Quantum Numbers Question

[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!

[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.

[Lauren Tindall]

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

[Mai V 4L]

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

[Melanie Lin 3E]

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!