Explanations of trends in atomic radii that do not work perfectly:We might argue that going from hydrogen through the elements that the number of electrons increase. Since electrons repel each other due to the like charges, and the size of the atom will increase. The more electrons the larger the atom. We might be able to use that argument to explain the trend within a group, but when we look at the atomic radius trend going across a period the radius decreases.So we could argue that going from hydrogen through the elements the number of protons increases. Since electrons are attracted to protons we might expect that the more protons the smaller the radius. That might explain the trend in atomic radii going across a period but it does not explain the trend going down a group. Cesium has a large number of protons, yet it is one of the largest atoms, not the smallest.Here is our lecture discussion on this issue. 
Element 
Nuclear

Electron

Inner Core

Valence

Effective Nuclear

Na 
11 
1s^{2}2s^{2}2p^{6}3s^{1} 
10 
1 
+1 
Mg 
12 
1s^{2}2s^{2}2p^{6}3s^{2} 
10 
2 
+2 
Al 
13 
1s^{2}2s^{2}2p^{6}3s^{2}3p^{1} 
10 
3 
+3 
Si 
14 
1s^{2}2s^{2}2p^{6}3s^{2}3p^{2} 
10 
4 
+4 
P 
15 
1s^{2}2s^{2}2p^{6}3s^{2}3p^{3} 
10 
5 
+5 
S 
16 
1s^{2}2s^{2}2p^{6}3s^{2}3p^{4} 
10 
6 
+6 
Cl 
17 
1s^{2}2s^{2}2p^{6}3s^{2}3p^{5} 
10 
7 
+7 
Ar 
18 
1s^{2}2s^{2}2p^{6}3s^{2}3p^{6} 
10 
8 
+8 
How would we explain why the atomic radius of a phosphorus atom is smaller than the atomic radius of a magnesium atom?How would we explain why the atomic radius of a sodium atom is smaller than the atomic radius of a cesium atom?Here is the explanation from lecture. 
Element 
I1 
I2 
I3 
I4 
I5 
I6 
I7 
Na 
490 
4560 

Mg 
735 
1445 
7730 

Al 
580 
1815 
2740 
11,600 

Si 
780 
1575 
3220 
4350 
16,100 

P 
1060 
1890 
2905 
4950 
6270 
21,200 
Element 
Electron

Electron

Inner Core/

Effective

Na 
1s^{2}2s^{2}2p^{6}3s^{1} 
3s 
1s^{2}2s^{2}2p^{6}3s^{1} 
+1 
Na^{+} 
1s^{2}2s^{2}2p^{6} 
2p 
1s^{2}2s^{2}2p^{6} 
+9 
Nuclear Charge 
Element 
Electronic Configuration 
Effective Nuclear Charge 
Valence Electrons 
Core Electrons 
11+ 
Na 
1s^{2}2s^{2}2p^{6}3s^{1} 
1+ 
1 
10 
11+ 
Na^{+} 
1s^{2}2s^{2}2p^{6} 
9+ 
8 
2 
8+ 
O 
1s^{2}2s^{2}2p4 
+6 
6 
2 
8+ 
O^{2} 
1s^{2}2s^{2}2p^{6} 
+6 
8 
2 
9+ 
F 
1s^{2}2s^{2}2p^{5} 
7+ 
7 
2 
9+ 
F^{} 
1s^{2}2s^{2}2p^{6} 
7+ 
8 
2 