## Quantum Numbers

Emma Healy 2J
Posts: 75
Joined: Wed Sep 30, 2020 9:45 pm

### Quantum Numbers

Can the first 3 quantum numbers be the same?

Christine Ma 3L
Posts: 61
Joined: Wed Sep 30, 2020 9:35 pm

### Re: Quantum Numbers

If by first 3 you mean n, l, and ml, then no, it's not possible for all three to be the same at the same time. l will always be less than or equal to n-1 but it is possible for l and ml to be the same number. Hope this helps!
Last edited by Christine Ma 3L on Tue Oct 27, 2020 11:59 pm, edited 1 time in total.

Yuelai Feng 3E
Posts: 61
Joined: Wed Sep 30, 2020 10:09 pm
Been upvoted: 2 times

### Re: Quantum Numbers

Hi! I don't think they can all be the same because the acceptable numerical values for each is different. For example, 'n' should be a natural number like 1, 2, 3, 4 ...; 'l' should be a non-negative integer from zero to (n-1); and 'ml' should be an integer from -l to l. So n and l can never be the same because l must be smaller than n, while l and ml might be equal.
But even if they have the same numerical value, their physical meaning is completely different. n indicates the energy and size, l indicates the angular momentum, and ml indicates the orientation of the electron.
Hope it helps! :)

BrittneyMyint2C
Posts: 77
Joined: Wed Sep 30, 2020 9:59 pm
Been upvoted: 2 times

### Re: Quantum Numbers

Hi, I'm a bit confused on the wording of the question, but I'll try answering from both of my interpretations:

If you mean "can the quantum numbers could be the same, like n =1, l = 1, ml = 1", then no, the first three quantum numbers cannot be the same since the allowed values of l is found from n-1. l and ml could be the same though.

If you mean "can the first three quantum numbers be the same between electrons", then yes. For example, two electrons in the 5s state of an atom could both have the quantum numbers n=5, l=0, and ml=0; but note that ms would not be the same if these electrons are in the same atom, since one would spin up and the other would spin down.

Hope this makes sense!