SOME COMMON RULES

Pauli Exclusion Principle

So, according to these rules, if we look at the first shell, it only contains two electrons in the first subshell. The quantum number can be described as 1s^2. However, another rule is that two electrons cannot have identical quantum numbers. So if two electrons have to fit inside one s subshell, how will this work?

This matter directly relates to the Pauli Exclusion Principle, which states that two electrons cannot exist in the same location, and thus electrons in the same orbital must have opposing spins. Hydrogen only has one electron in the 1s orbital and has a quantum number of 1s^1. Helium has two electrons in this field, so they must have opposing spins, and it has a quantum number of 1s^2.

This spin factor is the fourth quantum number, m, and is described as either +1/2 for a spin 'up' or -1/2 for a spin 'down'.

Hund's Rule

So now that we've reviewed the orbital structure, let's dive in to how the electrons fill these orbitals. Because electrons are both negatively charged, there is a certain amount of repulsion that prevents them from wanting to fill the same space. So according to Hund's Rule, electrons will fall into empty orbitals of the same energy before electrons begin to pair up into the same orbital.

Aufbau Principle

Closely related to Hund's Rule is the Aufbau Principle, which states that electrons will fill the lower energy levels before moving to higher energy orbitals. Remember that each orbital has two electrons and the number of orbitals at an energy level depends on the first two quantum number.