Final answer:
To rank ions by size, we look at the nuclear charge where greater charge results in a smaller ion in isoelectronic series, and the principal quantum number, where a higher number indicates a larger ionic radius down a group. The periodic table provides insights into likely ion formation and charges.
Step-by-step explanation:
To rank ions from biggest to smallest, we consider two main factors: the nuclear charge and the principal quantum number. Ions with the same number of electrons (isoelectronic) will have sizes that decrease with an increasing nuclear charge. For example, in a series from N³- to Al³+, although each ion has 10 electrons, the ionic radius decreases from N³- to Al³+ due to the increasing nuclear charge.
Furthermore, when considering ions with different principal quantum numbers (moving down a group in the periodic table), the ionic size increases despite the same charge. For instance, ions of successive elements down a group with the same charge typically have an increasing ionic radius. Hence, a V²+ ion has a radius of 79 pm while a smaller V³+ ion has a radius of 64 pm, due to the larger charge drawing electrons closer to the nucleus.
Finally, the periodic table can indicate the formation and charge of ions with elements on the far left generally forming positively charged cations and elements on the far right forming negatively charged anions. The charges correspond to the group numbers of the elements.
When comparing As³, Br, K+, and Mg2+, the increasing order of radii would typically be Mg2+ < K+ < Br < As³, due to the interplay between nuclear charge and the number of electrons.