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It seems to me that the addition of electrons and protons as you move across a period would cause an atom to become larger. However, I'm told it gets smaller. Why is this?

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A nice periodic chart showing the effect you mention can be found here. It's worth noting that compared to the halogens, the noble gases are quite large. If you think in terms of satisfying shell requirements, that's actually a bit counter-intuitive. Also, while in chemistry one usually speaks in terms of filling shells, the deeper reason why electrons sometimes seem to repel each other more than they are attracted to protons is because of Pauli exclusion of identical-state fermions. –  Terry Bollinger Apr 26 '12 at 0:23
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Where did You read about that fact, without finding the explanation for it? –  Georg Apr 26 '12 at 20:26
    
Chemistry and physics have developed different ways of describing phenomena that are really the same thing. Pauli exclusion, played against charge attraction by a point-like positive nucleus and the low mass (high quantum location uncertainty) of electrons, is what produces the complex patterns and geometries that chemistry summarizes as "shells." Shells are very convenient, since they exhibit simple rules (e.g. 8 electrons "fill" a shell) that are much easier to deal with than the lower-level exclusion analysis. Nonetheless, for a question like this, you need to drop to that deeper level. –  Terry Bollinger Apr 27 '12 at 2:11
    
Also: I'm serious about the sudden jump from the very small size of a fluorine atom to the far larger size of neon -- sort of like a baseball expanding to beach ball size -- and yet becoming hugely more stable is quite surprising in may ways. If electrons are extremely happy to reach 8 (vs 7) in a group, shouldn't they show it by doing something like getting into a tight little sphere? Instead, just the opposite happens! I've never seen that explained. I may even ask that one over in Physics just to see if someone knows why "stability = bloat" and "incomplete = tiny". –  Terry Bollinger Apr 27 '12 at 2:21
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Georg, you are correct. The table I used apparently was based on binding radii, which are bogus in this context. The discussion of this over in Physics S.E. can be found on this link. The less visual but correct neutral atomic radii table can be found here. Note that in this table, element 10 (neon) is correctly listed as smaller in radius than element 9 (fluorine). –  Terry Bollinger Apr 28 '12 at 6:42
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As you move from left to right across a period, the number of protons in the nucleus increases. The electrons are thus attracted to the nucleus more strongly, and the atomic radius is smaller (this attraction is much stronger than the relatively weak repulsion between electrons).

As you move down a column, there are more protons, but there are also more complete energy levels below the valence electrons. These lower energy levels shield the valence electrons from the attractive effects of the atom's nucleus, so the atomic radius gets larger.

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Can you explain why "this attraction is much stronger than the relatively weak repulsion between electrons"? Why are the repulsions weak? –  Yann Apr 25 '12 at 18:30
    
Just as a side note, there can also be more complete energy levels as one moves left across a row (the $d$ and or $f$ shells can get filled) but these will NOT be the outer shell. –  soandos Apr 25 '12 at 18:31
    
@Yann, I believe that it has to do with the basic principles of magnetism, where the distance between "individual" electrons in the cloud is large, and their individual charges are small, where the protons can "combine" their charges, allowing it to have far more strength over the distance. –  soandos Apr 25 '12 at 18:34
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Remember, the 'size' of an atom has nothing to do with the size of the nucleus. It has to do with the size of the valence shell (which itself is not well-defined*).

So, if we neglect change in electrical attraction, the size should stay the same—a shell is a shell and it need not 'expand' to accomodate electrons.

Now, as we add more protons and electrons, the attraction between the nucleus and shell increases and the shell contracts. Thus the atom gets smaller.

*Shells reach 'til infinity, so it's better to define the size on the basis of 'the electrons of the outermost shell will be within this region x% of the time.' This only changes this answer a tiny bit. Now, we say 'the probability of finding the electrons closer to the center increases due to increased nuclear charge.'

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