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Electrons have a few handfuls of properties. Four have been selected as the electron’s “quantum numbers.” The quantum numbers are inputs to two key parts of quantum mechanics: Schrodinger’s Equation and the Pauli Exclusion Principle.

Originally, there were three quantum numbers, the ones needed for the calculation of the key equation of quantum physics, Schrodinger’s Equation. The original three quantum numbers describe properties of the electron cloud (orbital).

Later, a fourth quantum number was added, the measurement of spin. All four quantum numbers are required when applying another important part of quantum physics, the Pauli Exclusion Principle.

## The Four Quantum Numbers

• Principle Quantum Number (symbol: n) – the size of the electron orbital. This is the same as the energy level of the electron. The bigger the orbital, the greater the distance of the electron from the atomic nucleus1. Also, the greater the energy level.
• Angular Quantum Number (symbol: l –cursive ell) – the shape of the electron orbital. Orbitals may be shaped like a sphere, a dumbbell, or a cloverleaf. With more electrons, even more complex shapes are assumed. The Angular Quantum Number is also called the “Azimuthal Quantum Number.”
• Magnetic Quantum Number (symbol: m) – the orientation in space of the electron orbital. A spherical orbital has only one orientation in space. But others, such as a dumbbell-shaped orbital, may have more than one orientation. The Magnetic Quantum Number is not the strength of the electron’s magnetic field. The name of this property derives from the way in which it was discovered. It was first observed when the electron was in the presence of a magnetic field.
• Spin Quantum Number (symbol: s) — This is the up/down or right/left spin of the electron2. It is responsible for the electron having a magnetic north pole at one end and a magnetic south pole at the other. Originally, it was thought that electrons spin on their axes like a toy top, thus the name “spin.” However, physicists soon realized that while spin is some kind of rotational motion, the electron is not simply spinning on its axis. The exact physical nature of spin is unknown to this day (2017). Spin is also called “intrinsic spin,” “inherent angular momentum,” and “intrinsic angular momentum.”

Footnotes

 1 This is an loose manner of describing the location of the electron. A good metaphor for electrons prior to measurement is “electron cloud.” They do not have a specific location until detected. It would be more accurate to speak of the distance from the nucleus at which the electron is likely to be detected. 2 The image that illustrates spin should be seen as metaphorical rather than technically accurate. When physicists develop a more accurate visualization, I’ll be happy to provide an image of it!
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