When an electron revolves around the nucleus, then the ratio of magnetic moment to angular momentum is

• Correct answer
  A

  $\frac{\mathrm{e}}{2\mathrm{m}}$
• B

  $\frac{2\mathrm{e}}{\mathrm{m}}$
• C

  $\frac{\mathrm{e}}{\mathrm{m}}$
• D

  ${\left(\frac{\mathrm{e}}{\mathrm{m}}\right)}^2$

Solution

Angular momentum : $\mathrm{L}=\mathrm{n}\frac{\mathrm{h}}{2\mathrm{\pi }}=\mathrm{m}\mathrm{v}\mathrm{r}$

Magnetic moment : $\mathrm{\mu }=\mathrm{i}\mathrm{A}=\frac{\mathrm{e}}{2\mathrm{\pi }\mathrm{r}}\mathrm{v}\times \mathrm{\pi }{\mathrm{r}}^2$



$\mathrm{\mu }=\frac{\mathrm{e}\left(\mathrm{v}\mathrm{r}\right)}{2}$

$\mathrm{\mu }=\frac{\mathrm{e}}{2}\left(\frac{\mathrm{L}}{\mathrm{m}}\right)$

Ratio of magnetic moment to angular momentum

$\frac{\mathrm{\mu }}{\mathrm{L}}=\frac{\mathrm{e}}{2\mathrm{m}}$

Hence, the correct answer is option: 'A'.