Question

discuss magnetic dipole moment of an electron revolving in an orbit in hydrogen atom and derive the expression for the ratio of the magnetic dipole moment and the angular momentum as gyro magnetic ratio for the revolving electron​

Answer 1

To find:

Gyromagnetic Ratio for an electron revolving in an orbit of an hydrogen atom?

Calculation:

The diamagnetic ratio is actually the ratio of magnetic dipole moment and the angular momentum of the electron revolving in the hydrogen orbit.

Let the ratio be denoted as r :

$\therefore \: r = \dfrac{M}{L}$

$\implies\: r = \dfrac{i \times area}{I \times \omega}$

$\implies\: r = \dfrac{( \frac{e}{t} ) \times area}{I \times \omega}$

$\implies\: r = \dfrac{ \bigg\{ \dfrac{e}{( \frac{2\pi r}{v} )} \bigg\}\times (\pi {R}^{2} )}{m {R}^{2} \times \dfrac{v}{R} }$

$\implies\: r = \dfrac{e}{2m}$

So, the gyromagnetic ratio comes as e/2m.