Page **1** of **1**

### 1D.23 on Homework

Posted: **Mon Oct 19, 2020 10:55 pm**

by **Breanna Ouyang 1I**

The question asks "How many orbitals can have the following quantum numbers in an atom: (a) n=2,l=1; (b) n=4,l=2,ml=−2; (c) n=2; (d) n=3,l=2,ml=+1?"

Can someone explain why the answers are 3, 1, 4, and 1, respectively?

### Re: 1D.23 on Homework

Posted: **Tue Oct 20, 2020 1:36 pm**

by **Arielle Sass 2A**

Hi! So these quantum numbers signify an orbital that an electron can be in. Each energy level, also called a "shell," has a certain amount of "subshells" and then within those subshells are individual orbitals. n is the symbol for the energy level or shell and it can have any value greater than zero. The next quantum number, l, can be any number from 0 to n-1, so there are n different possibilities for what l can be (for example, if n=4, then there can be four values of l:0,1,2, or 3. The next quantum number is m_{l}, which can have any value from negative l to positive l (for example, if l=3, then m_{l} can be -3, -2, -1, 0, 1, 2, 3.) Notice that when l=3, m_{l} can have 7 different values. If l=2, m_{l} can have 5 different values, if l=1 m_{l} can have 3 values, and if l=0 m_{l} can have 1 value.

So for the first example, n=2 and l=1, we already know the first two quantum numbers so we just have to find every possibility for what the third can be. Since l=1, and we know that the next quantum number m_{l} can be anything from -l to +l, then m_{l} can either by -1, 0, or 1. So those three possibilities for what m_{l} are the three orbitals in n=2 and l=1.

Hopefully this helps you understand it!

### Re: 1D.23 on Homework

Posted: **Tue Oct 20, 2020 1:38 pm**

by **Jay Solanki 3A**

Hello!

a) n=2 refers to the second energy level, and l=1 refers to the p orbital, and it is known that any p orbital has 3 orbitals.

b and d) Any time we are given an ml value, this refers to a single electron inside an orbital, so this will always be 1 (if I am not mistaken)

c)n=2 refers to the second energy level, which contains the 2s and 2p orbitals. S orbitals have 1 orbital and p orbitals have 3, so 1+3=4.

I know my terminology is not the best, but I hope this makes sense!

### Re: 1D.23 on Homework

Posted: **Tue Oct 20, 2020 1:52 pm**

by **Sophia Wendin 3L**

- For (a) n=2 and l=1 means we are looking at the 2p subshell. Since l=1, ml can be -1, 0, and 1, so the 2p subshell can have 3 orientations or 3 orbitals

- For (b) n=4 and l=2, which is the 4d subshell, and we are given ml = -2, so there is only 1 possible orientation, so 1 possible orbital.

- For (c), we only know the energy level, n=2, so it's all of the orbitals in n=2, so 1 orbital for 2s and 3 for 2p, which is 4 total.

- (d) is pretty much the same explanation as (b).

I don't think I explained this very well, but hopefully it helps a little bit!