Understanding the concept of electron per shell

[Chijioke]

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.

 

[DrClaude]

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]

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. See here: https://terpconnect.umd.edu/~wbreslyn/chemistry/electron-configurations/configurationCalcium.html

 

[Chijioke]

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.

 

[Drakkith]

There aren't two maximums and I never said there were.

 

[Drakkith]

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.