Irregular Webcomic! #1525

The Pauli exclusion principle is a fundamental law of quantum physics, formulated by Austrian physicist Wolfgang Pauli in 1924.

I've mentioned this before, in the annotation to strip #341 and, like there, I'm daunted by the idea of trying to explain this in layman's terms. The problem is that the Pauli exclusion principle requires an understanding of several underlying layers of quantum physics before you can fully appreciate it. But never let it be said that I didn't try...

Quantum mechanics is based on the observation that at the smallest scales of interaction, matter and energy behave in a quantised manner - that is, certain fundamental quantities such as the energy and momentum of subatomic particles do not vary in a continuous way, but can only exist at specific discrete values. This is the difference between being able to have $1.37 worth of potato chips, or $2.54 worth, or $3.97 worth, or whatever amount you want; and being restricted to only being allowed to have exactly $1, or exactly $2 worth, or exactly $3 worth, but none of the values in between.

It's the same thing with subatomic particle energies (only less fattening). For example, an electron attached to a proton in the configuration we know as a hydrogen atom may only have certain orbital energy levels, given by the equation

energy = -13.6 eV / n²

where "eV" stands for electron-volts, a convenient unit of energy when discussing subatomic particles, and n is an integer. The energy is negative by convention, because an electron bound to a proton in a hydrogen atom has less energy than a free electron able to move around by itself, which is defined as having zero energy. Anyway, the important thing is that the electron in the hydrogen atom may only have an energy of either -13.6 eV, or -3.4 eV, or -1.51 eV, and so on, taking higher numbers for n. The electron can never have energy of -10.3 eV, or -7.8 eV, etc. (The numbers here are approximate, and I have simplified things slightly, but the general gist is correct.)

The number n in the above equation is known as a quantum number (which Wikipedia article, by the way, I originally created, in March, 2004). It is the most important of several quantum numbers governing the structure of atoms, and is called the principal quantum number.

Now, electrons also have a quantum number of their very own, called spin, which may have either of two values: +1/2 or -1/2. Different subatomic particles have different allowable values for their spin quantum numbers, but the allowed values always vary by 1. Some particles can have spin of +1/2 and -1/2, some can have values +3/2, +1/2, -1/2, -3/2 - such particles are known collectively as fermions. There are other particles which have spins of 0; or of +1, 0, or -1; or of +2, +1, 0, -1, or -2 - such particles are collectively known as bosons.

Fermions obey the Pauli exclusion principle, which states simply that "no two fermions may share the same set of quantum numbers". What does this mean for an atom? Atoms larger than hydrogen can collect more than one electron. The first electron goes into the n=1 energy quantum state. Where does the second electron go? Well, remember the electrons also have a spin quantum number, and Pauli's principle applies to their entire sets of quantum numbers. So the second electron can also have n=1 as long as it has a spin quantum number different to the first electron. So the first two electrons in an atom have quantum numbers of (n=1, spin=+1/2) and (n=1, spin=-1/2). If we put a third electron in, there is nowhere for it to go at the lowest energy level, so it has to go in at n=2. It gets a little more complicated from there, because there are actually more quantum numbers than the two I've mentioned, but the basic idea is the same, and what I've said for the first few electrons is essentially true.

So that's what happens with fermions. Bosons, however, do not obey Pauli's exclusion principle! They can stack up as many as they like with the same quantum numbers, and they don't care. All the familiar particles we learn about in high school are fermions, by the way: electrons, protons, and neutrons. Bosons tend to be weirder things that we don't meet until university level physics, except for one: the photon. Photons, particles that are packets of light energy, are the best known bosons. They have quantum numbers just like electrons, but they don't really care about them, and they clump together in huge bunches that lets us do stuff like make television screens, and lasers, and see with our eyes. (In fact, we couldn't make lasers if photons weren't bosons.)

So there you go. Two electrons can happily share the same principal quantum number, but not a third. It's a bit like a park bench, that way.

2017-02-11 Rerun commentary: In hindsight that potato chip value example isn't the best, since although dollars can be subdivided, they are still generally quantised at the cent level. It would be better expressed as:

This is the difference between being able to have 1.37261 kilos of potato chips, or 2.549 kilos, or π+0.38 kilos, or whatever amount you want; and being restricted to only being allowed to have exactly 1 kilo, or exactly 2 kilos, or exactly 3 kilos, but none of the amounts in between.

Honestly, I have no idea what I was thinking when I wrote that example with money.