The size of an atom is defined by its atomic radius, which measures the distance from the nucleus to the outermost electrons. When an atom gains or loses electrons, it becomes a charged particle called an ion, and its size is then described by its ionic radius. The introduction of an electrical charge—either positive or negative—alters the balance of forces within the atom, leading to a change in size. A positive charge results in a smaller ion compared to the neutral atom, while a negative charge causes the ion to expand and become larger. This change in size is governed by how the new electron count affects the attraction between the nucleus and the electron cloud.
Effective Nuclear Charge: The Underlying Principle
The size of any atom or ion is a result of a balance between two opposing forces. The nucleus, containing positively charged protons, constantly pulls all the negatively charged electrons inward. This attractive force is known as the nuclear charge.
However, electrons do not experience the full pull of the nucleus because inner-shell electrons effectively shield the outer, or valence, electrons from the nuclear charge. The net positive pull that the valence electrons actually feel is called the Effective Nuclear Charge (\(Z_{eff}\)).
The \(Z_{eff}\) ultimately determines the radius. If the \(Z_{eff}\) is high, the electrons are pulled in close, resulting in a smaller radius. Changes in the number of electrons, which is what happens when an atom becomes an ion, directly impact this shielding effect and the resulting \(Z_{eff}\) value.
How Positive Ion Formation Reduces Size
An atom forms a positive ion, known as a cation, by losing one or more electrons, typically from its outermost energy shell. For example, a neutral sodium atom (\(\text{Na}\)) with 11 protons and 11 electrons loses one electron to become a sodium ion (\(\text{Na}^+\)) with 11 protons and 10 electrons. The number of positive charges in the nucleus remains constant, but the number of negative charges orbiting it decreases.
This loss of electrons contributes to the size reduction in two major ways. First, the remaining electrons are pulled by the same number of protons but face less electron-electron repulsion and less shielding. This causes the Effective Nuclear Charge experienced by each remaining electron to increase, pulling the entire electron cloud closer to the nucleus.
The second effect occurs if the atom loses all electrons from its outermost shell. When neutral sodium loses its single valence electron, it also loses its entire third electron shell. The outermost electrons are now in the second shell, which is much closer to the nucleus, causing the ionic radius to shrink substantially. Cations are always smaller than the neutral atoms from which they are formed.
How Negative Ion Formation Increases Size
An atom forms a negative ion, called an anion, by gaining one or more electrons into its outermost energy shell. A neutral chlorine atom (\(\text{Cl}\)), for instance, gains one electron to become a chloride ion (\(\text{Cl}^-\)), changing its electron count from 17 to 18 while its nucleus still holds 17 protons. The addition of this extra electron increases the total number of negative charges orbiting the nucleus.
The primary consequence of this electron gain is an increase in the repulsive forces between the electrons in the valence shell. With more electrons occupying the same physical space, they push each other further apart to minimize mutual repulsion. This outward push causes the entire electron cloud to expand.
Although the nuclear charge remains the same, the increased repulsion decreases the net pull of the nucleus on the outer electrons, leading to a smaller \(Z_{eff}\) per electron. This reduced pull forces the valence shell to swell, resulting in an anion that is always larger than its parent neutral atom.
Comparing Ions with the Same Electron Configuration
The relationship between charge and size is most clearly demonstrated by comparing ions that possess the same total number of electrons, a group known as an isoelectronic series. Consider the series \(\text{N}^{3-}\), \(\text{O}^{2-}\), \(\text{F}^{-}\), \(\text{Na}^{+}\), and \(\text{Mg}^{2+}\), all of which have 10 electrons. Despite the identical number of electrons, their radii vary widely because their nuclear charges—the number of protons—are different.
Nitrogen has the fewest protons (7), so its 10 electrons are held by the weakest nuclear pull, making the \(\text{N}^{3-}\) ion the largest in the series. Conversely, \(\text{Mg}^{2+}\) has the most protons (12), which exert the strongest attractive force on the same 10 electrons, resulting in the smallest radius. The size of these ions is determined solely by the number of protons: the greater the positive charge in the nucleus, the more tightly the fixed number of electrons is held, and the smaller the ion becomes.