What are Quantum Numbers?

James Doehring

In the prevailing theoretical model of the atom, there are four quantum numbers that describe the behavior of electrons. These include the principal, azimuthal, magnetic and spin quantum numbers. Together, these four numbers give the quantum state of an electron. A quantum state is the set of mathematical information required to fully describe a certain system of matter and energy, such as an atom. No two electrons can share the same four quantum numbers, according to the Pauli exclusion principle of quantum mechanics.

Scientist with beakers
Scientist with beakers

The first of the quantum numbers is called the principal quantum number. This number, which can be any positive integer beginning with 1, refers to the distance of an electron’s orbit from the atomic nucleus. Unlike planetary orbits, however, electrons are not free to orbit at any distance. Rather, they are confined to orbit at discrete energy levels, or quanta—a central tenet of quantum mechanics. Similar to planetary orbits, on the other hand, electrons orbiting further from the nucleus do possess higher kinetic energy.

The azimuthal quantum number signifies the angular momentum of an electron’s atomic orbital. This number tells something about the shape of an electron’s orbit around the nucleus. Electrons can orbit in more or less spherical swarms around the nucleus, or they can exhibit more complicated behavior. The idea of an electron as a solid particle orbiting the nucleus, however, is not correct. The uncertainty principle of quantum mechanics states that the position of an electron is fundamentally a matter of probability.

Building on the other quantum numbers, the magnetic quantum number tells something about the orientation of an electron’s orbital in space. This property was first discovered when scientists exposed gases to magnetic fields and then observed the way they interacted with light. The magnetic quantum number is also related to the energy levels of an atomic orbital.

Finally, the spin quantum number specifies one of two spin states of an electron. While the principal and azimuthal quantum numbers distinguish between different orbital positions of an electron, the spin quantum number can distinguish between two electrons in an otherwise identical quantum state. If two electrons in the same atom have the same three previous quantum numbers, their spin quantum numbers must be different. Electron spin is not exactly the same sense of “spin” that is commonly thought of, but it is one degree of freedom for an electron. It can take on one of two possible values: -1/2 or +1/2.

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Discussion Comments


@Charred - I wonder if there’s a software program that models the 4 quantum numbers and simulates the orbits and rotation of the electrons.

The end user would be able to change the numbers and see how the variables alter the behavior of the electrons.

I’m sure there’s probably something like that, as astronomy software does exist which does something comparable, and these electrons are operating in their own sort of mini universe.


@MrMoody - Yes, quantum mechanics is intriguing indeed.

It never occurred to me that atomic quantum numbers existed which defined the size, orientation and spin of electrons. It’s like these things are mini planets, orbiting within their own solar system with their revolutions and rotations just like regular planets do.

That’s absolutely fascinating. I’d also like to point out that, just as matter of general usage, people should stop using the term “a quantum leap.” Quantum doesn’t mean huge, it means little – very little in fact.


@SkyWhisperer - Like you, I know enough to be dangerous on these topics, and I’ve also gotten my information from shows on television, mainly public television.

The main thing I took away was that quantum mechanics completely upended Einstein’s view of the universe. Like you said, things behave differently, and it becomes difficult to reconcile the two concepts.

That's why it became impossible to create a "grand theory of the universe" which neatly explained how everything worked, at both the quantum and non-quantum level.


I am not a quantum physicist anymore than I am a rocket scientist, but like most people I’ve had a smidgeon of exposure to quantum mechanics from TV shows and some light reading. The basic stuff I’ve read talked about how that with quantum mechanics, physics behaves differently than with the non-quantum stuff.

Anyway, something interesting I’ve read once was that these electrons could behave differently depending on the circumstance. For example, when they do the laboratory experiments and “observe” the electrons, the very act of observing them makes their state change!

Also, pairs of electrons could be hooked up to other pairs of electrons, so that when the first pair changes orientation, the second pair changes too. It’s almost like synchronized swimming for electrons.

Like I said, I don’t know if I’ve expressed the concepts accurately, but weird stuff definitely does happen at the quantum level.

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