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Quantum Numbers - Concept

Teacher/Instructor Kendal Orenstein
Kendal Orenstein

Rutger's University
M.Ed., Columbia Teachers College

Kendal founded an academic coaching company in Washington D.C. and teaches in local area schools. In her spare time she loves to explore new places.

All electrons have four quantum numbers which describe the location of electrons in the electron cloud of an atom. The principle quantum number (n) describes the size of the orbital the electron is in. The angular momentum quantum number (l) describes the shape of the orbital. The magnetic quantum number (ml) describes the orientation of the orbital in space while the electron spin number (ms) describes the direction that the electron spins on its own axis.

Alright so we're going to talk about quantum numbers. Quantum numbers are essentially electrons address. There are four numbers that actually dictate where exactly an electron is located, and remember Pauli Exclusion Principle states that no two electrons can have the same location. So they're all unique, each electron has its unique set of quantum numbers and there are four sets which are denoted like this.

Okay so let's dissect what each one is, alright first we have n, n is a principal energy level it cannot be zero and it goes from 1 all the way up to wherever infinity and they're whole numbers, they're integers. So that's the first one, the second one l, it denotes a sub level s, p, d or f. Okay so whenever we talk about s we're going to see 0, p is going to be 1, d is going to be 2 and f is going to be 3. So remember that if you have n equals 1 you're going to be able to have a p sublevel because when n equals 1 you only have s that's it. And if you have n equals 3 you're not going to have f sublevel. So you're going to use, your l is going to be less than or equal to n minus 1. So whatever your n is you can subtract 1 and then your l is going to be equal to or less than that value.

The m sub l is going to denote the orbital which orbital it falls into. For example if you have an s we only have one orbital so we only have one choice which is why we're going to make it zero. If you have p orbital you so you have 3 orbitals that could fall into. So we're going to denote the first one is negative 1, the second one is 0, the third one is positive 1.

This sublevel it goes from negative 2 all the way up to positive 2 denoting that there are five possible orbitals within the d sublevel and f goes from negative 3 to positive 3 denoting that there are 7. Easy way to remember this if you remember a sublevel the l for sublevel that can only expand the negative to the positive of that particular number.

And lastly we're going to go to the spin, remember that two electrons can fit in each orbital so we're going to go as positive or negative one half depending on which lecture we're talking about within that orbital. So let's do one for example, let's say we're talking about let's just pick this electron, okay alright so what we're going to say n equals 1 so we're going to say the first number is 1, the second it's in the s sublevel so we're going to say the notation for the s sublevel 0, so we're going to make it 0 which orbital is it in? Well s only has one orbital to chose from so it's also 0 and in this case it's going up so just arbitrarily so we're going to make it positive one half. If we're talking about this one the one next to it we'd make that a negative one half. Remember they're not going to be the same.

Let's pick another one, let's just do one last one, let's do this one, okay it's in the second of n equals 2, so we're going to say 2, it's in p so we're going to say that's a 1, it's in the negative 1 0, positive one location so we're going to say 1 and this one is going up also so we're going to say one half. And that is how you denote quantum numbers.