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(D) For a particle of mass '$m$' and charge '$q$' moving in a magnetic field '$B$',the cyclotron frequency is given by $\omega = qB/m$.According to th

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$nhqB/4\pi m$

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(D) For a particle of mass '$m$' and charge '$q$' moving in a magnetic field '$B$',the cyclotron frequency is given by $\omega = qB/m$.According to the Bohr quantization condition, the angular momentum is $L = n\hbar = nh/2\pi$.For a particle in a circular orbit, the energy is $E = (1/2)m v^2 = (1/2)m (r\omega)^2 = (1/2)m r^2 \omega^2$.Since $L = mvr = mr^2\omega$, we have $r^2 = L/(m\omega) = (nh/2\pi) / (m \cdot qB/m) = nh / (2\pi qB)$.Substituting $r^2$ and $\omega$ into the energy expression: $E = (1/2)m \cdot [nh / (2\pi qB)] \cdot (qB/m)^2$.$E = (1/2)m \cdot [nh / (2\pi qB)] \cdot (q^2 B^2 / m^2) = nhqB / (4\pi m)$.

Bohr model is applied to a particle of mass '$m$' and charge '$q$' 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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