Chemistry Understanding the concept of electron per shell

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Calcium has an electron arrangement of 2, 8, 8, 2 across its four shells, totaling twenty electrons. The formula 2n^2 indicates the maximum capacity for each shell, but actual electron distribution can differ due to energy levels and orbital filling. In calcium, the last two electrons occupy the 4s orbital rather than filling the 3rd shell completely. This results in the observed electron configuration, which reflects the principles of electron filling in many-electron atoms. Understanding this distinction between maximum capacity and actual electron distribution is crucial for grasping atomic structure.
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Homework Statement
Is shell number same as energy level
Relevant Equations
The maximum number of electron per shell is given as $$2(n^2)$$ where n is energy level number. And energy level is same as electron shell.
Looking at Cacium for th electron arrangements according to shell numbers is 2, 8,8,2 since Cacium have four shells.
Going by the formula
1st shell has:$$2n^2=2\times 1^2= 2 ~electrons $$
2nd shell has:$$2n^2=2\times 2^2= 8 ~electrons $$
3rd shell has:$$2n^2=2\times 3^2= 18 ~electrons $$
But unfortunately, Cacium has only twenty electrons.
I am thinking that the remaining 10 electrons should go into the 3rd energy level. But if that happens then Cacium would not be fit to still remain in period 4.
So why is the electron filling per shell for Cacium 2,8,8,2 and not 2,8,10 according to the formula giving for the maximum number of electron that can be found in a shell?
Thank you.
 
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The formula ##2n^2## gives the maximum number of electrons that can have the same principal quantum number ##n##, and given the name electron shell. However, for many-electron atoms, the energy does not only depend on ##n##. It turns out that electrons will be found in the ##n=4## shell before the ##n=3## shell is filled.
 
Drakkith said:
That formula is for the maximum number of electrons per shell, not the actual. In calcium, the last two electrons go into the 4s orbital.
You reply makes it look like as if there two types of maximum electrons in a shell:
1. Maximum number of electron and
2. Actual maximum number of electrons.
Please I need to understand something here.
 
There aren't two maximums and I never said there were.
 
Chijioke said:
Please I need to understand something here.
I'm not sure what you are looking for. If I can put 20 apples in a box, but I only put 12 into the box, then there's the maximum number of apples per box and the actual.

The details of how electrons go into their orbitals is probably beyond the scope of your class.
 
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