Name the element in the third period (row) of the periodic table with: (a) three valence electrons (b) a total of four \(3 p\) electrons (c) \(\operatorname{six} 3 p\) electrons (d) two 3 s electrons and no \(3 p\) electrons

Valence electrons are the electrons located in the outermost shell of an atom, which can participate in the formation of chemical bonds with other atoms. These electrons determine many properties of an element, including its reactivity and how it bonds with other elements. For instance, aluminum (Al), with its three valence electrons, tends to lose electrons to achieve a stable octet, making it typically trivalent in its compounds.

In the context of the exercise, identifying the element with three valence electrons in the third period directs us to aluminum (Al), which has an electron configuration of 1s2 2s2 2p6 3s2 3p1. The last two digits represent the valence electrons: two in the 3s subshell and one in the 3p subshell.

Periods on the periodic table are the horizontal rows that categorize the elements according to their electron shell filling order. The third period, notably, consists of the elements from sodium (Na) to argon (Ar). Elements in the same period have the same number of electron shells but differ in the number of electrons within the valence shell, which increases progressively as you move from left to right.

For example, magnesium (Mg) sits at the start of the 3s subshell filling, while sulfur (S) and argon (Ar) follow thereafter, indicating their positions in the third period based on the progressive filling of their valence shells with electrons.

The letter 'p' in 3p electrons refers to the type of orbital within the electron shell, which corresponds to the subshell being filled by the electrons. The '3' denotes the third energy level. 3p electrons are found in the third energy level's p orbital, and an element can have up to six 3p electrons before the subshell is filled.

In our exercise, sulfur (S) is identified as the element with four 3p electrons due to its electron configuration 1s2 2s2 2p6 3s2 3p4. Argon (Ar), with a fully-filled 3p subshell having six 3p electrons, has an electron configuration of 1s2 2s2 2p6 3s2 3p6, making it the last element in the third period.

Electron shells around an atom fill according to a specific sequence governed by the quantum mechanical properties of electrons. The filling order typically begins with the lowest energy levels, proceeding from 1s to 2s, then 2p, and so on. In accordance with the Pauli exclusion principle and Hund's rule, each orbital within a subshell gets one electron before any orbital gets a second one, and the electrons keep the same spin to maximize their repulsion until the subshell is fully occupied.

By following these rules of shell filling, magnesium (Mg) is recognized as the element that has completed the 3s subshell with two electrons, while the 3p subshell remains empty. Its electron configuration, 1s2 2s2 2p6 3s2, reflects this precise order of filling, and the absence of 3p electrons distinguishes Mg from other elements in the third period.