Sulfur is a nonmetal element with the chemical symbol \(S\) and an atomic number of 16, meaning every sulfur atom contains sixteen protons in its nucleus. Understanding the size of this atom requires defining its atomic radius, which measures the distance from the nucleus to the boundary of the outermost stable electron orbital. This measurement is not a single fixed number, but rather a concept that changes based on how the atom is interacting with its environment. The precise value depends entirely on the forces acting on the electron cloud, such as whether the atom is bonded to another or existing freely in a solid state.
The Specific Radii of Sulfur
The size of the sulfur atom is quantified by several distinct radius values, measured in picometers (\(\text{pm}\)). When sulfur is chemically bonded to another atom, its covalent radius is approximately \(105 \text{ pm}\). This measurement is derived from the distance between the nuclei of two sulfur atoms sharing a pair of electrons in a molecule. In contrast, the Van der Waals radius of sulfur is significantly larger, measuring about \(180 \text{ pm}\).
Sulfur also forms ions with varying sizes depending on whether it gains or loses electrons. The ionic radius of the most common sulfur anion, the sulfide ion (\(S^{2-}\)), is much larger than the neutral atom at approximately \(184 \text{ pm}\). Conversely, the highly positive hexavalent sulfur ion (\(S^{6+}\)), which has lost all six valence electrons, is extremely small, measuring approximately \(29 \text{ pm}\).
Why Atomic Radius Varies
The absence of a single atomic radius value for sulfur stems from the quantum mechanical nature of the atom, where the electron cloud lacks a defined, hard boundary. Instead of a sharp edge, the probability of finding an electron gradually fades away as the distance from the nucleus increases. Therefore, the reported radius must be calculated or measured within a specific context, leading to different definitions.
The covalent radius is determined by taking half the distance between the nuclei of two identical atoms that are joined by a single bond. This method represents the atom’s size when its electron cloud is slightly compressed due to the sharing of electrons. The Van der Waals radius, however, is half the distance between the nuclei of two non-bonded atoms that are in the closest possible contact in a solid crystal structure. This larger value reflects the size of the atom when only weak intermolecular forces are present, without the compression of a chemical bond.
The ionic radius specifically reflects the size of the atom after it has gained or lost electrons to form an ion. When sulfur gains two electrons to form \(S^{2-}\), the increased number of electrons in the outer shell leads to greater repulsion among them, causing the electron cloud to expand significantly. Conversely, when sulfur loses six electrons to form \(S^{6+}\), the remaining electrons are pulled much closer to the nucleus by the full force of the sixteen protons, resulting in a dramatic reduction in size.
Periodic Trends That Determine Sulfur’s Size
Sulfur’s position in Period 3 and Group 16 of the periodic table explains the relative magnitude of its atomic size compared to its neighbors. The size of an atom is governed by the number of electron shells and the effective nuclear charge (\(Z_{eff}\)) experienced by its outermost electrons. The \(Z_{eff}\) is the net positive charge felt by a valence electron after accounting for the shielding effect of the inner core electrons.
Moving across the third period, from sodium to chlorine, the atomic radius progressively decreases. This occurs because, although electrons are being added to the same principal energy level (the third shell), the number of protons in the nucleus is also increasing. Sulfur, with 16 protons, has a higher nuclear charge than elements to its left, like phosphorus.
The increased number of protons pulls the electron cloud inward more strongly, while the shielding provided by the inner electrons remains relatively constant across the period. This greater attractive force, or higher \(Z_{eff}\), causes the atom’s boundary to contract, making sulfur smaller than elements like silicon or aluminum.
Moving down Group 16, from oxygen to sulfur and then to selenium, the atomic radius increases substantially. This vertical trend is driven by the addition of entirely new principal quantum shells as the element’s atomic number increases. Sulfur has electrons occupying the third shell, while oxygen only fills the second shell.
The addition of a new shell places the outermost electrons farther from the nucleus, which overrides the effect of the increased nuclear charge. The inner shells of electrons effectively shield the valence electrons from the full nuclear attraction, resulting in a larger atomic size for sulfur compared to oxygen.