The wave function gives three quantum numbers:
n, l, and ml

Where n and l decides the Energy of an atom

Principal Quantum Number (n):
The HIGHER the n-value the further away it is from the nucleus, so it’s easier for it to leave
As the n-value goes to “infinity” then the energy level is 0, which means it’s FREE
The n-value of 1 is the ground state.

Orbital Angular Momentum Quantum Number (l):
Related to the shape AKA sub-shells where the electron is
L = 0, 1, 2, 3 … n-1
There are n different values of l

S-shape: Sphere
P-shape: Two lobes separated by an angular node
D-shape: Four lobes separated by two angular nodes
F-shape: Six lobes separated by three angular nodes

The number of electrons: is simply just the number of possible orbitals AKA ms values multiplied by 2.

Magnetic Quantum Number (ml):
The description of the shape, like orientation
Range = -l to +l
There are 2*l + 1 ml values

Electron Spin (ms):
Two electrons can have the same n, l, ml, but different spins.
Either 0.5 or -0.5

Pauli Exclusion Principle:
There can not be more than two electrons in a given orbital, they have different spins.

Hund’s Rule:
As electrons are added to an atom, they go to each orbital alone, and then when each orbital has ONE electron, then electrons are added randomly to the orbitals to make them “full”.
ALSO, the first electron will always be +0.5 spin.
It’s because electrons don’t want to share orbitals, so they look for empty orbitals.
Kinda like the Kalaha game.

Chart of possible Atomic Orbitals up to n=6: