Which of the following species has the most unpaired electrons: \(\mathrm{S}^{+}, \mathrm{S},\) or \(\mathrm{S}^{-} ?\) Explain how you arrive at your answer.

Electron configuration describes how electrons are distributed within an atom's electron shells and subshells, denoted by quantum numbers. For instance, sulfur (S), located in the third period and sixth group of the periodic table, generally has 16 electrons. Given an extra or missing electron, as in the ions \(S^{+}\) or \(S^{-}\), the configuration changes accordingly.

The configuration is written in a series of numbers and letters, where numbers define the energy level, while letters (s, p, d, f) represent the type of orbital. For example, in \(S^{+}\), which has 15 electrons, this is expressed as \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{5}\), showing the filling of each orbital up to the 3p subshell with 5 electrons. Understanding electron configuration is crucial for predicting chemical behavior and bonding patterns.

Hund's rule is a fundamental principle used to determine the electron configuration of atoms in their ground states. The rule states that for degenerate orbitals (those with the same energy level, such as the three 3p orbitals in sulfur), one electron enters each orbital until all are half-filled before any is fully occupied.

Building upon the concept of electron configuration, it's Hund's rule that explains why the neutral sulfur atom (\(S\)) with the electron configuration of \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{4}\) has two unpaired electrons rather than having paired electrons in one orbital while leaving other orbitals empty. This adherence to Hund's rule promotes the greatest number of unpaired electrons, lowers the repulsion between electrons occupying the same orbital, and ultimately makes the atom more stable.

The periodic table is a concise, organized chart of all known elements arranged by increasing atomic number while grouping elements with similar properties into columns known as groups or families. Elements positioned in the same period (horizontal rows) share the same number of atomic orbitals. For example, sulfur is found in the third period, signifying it has electrons in three different energy levels.

The periodic table is a key tool in chemistry, as it not only reveals relationships among the elements but also guides the determination of electron configurations, which further governs an element's reactivity and chemistry. For instance, sulfur's position in the sixth group provides insight into its typical number of valence electrons and its tendency to form certain ions, like \(S^{+}\) or \(S^{-}\), which is pivotal in predicting how many unpaired electrons might be present in these species.