Someone help me develop a mental picture of electron configurations (n, l, m sub l, m sub s)?

Question

I'm trying to get a mental picture of these quantum numbers in a multielectron atom

Can someone tell me if this is correct ...this is what I imagine now ...but I don't know if it's right

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above the nucleus ..there's shells determined by the principle quantum # n that extend to infinity

Then within each of these shells ...(I picture them as a transparent sphere ...but that's probably wrong) there's X number of electrons ....some have the same angular momentum going really fast, some are going slower around this shell ....

The ones with the same velocity are traveling around the same circumference of the shell .....and the ones with different angular momentum l numbers are going on a slightly different circumference so it looks like a cloud ...and then there's a max of 2 electrons who can have the same angular momentum in this shell ....
????

Answer 1

The shells don't go to infinity in reality The only ones found in nature so far are K,L,M,N,O,P which correspond to n=1,2,3,4.5.6, that make some sense.

When you think of electron moving around the shell ( a sphere) think of them vibrating very fast as they go around the sphere which means their position is fuzzy. They are also not going around a circle, but they are going around different circles at the same time because the motion is not planar but spherical. The electrons in any shell surface, inspite of the fact they are paired by their parity because of their fuzzy path ( quantum mechanical probability wave) they also are bumping and interacting with other electrons in the adjacent shell surface also.

For example l can be s,p,d,or f orbital in any single spherical shell surface corresponding to the values of 1,2,3, or4 and the number of electrons in each orbital = 2 or 1 depending on pairing of spins (and p orbital has 3 sub orbitals). And each orbital can have upto 2, 6,10 or14 electrons in total depending on their magnetic momentum.
Even though s orbitals are pretty much independent and spherical, the p, d, and f orbitals particularly for the elements of higher atomic numbers, interact with the orbitals of the next shell. So you see everything in reality is very fuzzy around the nucleus. The language of shells and orbitals came about because of the breaking down of the probability wave function into a series representation. The first term of the series represents s orbital, the second p orbital and so on. This helps us to think of a combination of simplified geomerical figures than one fuzzy meaningless glob.

So in order for you to visualize the situation, break down the electron cloud into shells, but super impose on the shell surface in your mind,1 s orbital, 3 p orbitals, 5 d orbitals and so on, one at a time and then think of each of these orbitals changing positions in a fuzzy way all around the shell surface. Then go to the next shell surface in your mind and do the same. Now go back and super impose the previous shell picture with the current shell picture. And you continue this process in your visual mind until you are done with all the shell surfaces for that particular element under consideration.

Another way I found easy is to think of the symbol used by Atomic Energy people with a nucleus and a swarm of electrons going around in spherical or elliptical orbitals and create that picture for each shell and superimpose them.
Fantastic. Ha!. Pretty challeging to your mind to create such a complex picture. That's why to understand the behavior of each orbital and study it, the text books give you simplified pictures. But in reality it is a very complex and challenging vision. Good Luck.