## Good way to understand quantum numbers/shells?

Eve Gross-Sable 1B
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### Good way to understand quantum numbers/shells?

Hi! I remember having a good understanding of orbital shells and quantum numbers in high school but I cannot seem to get the same grip on it that I used to have. Does anyone have any tips or good videos for understanding it and being able to apply it to problems? Thanks

Sam Wentzel 1F 14B
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### Re: Good way to understand quantum numbers/shells?

"n" correlates to the leading number of the subshell, and represents the main shell that an electron occupies.

For example, in "3s2," n = 3 because of the leading "3" before the "s2".

l correlates to the subshell of the electron. l = 0 correlates to the s subshell, l = 1 to the p subshell, l = 2 to the d, and l = 3 to the f.

The l value of 3s2 would be 0, as it is in the s subshell.

ml defines the sub-orbital that the specified electron occupies. If we are specifying the last electron in say, 3p6, then ml would be equal to 1.
The way you determine ml, is the middle pair of electrons is always at ml = 0. The pair of electrons before that will be at ml = -1, -2, and so on.
The pair of electrons after the middle pair will always be positive, at ml = 1, 2, and so on.

The quantum number ms corresponds to which electron in an electron pair is being specified. The "first" electron in each electron pair will always have upward spin, with an ms value of ms = +1/2. The second electron in each electron pair will always have an ms value of -1/2, with a downward spin.

The only real thing to memorize is what each quantum number correlates to in terms of electron configuration. After knowing this, one can determine the quantum numbers of a specified electron / element simply by using logical application of what each quantum variable corresponds to.

As for the subshells, it really helped me to look at orbital diagrams for each subshell. It helps to visualize the suborbitals of each subshell (like how the p subshell has 3 suborbitals) and also seeing the opposite spin of each paired electron, upward and downward. Knowing how to fill out these diagrams helped me a lot.

Hope this helps :)

Olivia Smith 2E
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Joined: Wed Sep 30, 2020 9:43 pm

### Re: Good way to understand quantum numbers/shells?

Also if you are more a visual/auditory person and videos help. My go to is always Khan Academy first. They always have some really good and thorough videos on a wide range of concepts that have following transcripts and the whole shebang. And depending on the topic will also have some practice problems. Also have heard really good things about the Organic Chemistry Teacher on youtube, seems to have very thorough videos on all topics you could think of for chemistry. Try them both out and see which one you like the most! Hopefully this helps!

Sami Siddiqui 1J
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### Re: Good way to understand quantum numbers/shells?

I assume you have a grip on how to get each of these numbers based on the value of n you're given and the subshell you want to focus on, so for the purpose of simplicity, I'm just going to state what each quantum number means in the shortest way possible:

Principal quantum number (n): This value pertains to the energy level of the orbital of focus. A higher value of n is indicative of a larger shell size and vice versa.

Angular momentum quantum number (l): This number pertains to the shape of a specific subshell. For example, a value of 0 would indicate that the subshell of the energy level you're looking at is an s-orbital and is, therefore, a symmetrical sphere.

Magnetic quantum number (ml): This corresponds to the orientation of the orbitals (in terms of its position on the x, y, and/or z-axis).

Spin quantum number: This indicates the direction in which the electrons in a given orbital are spinning. A value of +1/2 means spin up and -1/2 means spin down.

Keep in mind that the first three quantum numbers are used to pinpoint a specific orbital, while the last quantum number (along with the other three numbers) is used to specify a specific electron in a given orbital.