Orbital angular momentum of free electrons

Imagine you have a toy car that can spin around in a circle as it rolls forward. This spinning motion is called "angular momentum". Now, imagine instead of a toy car, we have a tiny particle called an electron. This electron can also spin around as it moves, just like the toy car. But because it's so small, we need a different way to describe its motion. That's where "orbital" comes in.

Orbital angular momentum is a fancy way of saying how much the electron is spinning around its center as it moves through space. Imagine the electron is like a bee buzzing around a flower. The bee can fly in circles around the flower, or it can zip in and out at different angles. The electron can do the same thing, but since it's moving incredibly fast and is much smaller than a bee, it's hard to see exactly what's going on. Scientists use advanced equations and calculations to figure out the precise amount of angular momentum the electron has based on its behavior.

This orbital angular momentum is important because it determines how the electron interacts with other particles and fields around it. It can affect how the electron is affected by a magnetic field, for example, or how it interacts with other atoms in a material. So, even though it might seem like a small and simple thing, understanding the orbital angular momentum of electrons is crucial to understanding the behavior of matter on a very small scale.