The answer is:
1. Au3+ is smaller than Au+
2. P3− is smaller than As3−
3. Na+ is smaller than K+
1. Au3+ is smaller than Au+ because an atoms get smaller when electrons are removed. So, the more electrons, the greater is the ionic radius. Au3+ has two less electrons than Au+ so Au3+ must be smaller than Au+.
2. P3- is smaller than As3- because P3- has a smaller ionic radius. Although these two ions have the sam number of electrons, they are not the same size. As is located below P in the Periodic table of elements. Going down the group of elements, extra layers of electrons are added resulting in bigger ionic radius. So, As3- has bigger ionic radius than P3-.
3. Na+ is smaller than K+ for the same reason as the P3- is smaller than As3-. Na is located above K in the Periodic table of elements.