The easiest way to understand the ionic radius trend is to see it.
Within the positive ions, the trend
matches the trend for atomic radius -- decreasing to the right -- as does
the reason (more positive nucleus pulling the electrons in tighter).
The same is true within the negative ions. The discrepancy is between
the positive ions and the negative ions.
To understand the change in size from
the small positive ions to the larger negative ions we need to look at
the electron configurations of the ions. The electron configurations for
the ions above are listed below.
Li+1: 1s2
Be+2: 1s2
B+3: 1s2
C+4: 1s2
N-3: 1s22s22p6
O-2: 1s22s22p6
F-1: 1s22s22p6
What you need to notice is that the electron configuration for all of the positive ions is the same and that all of them are isoelectronic with He.
All of the negative ions are also identical with each other, but they are isoelectronic with Ne.
Since Ne has an entire extra energy level, we would expect anything with the electron structure of Ne to be larger than anything that has the electron structure of He.
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