Write electronic configurations for the valence electrons of \({ }_{14} \mathrm{Si},{ }_{15} \mathrm{P}\), and \({ }_{16} \mathrm{~S}\). Indicate the spins of the electrons in the \(3 p\) orbitals with a small up or down arrow.

Atomic numbers are fundamental properties of elements that are simply the count of protons in an atom's nucleus. They determine the element's identity and its position on the periodic table. For instance, in the given exercise, the atomic numbers for silicon (Si), phosphorus (P), and sulfur (S) are 14, 15, and 16 respectively. This sequential increment explains their positioning on the periodic table, influencing their chemical behavior as well.

The electron configuration of an element illustrates the arrangement of electrons in its atomic orbitals. Electrons fill orbitals in a way that minimizes energy, starting from the lowest energy level (1s) upwards. For instance, the full electron configurations for Si, P, and S up to the 3p orbitals are:
Si: 1s² 2s² 2p⁶ 3s² 3p²
P: 1s² 2s² 2p⁶ 3s² 3p³
S: 1s² 2s² 2p⁶ 3s² 3p⁴
This distribution is essential for predicting chemical properties and reactivity. It is also worth noting that the order in which orbitals are filled is based on the Aufbau principle, which states that lower-energy orbitals fill before higher-energy ones.

Hund's rule is a fundamental principle that predicts the distribution of electrons in orbitals of the same energy (degenerate orbitals). Simply put, electrons will occupy empty orbitals singly and with parallel spins before pairing up in the same orbital. This helps minimize electron repulsion and creates a more stable configuration. In the case of the 3p orbitals of Si, P, and S, Hund's rule determines how the electrons fill these orbitals. Here is an example for each element:
Si: 3p², with one electron in 3pₓ and one in 3p_y (both ↑).
P: 3p³, with one electron in each 3pₓ, 3p_y, and 3p_z (all ↑).
S: 3p⁴, with one paired (↑↓) in 3pₓ, and one each in 3p_y and 3p_z (both ↑).
This ensures the most stable electron arrangement by following Hund's rule.

Valence shell orbitals are the outermost orbitals of an atom and hold the valence electrons, which are crucial for chemical bonding and reactions. For elements like Si, P, and S, these include the 3s and 3p orbitals. These valence electrons determine the chemical properties and reactivity of an element. For example:
Si (Valence Configuration): 3s² 3p²
P (Valence Configuration): 3s² 3p³
S (Valence Configuration): 3s² 3p⁴
Identifying valence shell orbitals and electrons helps in predicting how atoms will interact, form bonds, and create molecules during chemical reactions, which is why understanding them is fundamental in chemistry.