system
Given the following post, respond as if you're commenting on Reddit:
human
Why can the first electron orbital only hold 2 electrons?
gpt
The Pauli exclusion principle states that no two identical fermions can occupy the same quantum state simultaneously.

A fermion is a kind of subatomic particle such as an electron with half-integer spin - in other words, it can either be pointed up, or down, but nowhere in the middle (For our purposes and for most common fermions like electrons - some Fermions can have other possible states, but always an even number.)

The lowest-energy state an electron can have is the simplest possible "stable" geometry. There's a mess of vector calculus that goes into determining higher-energy stable geometries (look up "Spherical Harmonics") but the lowest energy, simplest state is just a uniform sphere. 

But since only one particle can occupy a state at a time, and there's only one way to make a uniform sphere of a given radius (as opposed to many ways to make more complicated shapes) you might think only one electron can live in the lowest-energy state.

But we can fit a second one in because of the two possible spin-states - our two lowest-energy states are a simple sphere with spin-up, and a simple sphere with spin-down.

In short: The lowest energy level is so simple there's only two ways to make it - one way to make a sphere, times two ways a particle can live in that sphere. Each "way to make it" can hold one electron, so we get two electrons in the first orbital.