There are no simple formulas like the ones you are looking for.
I found out that also subshells affect so it got too complicated for me at the moment to create a precise formula...
And subshells are one of the easiest parts.
In general - to calculate properties like the ones you are looking for you have to solve Schroedingers equation. This equation has exact solutions only for the simplest case - hydrogen atom. For many other cases we can find numerical solutions - but almost always they are only approximate. The more atoms - the more approximate solution.
Yes well, they probably are, but even approximate could help me.
About the subshells, okay, they are easy yes, but constructing a formula is another thing : ). Anyway what I have thought so far of atomic radius:
I've used this one to try and clear things for me:
http://en.wikipedia.org/wiki/Atomic_radius#Calculated_atomic_radiussince it's calculated I thought it would be the easiest one to find logic in..
What I found was:
since H has 53 and He has 31, and only difference they have is that He has more electrons and protons in it. From that I was able to tell that each electron or proton makes atomic radius smaller.
Going on to the next line, I can see that each shell adds more to it ( since Li has 167 compared to H's 53. )
Okay.. Now I'll skip a little and start from K.
Difference between K and Ca is much much greater than the difference between rest of elements in this period. I explained that to myself that they are the ones who have only s orbital filled. And since K has two times less electrons it has a lot bigger atomic radius. (K has 1 while Ca has two, which means s orbital is filled). And by that logic I also found out that if an orbital fits more electrons the lesser the gap of atomic radius change goes... So all the elements from Sc to Zn have the difference quite low ( since they have d orbital ).
And from Ga to Kr the difference gets bigger, because their last orbital fits just 6 electrons.
Actually after writing this text, I think it should be fairly easy to calculate the formula ( I don't know why I thought it was way too difficult for me before ).
Anyway, I hope you understood my text, because I had hard times explaining it, because I'm not even slightly sure if I'm on the right track.
And if you see some logic errors then please tell me : )