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MHT CET 2019 (2 May, Shift 1) · Bohr Model: Orbits, Speed & Angular Momentum

Bohr Model: Orbits, Speed & Angular Momentum question from MHT CET 2019 (2 May, Shift 1)

Q104MHT CET 2019 · 2 MAY · SHIFT 1Difficult

Bohr Model: Orbits, Speed & Angular Momentum

Bohr model is applied to a particle of mass ' $m$ ' and charge ' $q$ ' is moving in a plane under the influence of a transverse magnetic field ' $B$ '. The energy of the charged particle in the $n$ th level will be ( $h =$ Planck's constant)

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Answer: (c)

$qvB = \frac{mv^2}{r} \Rightarrow r = \frac{mv}{qB}$ .
Bohr condition: $mvr = \frac{m^2 v^2}{qB} = \frac{nh}{2\pi} \Rightarrow v^2 = \frac{nhqB}{2\pi m^2}$ .
Energy is only kinetic: $E = \frac{1}{2}mv^2 = \frac{nhqB}{4\pi m}$
So the answer is (c) $nhqB/4\pi m$ .

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