Why is the distribution of electrons of calcium in K,L,M,N shells 2,8,8,2 instead of 2,8,9,1?

I'm a beginner to this topic, so this would likely sound dumb. As far as I know, when distributing electrons in energy shells, the last energy shell can't have more than 8 electrons. So for calcium, it can't be 2,8,10. However, why isn't it 2,8,9,1?




The answer of your problem lies in the existence of sub-shells, that you seem not to know. Let me explain.


If you give a number $n$ to the successive shells, $K$ shell gets $1$, $L$ gets $2$, $M$ gets $3$, etc. The maximum amount of electrons per shell is $2n^2$ , which is $2$ for $K$ shell, $8$ for $L$ shell, $18$ for $M$ shell, etc. $n$ is called first quantum number or principal quantum number.


But whatever the $n$ value, the $2$ first electrons of any shell are called with the letter $s$ after the first quantum number $n$. Their energy is always a little bit lower than the other electrons of the same shell. They form what we call the sub-shell $s$. Examples of sub-shells $s$ : $1s, 2s, 3s, 4s$, etc.


If a shell has more than $2$ electrons, the supplementary ones are called $n$ plus the letter $p$. They form a sub shell $p$. Example of sub-shells $p$ : $2p, 3p, 4p$, etc. There may be up to six such $p$ electrons, and their energy is a little bit higher than the two $s$ electrons of the same shell.


If a shell has more than $8$ electrons, the ten supplementary ones are called $n$ plus the letter $d$. They form a sub-shell $d$ and their energy is higher than the electrons $s$ and $p$ of the same shell. Examples of sub-shells $d : 3d, 4d$. etc.


But surprisingly, electrons of the sub-shell $4s$ have a lower energy than $3d$. So when filling up the electronic configuration of Calcium ($Z = 20$), the sub-shell $4s$ will be filled before the $3d$. This is why Calcium contains $2$ electrons in the $K$ shell, $8$ in the $L$ shell, and not more then $8$ electrons in the $M$ shell. After finishing the $3p$ sub-shell, the two last electrons are not going to the $3d$ sub-shell of the $M$ shell. They will prefer going to the $4s$ sub-shell of the $N$ shell. This is why Calcium is not $2,8,9,1$ or $2,8,10,$ as you wrote. It is $2, 8, 8, 2$


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