In the following series indicate which one of the species is the smallest. au, au+, au 2+, au 3+

would likely be the smallest.

Explanation:

In this question, likely represents a gold atom.

, , and are gold ions. The plus sign in the superscript shows that these ions are positive. In other words, each is formed when a atom loses one or more electrons. The number shows the charge on each of these ions. That's the same as the number of electrons that the atom needs to lose before forming this ion. The charge on is more positive than that on the other two gold ions. As a result, each ion contains fewer electrons than each of the other two ions.

Consider the electron-cloud model of an atom or an ion. The nucleus is very small and doesn't take up much space. The atom or ion takes space mainly because of the electron cloud that surrounds the nucleus. The nucleus attracts the valence electrons and pulls them inwards. At the same time, the electrons repel each other.

For the same nucleus (attractions on the electrons stay the same,) as the number of electrons decreases, the size of the repulsion decreases. As a result, for a series of ions or atoms with the same nucleus, the one with the smallest number of electrons will take up the least space. All four choices involve the nucleus. However, since each particle contains the least number of electrons, it would also be the smallest.