Number of Electrons per Shell

[Raashi Chaudhari 3B]

During today's lecture (10/30) Dr. Lavelle mentioned that there is a mathematical way to determine the number of electrons per shell. Would someone mind explaining this to me? I don't know how to determine the number of electrons in a shell when it only gives the quantum number n.

[Kyle Walsh 2J]

Hi! I believe that in the lecture Dr. Lavelle was referring to using the electron configurations, which are just numbers we have to memorize. s shells take 2 electrons, p shells take 6 electrons, d shells take 10 electrons, and f shells take 14 electrons. I don't believe you can determine the exact electrons just from n.

[Juliet Carr 1F]

I have not watched the lecture yet so I'm not completely sure what he's referring to but in general there is a formula 2n^2, where n is the principal quantum level/shell, and this formula gives the maximum amount of electrons that can occupy each shell.

[Vince Li 2A]

Yes, Kyle is right. The s orbital carries at most 2 electrons, the p orbital carries at most 6 electrons, due to how there is the Px, Py, and Pz, three orientations for the energy level (two electrons per orientation you could say), and the d orbital carries 10 electrons, because there are 5 orientations that can have two electrons in each of them, as said by I think Pauli.

[RitaThomas_3G]

I also looked a bit more into this after he said it and I believe the equation is 2(n^2), where n is the shell (principle quantum number). We can see that this equation does work in the following examples:

n = 1, 2 electrons
- 2(1^2) = 2 electrons

n = 2, 8 electrons
- 2(2^2) = 8 electrons

The equation also works for the other principle quantum numbers as well!

[Rohit Srinivas 2D]

You can calculate it by understanding the ml quantum number. this tells you how many orbitals are available, each orbital has 2 so it would be ml options *2. If we look at the shells we know so far:
s has only 0 as ml so 1*2=2
p has -1,0,1 as ml so 3*2=6
d has -2,-1,0,1,2 so 5*2=10
f has -3,-2,-1,0,1,2,3 so 7*2=14
every shell essentially adds two shells and u multiply shells by 2 to get electrons

So a hypothetical "g" shell would be
-4,-3,-2,-1,0,1,2,3,4 or 9*2= 18 electrons.