Finding Electrons with Quantum Numbers

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Quinton Sprague 1A
Posts: 91
Joined: Wed Sep 30, 2020 9:35 pm

Finding Electrons with Quantum Numbers

Postby Quinton Sprague 1A » Fri Oct 30, 2020 5:21 pm

On the Sapling homework I have been having trouble solving these two questions. Both ask you to find the maximum number of electrons that could have the sets of quantum numbers.
The first is n=4 and l=2. My thought was that regardless of the principal shell, theres atleast 2 electrons. Then since l=2 this means electrons are occupying the d sub shell, therefore if the maximum for this shell is 10 and its after the p sub shell with a maximum of 6, I did 2+6+10=18. But I was incorrect.
The next is n=7, l=1, and ml=-1. My initial idea was that I still only had 2 electrons in the 7s, but being that this is dealing with the p subshell the max is 6. Since it has a spin of -1 I figured it had electrons in the pz, therefore 3 or 6 in the p subshell altogether. I did 2+3=5, incorrect, and tried 2+6=8 and was also incorrect.
Please let me know where I am going wrong in my thinking, thanks!

Lucy Wang 2J
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Joined: Wed Sep 30, 2020 10:09 pm
Been upvoted: 2 times

Re: Finding Electrons with Quantum Numbers

Postby Lucy Wang 2J » Fri Oct 30, 2020 5:36 pm

Hi Quinton,

So for the first question since n=4 AND l=2, this is referring to electrons that are in the 4d subshell only. The value of l for the electrons from the 4s or 4p subshells do not equal 2 so they don't apply to this question. I think the answer should be 10.

For the second question, when n=7 and l=1, this indicates we are in the 7p subshell which has a max of 6 electrons. However, it also specifies the ml which indicates which orbital the electron is located in.And only 2 electrons can have the same orbital so that is the answer.

VincentLe_3A
Posts: 91
Joined: Wed Sep 30, 2020 10:01 pm

Re: Finding Electrons with Quantum Numbers

Postby VincentLe_3A » Fri Oct 30, 2020 5:40 pm

For the first problem with n=4 and l=2, you must consider that this is specifically the 4d orbital, which does not include the 4s or 4p orbitals. I think you are grouping all these orbitals together, which is incorrect because electrons in the 4s would have the quantum numbers of n=4 and l=0 while electrons in 4p would have n=4 and l=1. Therefore, it is important to distinguish these orbitals from each other, as the problem is asking specifically for electrons within the 4d orbital only. As for the second one, from the first two quantum numbers, it tells you that only the 7p orbital is considered, so you should immediately think only 6 possible electrons can have those numbers. Then it specifies even further that the magnetic quantum number (ml) is -1 (which eliminates the possibility of the 4 other electrons since only two electrons can be paired within the same orientation), so the only number left that can be added to complete the full 4 quantum number sequence is spin (either 1/2 or -1/2), so there are only two possible electrons which can have these numbers.

Hope this helps.

Quinton Sprague 1A
Posts: 91
Joined: Wed Sep 30, 2020 9:35 pm

Re: Finding Electrons with Quantum Numbers

Postby Quinton Sprague 1A » Fri Oct 30, 2020 5:46 pm

Thank you both! I finally solved the complete question after my eleventh try. I was unclear that it was asking specifically for each subshell, I appreciate the help!


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