 m/s3 \times 10^{5}\text{ m/s} and 2.5×105 m/s2.5 \times 10^{5}\text{ m/s} respectively. If the radii of these orbits are nearly same then the possible order of energy states are ______ respectively.

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Answer: (d)

  1. r∝n2Zr \propto \frac{n^2}{Z} and v∝Znv \propto \frac{Z}{n}.
  2. From rr: Z∝n2rZ \propto n^2 r, so v∝n2rn=nrv \propto \frac{n^2 r}{n} = nr; with equal rr, v∝nv \propto n.
  3. n1n2=3×1052.5×105=65\frac{n_1}{n_2} = \frac{3\times10^5}{2.5\times10^5} = \frac{6}{5}
  4. So the answer is (d) 6 and 5.
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