Physics - Modern Physics Question with Solution | TestHub

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

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

$q\mathrm{V}B=\frac{m{v}^2}{R}$

$\Rightarrow m{v}^2=q\mathrm{V}BR$

$\Rightarrow \frac{1}{2}m{v}^2=\frac{q\mathrm{V}BR}{2}$

$\Rightarrow Energy=\frac{q\mathrm{V}BR}{2}(1)$By Bohr's quantization condition,

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

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

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

Put $(2)$ in $(1)$

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

$=\frac{qBnh}{4\pi m}$