Sapling Question

[Inderpal Singh 2L]

How many electrons in an atom could have these sets of quantum numbers?
n=3
n=5,ℓ=0
n=6,ℓ=2,mℓ=−1

Can someone explain how this is done/how to start it? I am very confused about orbitals and quantum numbers at the moment.

[Arielle Sass 2A]

Hi!
So, whatever the value for n is, the value for ℓ can be anything from 0 up to n-1. mℓ can take on any value from -ℓ to +ℓ. And every set of three quantum numbers applies to two electrons (as in, every orbital mℓ holds 2 electrons).

For the first problem, n=3, ℓ can either be 0, 1, or 2. If ℓ is 0, then mℓ must be 0. If ℓ is 1, mℓ can be -1, 0, or 1. And if ℓ is 2, mℓ can be -2, -1, 0, 1, or 2. If you count up all these different possibilities for sets of three quantum numbers ((3, 0, 0), (3, 1, -1), (3, 1, 0), (3, 1, 1), (3, 2, -2), (3, 2, -1), (3, 2, 0), (3, 2, 1), (3, 2, 2)), you will find that there are 9 possible orbitals for n=3, and thus 18 electrons that could have n=3.

Applying the same rationale to the next problem, since ℓ=0, mℓ must be 0, so only 2 electrons can have those quantum numbers

And if n=6, ℓ=2, and mℓ=-1, we are already given a specific orbital, so there can only be 2 electrons with those quantum numbers.

[Stuti Pradhan 2J]

The main thing to remember here is that 4 quantum numbers specify a single electron. Therefore, n=6,ℓ=2,mℓ=−1, which has three quantum numbers and simply does not include the magnetic spin quantum number is referring to two electrons that are in the sixth shell in the d orbital. The mℓ number tells you what the orientation of the orbitals are. Since ℓ=2, there are 5 options for mℓ, each of which could hold 2 electrons to fill the d block which can hold a total of 10 electrons. So, three quantum numbers will give you 2 possible electrons.

n=5,ℓ=0 refers to the 5s orbital. Since this is an s orbital, it only has one orientation, and can only hold 2 electrons.

n=3 refers to the 3s, 3p, and 3d subshells, which can hold 2 electrons in the s orbital, 6 electrons in the p orbital, and 10 electrons in the d orbital for a total of 18 electrons.

Hope this helps!

[Gillian Gabrielsen2F]

n is is energy level, or the shell. s,p,d and f are all subshells that make up the particular shell.
For a particular element, n is based on the period(row) of the periodic table, and it's the number in front of s,p,d,f.
for s and p block, n = # row. For d block, n = # row - 1. For f block n= # row - 2
(for example, Ti is in row 4 in the dblock, so it would reach up to 3d.)
ℓ is based on the type of orbital. s=0, p=1, d=3, f=3
mℓ= ℓ, (ℓ-1), (ℓ-2),...,-ℓ
so for p it would be 1,0,-1
Keep in mind that s is 2 orbitals, p is 3 orbitals, d is 5 orbitals, and f is 7 orbitals. Each orbital can hold 2 electrons, one spinning up(+1/2) and one spinning down(-1/2)

For example, for n=5 and ℓ=0,
n=5 means you're looking at 5s, 5p, and 5d. However, since you see ℓ=0, you know you're ONLY looking at 5s. s-orbital can hold 2 electrons, so two electrons can have 5=s and ℓ=0.

Hope this helped, I know this stuff is kind of confusing

[Madison Muggeo 3H]

I had a hard time understanding this stuff at first, but all these explanations really helped! Thanks guys!