CHEMISTRY COMMUNITY

Can someone please explain the differences between n, l, and m conceptually?

Also, how do you translate it to each other (like finding how many subshells are in a given n or how many orbitals are in subshells with l equal to a certain number)?

"n" is the principal quantum number, which defines the size and energy of the orbital. "l" indicates the orbital's shape (s, p, d, or f) or its angular momentum (how 'fast' the electron moves around the nucleus). "m" tells us the electron's orientation in the orbital.

When n has a given value, l can have any value from 0 to n-1 and m can have the values l, l-1, ... -l.

n, l, and m are all quantum numbers

n = principle quantum number
- it measures energy and size of an orbital, also called the "shell"
- it has values of integers (0,1,2,3,4...)

l = angular momentum quantum number
- it measures shape of an orbital, called "subshell"
- it has values of (0,1,2,...n-1)

m = magnetic quantum number
- it measures orientation of an orbital; different orbitals of a subshell
- it has values of (l, l-1, l-2,... -l)

n is the principal quantum number, which describes the electron's energy and size (which shell it's in). l is the Angular Momentum Quantum number, which describes the shape of the orbital of the electron. In this class, we will likely only see l = 0 (s-orbital), 1 (p-orbital), 2 (d-orbital), or 3 (f-orbital). l is also called the subshell and is dependent on n. m is the magnetic quantum number. This labels different orbitals of a subshell. In other words, it is the electron's orientation.