What principle do we use in writing the formula of an ionic compound such as NaCl or MgI2? How do we know that two iodide ions are needed for each magnesium ion, whereas only one chloride ion is needed per sodium ion?

We know based on the charges of each ion and the fact that they must always sum to 0

Explanation:

Na only has one outer electon to give so it is always +1

Mg has two outer electrons so it always gets +2

Halogens have one "missing" electron in their outer shell so they get a -1

For NaCl  (+1) + (-1) = 0

For MgI2 (+2) + 2(-1) = 0

periodic trends is an atom that gets larger as the number of electronic shells increase, the radius of atoms increases as you go down a certain group in the periodic table of elements. in general, the size of an atom will decrease as you move from left to right of a certain period.