Using complete subshell notation (not abbreviations, \(1 s^{2} 2 s^{2} 2 p^{6},\) and so forth), predict the electron configuration of each of the following atoms: (a) \(\mathrm{C}\) (b) \(\mathrm{P}\) (c) V (d) Sb (e) Sm

Understanding the electron subshell notation is essential for mastering the basics of chemistry, particularly when dealing with the arrangement of electrons within an atom. The notation indicates the energy levels, subshells, and number of electrons that occupy those subshells.

Electrons fill subshells in an order based on energy levels, starting with the lowest energy subshell and moving to higher ones, a concept known as the Aufbau principle. The subshells within each energy level are designated by the letters s, p, d, and f, which have increasing energy levels in that order. For instance, the 1s subshell is the lowest energy subshell, while the 3d comes after 3s and 3p.

The use of superscripts in the notation, such as in the carbon electron configuration, indicates the number of electrons in a subshell. In the example given, carbon (C) with an atomic number of 6, has its electrons distributed as follows: 1s^{2}2s^{2}2p^{2}

This notation shows that carbon has two electrons in the 1s subshell, two in the 2s subshell, and two in the 2p subshell—adding up to six electrons in total. Through this system, we are able to see at a glance how the electrons of an atom are organized based on the principles of quantum mechanics.

The atomic number of an element is a fundamental property that reveals the number of protons in the nucleus of an atom and, by extension, its number of electrons when the atom is neutral. The atomic number is a unique identifier for each element and determines its position on the periodic table.

For example, in the step-by-step solutions provided, vanadium (V) has an atomic number of 23, which means it has 23 protons in its nucleus and, when neutral, the same number of electrons. The atomic number guides us through the process of filling electron subshells systematically to arrive at the correct electron configuration: 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{3}4s^{2}. This shows that vanadium has filled its lowest energy levels and has three electrons in the 3d subshell and two in the 4s, totaling 23 electrons.

The atomic number is invaluable when predicting the chemical properties of an element, as elements with similar electron configurations, particularly in their outer shells, tend to exhibit similar behaviors.

The periodic table is an organized chart of all known elements, arranged in order of increasing atomic number and grouped by similar properties. This arrangement highlights the periodic trends and the relationship between the elements' chemical behaviors and their electron configurations.

Elements are arranged into periods (rows) and groups (columns). For instance, samarium (Sm), with its electron configuration shown in the exercise, belongs to the lanthanides series, elements known for having electrons in the 4f subshell. This is indicated by the placement of Sm in the sixth period and within the row of lanthanides:1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^{2}4p^{6}4d^{10}5s^{2}5p^{6}4f^{6}6s^{2}.

The periodic table not only helps us visualize the organization of the elements but also aids in the prediction of an element's electron configuration, especially for transition metals and inner transition metals like the lanthanides and actinides, where the order of orbital filling can become less intuitive.