### Quantum Numbers Question

Posted: **Tue Nov 05, 2019 9:54 pm**

by **Bita Ghanei 1F**

Q: What is the maximum number of electrons that can occupy the orbitals with principle quantum number = 4?

A: 32

Can someone please explain why the answer is 32? Thanks!

### Re: Quantum Numbers Question

Posted: **Tue Nov 05, 2019 10:15 pm**

by **Sebastian Lee 1L**

Okay so if n=4:

l=0, 1, 2, 3

For l=0:

m_{l} = 0

For l=1:

m_{l} = -1, 0, 1

For l=2:

m_{l} = -2, -1, 0, 1, 2

For l=3:

m_{l} = -3, -2, -1, 0, 1, 2, 3

For each orbital there can be two electrons (one with spin up (m_{s} = +1/2) and one with spin down (m_{s} = -1/2)).

If we add up all the orbitals, there are 16. Since there can be up to two electrons per orbital, that equals 32 total possible electrons when n=4.

### Re: Quantum Numbers Question

Posted: **Tue Nov 05, 2019 10:17 pm**

by **Lauren Tindall**

The number of electrons that can occupy a given energy shell is given by the equation eā=2n^2. n represents the principal quantum number that describes the energy shell. We have n=4 which means that the number of eā is 2ā
4^2=32.

### Re: Quantum Numbers Question

Posted: **Sun Dec 08, 2019 9:20 am**

by **Mai V 4L**

Does anyone have a video they thinnk is a good reference for this topic?

### Re: Quantum Numbers Question

Posted: **Fri Oct 16, 2020 4:01 pm**

by **Melanie Lin 3E**

Mai V 4L wrote:Does anyone have a video they thinnk is a good reference for this topic?

Hey Mai! I was actually recommended this by my high school chemistry teacher but I think anyone should appreciate our Chemistry Jesus: [https://youtu.be/Aoi4j8es4gQ]. Feel free to check it out!