Physics - Modern Physics Question with Solution | TestHub

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$\left(1\right)$

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

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