Question

What do the four quantum numbers stand for?

Answer 1

Principal quantum number (`n`) - the energy the electron occupies, where `nge1, and ninZZ`.

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 `2l+1` orbitals per subshell. This is proven as if `ℓ=1`, then `2(1)+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 = -1/2 or +1/2`, where `-1/2` means spin down, and `+1/2` means spin up.