# How come noble gases have full outer shells? [closed]

Argon has $18$ electrons overall and $8$ in the outer shell. But the $3^{rd}$ shell is supposed to have $18$ electrons.

Please use A-level terms so that I can understand.

## closed as unclear what you're asking by Todd Minehardt, Jannis Andreska, jerepierre, Wildcat, pentavalentcarbonMay 23 '17 at 17:12

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What you're referring to is the $\pu{KLMN}$ configuration, so the electronic configuration which is on your mind for argon is: $2, 8, 8$. So far so good, the third shell can hold $18$ electrons, no doubt, but there's another side to this coin.

Every shell is made up of subshells. Nah, it's not that weird; basically each of $\pu{K,L,M,N}$ is divided into $s, p, d, f \ldots$ Hey, writing $\pu{K,L,M,N}$ is getting cubersome (I'm really lazy) why don't we switch to simply $1,2,3,4 \ldots$? Alright, sounds good. Now we'll try to look at how many subshells are there in a shell.

Here's a formula for that: $n^2$. So basically the first shell ($n=1$) has $(1)^2=1$ a single subshell. And every subshell can hold $2$ electrons. So you can have $2$ electrons in your first shell. So we've reached at $2, 8, 18, \ldots$ Another similar formula, and some more calculations, I was finally able to figure out that, these shell actually look like this:

Each square $\square$ box can hold $2$ electrons. Now when you fill up argon's $\pu{K}$ shell (that's $1s$) and $\pu{L}$ shell (that's $2s$ and $2p$ together) and then finally you fill up $3s$ and $3p$, you've already filled $18$ electrons.

Think of electrons as food and argon as a gentleman. When you ask him: "Hey argon, there are more electrons!", he replies: "Oh sorry, my $\pu{M}$ shell feels full, can you please move it to over to $4s$? I'll fill up my $3d$ after a while."