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MHT CET 2023 (14 May, Shift 1) · Bohr Model: Orbits, Speed & Angular Momentum

Bohr Model: Orbits, Speed & Angular Momentum question from MHT CET 2023 (14 May, Shift 1)

Q66MHT CET 2023 · 14 MAY · SHIFT 1Easy

Bohr Model: Orbits, Speed & Angular Momentum

Magnetic field at the centre of the hydrogen atom due to motion of electron in $n$ th orbit is proportional to

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Answer: (d)

$B = \frac{\mu_0 I}{2r}$ , with $I = \frac{ev}{2\pi r}$ .
$v \propto n^{-1}$ , $r \propto n^2$ , so $I \propto n^{-3}$ .
$B \propto \frac{n^{-3}}{n^2} = n^{-5}$
So the answer is (d) $n^{-5}$ .

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