If hydrogen atom in ground state is passed-through an inhomogeneous magnetic field, the beam splits in two parts. This interaction with magnetic field shows: (a) existence of ortho and para hydrogen (b) existence of magnetic moment associated with orbital motion of electron (c) existence of spin magnetic moment of electron (d) existence of magnetic moment of proton

The concept of quantization of angular momentum is a cornerstone in quantum mechanics, providing us with a fundamental understanding of how microscopic particles such as electrons behave. Unlike classical angular momentum, which can take on any value, the angular momentum of electrons is quantized. This means it can only have specific, discrete values.

Imagine angular momentum as a series of steps rather than a smooth ramp; electrons can only 'step' on these fixed levels and not in between. This quantization principle was observed in the Stern-Gerlach experiment when a beam of silver atoms was passed through an inhomogeneous magnetic field and split into discrete beams at determined angles. This deflection was the first direct proof of quantized angular momentum, leading to the understanding that such quantization is an intrinsic property of all particles with angular momentum.

In quantum mechanics, angular momentum is related to the wave function of a particle and comes with associated quantum numbers. For electrons, these numbers correspond to their orbital motion around the nucleus and their intrinsic spin, with each allowed state of angular momentum resulting in distinct energy levels.

Electron spin is a fundamental concept describing the intrinsic angular momentum possessed by electrons. It is a quantum property, meaning it cannot be understood by classical physics, and it's what causes electrons to behave like tiny magnets. Spin is what the Stern-Gerlach experiment revealed when it demonstrated the splitting of a hydrogen atom's beam.

The discovery of the electron spin filled a gap in the explanation of the periodic table's structure and the fine details in the spectra of atoms. In essence, spin can be thought of as a 'twirl' of the electron around its own axis, with two possible orientations: spin-up and spin-down. These orientations, under the influence of a magnetic field, will deflect in opposite directions due to the forces acting on their magnetic moments. It's this property that polarizes a beam of atoms or electrons into distinct paths when they pass through a magnet, much like in the Stern-Gerlach experiment with hydrogen atoms.

A magnetic moment is a vector quantity that represents the strength and direction of an object's magnetism. In the context of subatomic particles like electrons, the magnetic moment is closely linked to spin and orbital angular momentum. The electron's magnetic moment is particularly significant because it's directly related to the peculiar property of electron spin.

When placed in an external magnetic field, the electron's magnetic moment will experience a torque, causing the electron to align itself with or against the field's direction. This behavior forms the basis for the splitting observed in the Stern-Gerlach experiment. The inhomogeneous magnetic field applied in the experiment interacts with the magnetic moment associated with the electrons' spin, resulting in a force that causes the observed separation of the hydrogen atoms' beam. As such, the magnetic moment is a fundamental aspect that enables us to understand and predict the behavior of atoms and molecules in magnetic fields, leading to technologies like MRI machines and other applications in the field of spectroscopy and materials science.