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### Number of Electrons per Shell

Posted: **Fri Oct 30, 2020 12:00 pm**

by **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.

### Re: Number of Electrons per Shell

Posted: **Fri Oct 30, 2020 12:18 pm**

by **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.

### Re: Number of Electrons per Shell

Posted: **Fri Oct 30, 2020 7:21 pm**

by **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.

### Re: Number of Electrons per Shell

Posted: **Fri Oct 30, 2020 10:43 pm**

by **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.

### Re: Number of Electrons per Shell

Posted: **Sun Nov 01, 2020 4:14 pm**

by **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!

### Re: Number of Electrons per Shell

Posted: **Sun Nov 01, 2020 4:46 pm**

by **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.