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JEE Main 2019 (12 Jan, Shift 1) · Bohr Model: Orbits, Speed & Angular Momentum

Bohr Model: Orbits, Speed & Angular Momentum question from JEE Main 2019 (12 Jan, Shift 1)

Q105JEE Main 2019 · 12 JAN · SHIFT 1Difficult

Bohr Model: Orbits, Speed & Angular Momentum

A particle of mass m moves in a circular orbit in a central potential field U(r) = $\frac{1}{2}$ kr2. If Bohr 's quantization conditions are applied, radii of possible orbitls and energy levels vary with quantum number n as:

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Answer: (a)

$F = kr = \frac{mv^2}{r} \Rightarrow v = r\sqrt{k/m}$ .
Bohr condition: $mvr = \sqrt{mk}\, r^2 = \frac{nh}{2\pi} \Rightarrow r_n \propto \sqrt{n}$ .
$E = \frac{1}{2}mv^2 + \frac{1}{2}kr^2 = kr^2 \propto n$
So the answer is (a) $r_n \propto \sqrt{n}$ , $E_n \propto n$ .

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