Exploring Energy Levels and Electron Configurations in Atomic Models

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Hello, why in the normal atomic configuration every layer except the second can contain only up to 8 electrons if for example the level with quantic number 3 contain up to 18 electrons?
What relation is there between this two models?

Thank you!
 
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You have the K,L,M,N (and so on) shells, which contain 2,8,18,32.. electrons.

Those numbers come from the sub-shells which make up the shells, which are denoted s,p,d,f.
The sub-shells contain 2, 6, 10, 14 electrons, respectively. (twice the odd numbers 1,3,5,7)

The K shell contains only an s sub-shell, so it has two electrons in total. The L shell has one s and one p, giving 2+6=8 electrons in total.
The M shell has an s,p and d, so 2+6+10 = 18, and the N shell has an f sub-shell as well, so 2+6+10+14 = 32 electrons.
 
An electron in the last layer require less energy to be removed, so why the last layer has more energy than the layer nearest the nucleum?
 
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