I start it with a simple example of a classroom. As you know, in the classroom when there is no teacher students sit in random directions. While the teacher enters the classroom all the students get aligned towards the teacher. The orientation of students because of the teacher, this is equivalent to the external magnetic field source. Here, students are like the atomic dipole moment.

Atomic Dipole Moment

The same thing happens in the magnetic materials when placed in an external magnetic field, they get magnetized. You may have used many times this concept of the magnetization. Magnetization is a process in which the orientation of atomic dipole moments aligns in the applied magnetic field direction. So, to understand the magnetization atomic dipole moment is the key concept and on its basis, you can understand the magnetic properties like paramagnetism, diamagnetism, and ferromagnetism. Also, how it can store the data in a hard disk.

Let’s start the concept of the atomic dipole moment. Suppose, we consider an orbit of the electron, in which the electron is revolving around the nucleus. The charge of the electron is ‘e’, mass ‘m’, liner velocity’v’ and radius is ‘r’.

Atom Equivalence to Bar Magnet:

In this picture, you can see that in part (a) electron is revolving around the nucleus. As you know that the rate of charge is current so this electron motion is considered equivalent to the current loop in the second part (b). Further, when the current flow in a conductor you know it produces the magnetic field. Same here the current loop produces the magnetic field, the direction of the magnetic field you can judge by the right-hand thumb rule.

Here, the direction of the current is anti-clockwise so the magnetic field starts from the upper surface and enters into the lower plane of the loop. It means the upper plane of the loop will behave like the North pole, obviously lower plane will behave as a  South pole. So, in the third part, you can see a tiny bar magnet equivalent to the atom having one electron in orbit. This is the point of discussion.

$\fn_jvn&space;\large&space;\vec{\mu}=I\vec{A}&space;\newline&space;\mu=IA&space;\\&space;I=-\frac{q}{T}\\&space;q=e;T=\frac{2\pi&space;r}{v}$

By substituting the values of I and A,

$\fn_jvn&space;\large&space;\mu&space;_{l}=IA=\left&space;(&space;\frac{-ev}{2&space;\pi&space;r}&space;\right&space;)\pi&space;r^{2}&space;=-\frac{evr}{2}\times&space;\frac{m}{m}&space;\hat{n}\\&space;\mu_{l}=-\frac{e}{2m}\vec{L}&space;\left&space;[&space;\vec{L}=\vec{r}\times\vec{p}&space;\right&space;]$

This orbital angular momentum is quantized, so

$\fn_jvn&space;\large&space;\vec{L}=mvr\hat{n}\\&space;L={\hbar}\sqrt{l\left&space;(&space;l+1&space;\right&space;)}\\&space;\mu_{l}=-\frac{e{\hbar}}{2m}\sqrt{l\left&space;(&space;l+1&space;\right&space;)}\\&space;\mu_{B}=\frac{e{\hbar}}{2m}=4.94\times10^{-27}A/m^{2}\\&space;\mu_{l}=-\mu_{B}\sqrt{l\left&space;(&space;l+1&space;\right&space;)}\\&space;similarly\\&space;\mu_{s}=-\mu_{B}\sqrt{s(s+1)}\\&space;\mu=\mu_{l}+\mu_{s}$

Where μ is the total magnetic moment, a sum of orbital and spin angular momentums.

Book Suggested

This book is useful for those who are interested to know more about the physical concept related to the atom, molecule, and nucleus. If you are a M.Sc. Students or preparing for the NET or any research fellowship you will need this book. It is useful for all the students of Physics and Chemistry.

Discussion:

1. The magnetic dipole moment is due to the single electron, two electrons in the same orbital will have zero magnetic moment. Because of the opposite spin.
2. The atom has one electron in the outer most orbit (like Na) when placed in an external magnetic field the torque acting on it and try to align in the field direction.
3. This work was done by the field on the dipole, stored as a potential energy ina magnetic dipole. Hence the total energy of the electron in the particular orbit changes.
4. This change in energy can be seen by the emission of radiation from this atom.
5. This type of concept we use to explain the Zeeman effect.