# What do the four quantum numbers stand for?

Jul 28, 2017

Principal quantum number ($n$) - the energy the electron occupies, where $n \ge 1 , \mathmr{and} n \in \mathbb{Z}$.

Angular momentum quantum number (ℓ) - This describes the type of orbitals the electron resides in, where ℓge0, ℓinZZ, and ℓltn. It also gives the number of angular nodes, and therefore describe its shape.

If ℓ=0 it is the s-orbital, if it is 1 then it is the p-orbital, 2 means d-orbital, etc. This number is often pair with n, so that if n=4, and ℓ=2, it is in the 4d subshell.

Magnetic quantum number (m_ℓ) - describes the orientation of the orbital, where m_ℓ can be anywhere from -ℓ to +ℓ, and m_ℓinZZ

There are $2 l + 1$ orbitals per subshell. This is proven as if ℓ=1, then $2 \left(1\right) + 1 = 3$, there are three orbitals for the p subshell. If ℓ=2, then m_ℓ =-2, -1, 0, 1, 2, 5 orbitals for d-subshells.

Spin quantum number (${m}_{s}$) - describes the spin of an electron where ${m}_{s} = - \frac{1}{2} \mathmr{and} + \frac{1}{2}$, where $- \frac{1}{2}$ means spin down, and $+ \frac{1}{2}$ means spin up.