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(B) According to the Bohr quantization condition,the angular momentum is given by $mvr = \frac{nh}{2\pi}$.For a particle of mass $m$ and charge $q$ mo

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$n \left( \frac{hqB}{4\pi m} \right)$

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(B) According to the Bohr quantization condition,the angular momentum is given by $mvr = \frac{nh}{2\pi}$.For a particle of mass $m$ and charge $q$ moving in a circular path in a magnetic field $B$,the magnetic force provides the centripetal force: $qvB = \frac{mv^2}{r}$,which implies $r = \frac{mv}{qB}$.Substituting the expression for $r$ into the angular momentum equation: $mv \left( \frac{mv}{qB} \right) = \frac{nh}{2\pi}$.This simplifies to $\frac{m^2v^2}{qB} = \frac{nh}{2\pi}$,or $mv^2 = \frac{nhqB}{2\pi m}$.The kinetic energy $E$ of the particle is given by $E = \frac{1}{2}mv^2$.Substituting the value of $mv^2$,we get $E = \frac{1}{2} \left( \frac{nhqB}{2\pi m} \right) = \frac{nhqB}{4\pi m}$.

If one were to apply the Bohr model to a particle of mass $m$ and charge $q$ moving in a plane under the influence of a magnetic field $B$,the energy of the charged particle in the $n^{th}$ level will be:

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