If one were to apply the Bohr model to a particle of mass ' m ' and charge ' q ' moving in a plane under the…

1. $n\left(\frac{hqB}{\pi m}\right)$
2. $n\left(\frac{hqB}{4\pi m}\right)$
3. $n\left(\frac{hqB}{2\pi m}\right)$
4. $n\left(\frac{hqB}{8\pi m}\right)$

Solution

For a charge $q$ moving in a uniform magnetic field $B$




$f_m=\frac{m{v}^2}{R}$

$qVB= \frac{m{v}^2}{R}$

$\Rightarrow m{v}^2=qVBR$

$\Rightarrow \frac{1}{2} m{v}^2=\frac{qVBR}{2}$

$\Rightarrow Energy=\frac{qVBR}{2} \left(1\right)$

By Bohr's quantization condition, 

Angular momentum $L=n\frac{h}{2\pi }$

$\Rightarrow mvR=\frac{nh}{2\pi }$

$\Rightarrow vR=\frac{nh}{2\pi m} \left(2\right)$

Put $\left(2\right)$ in $\left(1\right)$

$\Rightarrow Energy=\frac{qB}{2} \left(\frac{nh}{2 \pi m}\right)$

$= \frac{qB nh}{4 \pi m}$

Asked in: JEE Main 2015 (10 Apr Online)

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