Mineralogists and geologists often need to identify the relative sizes of atoms to judge whether one mineral might be modified by the inclusion of “alien” ions. For example, the different colors of some gemstones result from this type of insertion.

Arrange each of the following pairs of ions in order of increasing ionic radius:

(a) Mg²⁺ and Ca²⁺;

(b) O²¯ and F¯.

PLAN The smaller member of a pair of isoelectronic ions in the same period will be an ion of an element that lies farther to the right in a period, because that ion has the greater effective nuclear charge. If the two ions are in the same group, the smaller ion will be the one that lies higher in the group, because its outermost electrons are closer to the nucleus.