Question

Show that the ratio of the magnetic dipole moment to the angular momentum (l = mvr) is a universal constant for hydrogen-like atoms and ions. Find its value.

Answer 1

The value is found to be $\frac{e}{2m}$

Explanation:

Let us consider that the velocity of electron is ‘v’. We know that the electrons revolve around the orbit and its radius is denoted as radius ‘r’. The mass of the electron can be denoted as ‘m’ and the charge of the electron can be denoted as ‘e’.

Magnetic dipole moment,  $\mu = IA$

                                                 $=\left ( \frac{e}{T} \right )\cdot \pi r^{2}= \frac{e}{\left ( \frac{2\pi r}{v} \right )}\cdot \pi r^{2} = \frac{evr}{2}$

Now, the electron’s momentum is calculated as L = mvr.

Therefore,

                  $\frac{\mu}{L} = \frac{ evr}{2.mvr}$

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

Answer 2

Answer:

Above answer is correct ..........