## 1D.23 on Homework

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Breanna Ouyang 1C
Posts: 42
Joined: Wed Sep 30, 2020 9:48 pm

### 1D.23 on Homework

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?

Arielle Sass 1L
Posts: 41
Joined: Wed Sep 30, 2020 9:43 pm

### Re: 1D.23 on Homework

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 ml, which can have any value from negative l to positive l (for example, if l=3, then ml can be -3, -2, -1, 0, 1, 2, 3.) Notice that when l=3, ml can have 7 different values. If l=2, ml can have 5 different values, if l=1 ml can have 3 values, and if l=0 ml 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 ml can be anything from -l to +l, then ml can either by -1, 0, or 1. So those three possibilities for what ml are the three orbitals in n=2 and l=1.

Hopefully this helps you understand it!

Jay Solanki 3E
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Joined: Wed Sep 30, 2020 9:59 pm
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### Re: 1D.23 on Homework

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!

Sophia Wendin 2B
Posts: 40
Joined: Wed Sep 30, 2020 9:48 pm

### Re: 1D.23 on Homework

- 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!

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