Regarding primary quantum number \(n\), which representative elements have valence electrons with an \(n\) value that is three times the \(n\) value of lithium's valence electrons? What period are they in?

Valence electrons are the electrons in the outermost shell, or energy level, of an atom, which play a critical role in chemical reactions and bonding. Understanding valence electrons is essential for predicting how an element will interact with others. In the case of lithium, which has the atomic number 3, its electron configuration can be written as \(1s^2 2s^1\). The outermost shell here is represented by the 2s orbital, meaning lithium has one valence electron with a primary quantum number (\(n\) of 2. Electrons in the outermost shell determine an element's reactivity and are involved in the formation of chemical bonds. Elements in the same group of the periodic table typically have the same number of valence electrons, which accounts for their similar chemical properties. By understanding how to identify the number of valence electrons in an atom, you can better grasp concepts like reactivity and bonding patterns within the periodic table.

Electron configuration refers to the distribution of electrons among the orbitals of an atom. An important part of this configuration is the primary quantum number \(n\), which indicates the main energy level or 'shell' where an electron resides. For lithium, with its electron configuration \(1s^2 2s^1\), the primary quantum number is 2 for its valence electron. This number is fundamental in determining the overall energy and position of the electron within the atom.

As we explore elements with more electrons, these electrons fill up orbitals following a set of rules, including the Aufbau principle, Hund's rule, and the Pauli exclusion principle. These rules ensure that the electron configuration of each element reflects the lowest energy state possible. The primary quantum number increases as we move outwards from the nucleus, and understanding the quantum numbers helps chemists to predict an atom’s chemical behavior and various properties.

The periodic table is an organized chart of the elements arranged by increasing atomic number. Elements are positioned in specific periods (rows) based on their highest primary quantum number \(n\). The period number is equivalent to the value of \(n\) for the valence electrons of the element's atoms. For instance, the 6th period of the periodic table includes elements with valence electrons having \(n=6\), which is three times the \(n\) value of lithium's valence electron.

Representative elements, which include groups 1 to 2 and groups 13 to 18, showcase a wide range of chemical properties. The group number (for groups 1 to 18) typically represents the number of valence electrons for the elements in the main-group elements. By understanding the periodic table's structure, one can infer information about an element's properties and reactivity simply based on its position. For those aiming to understand chemistry at a deeper level, mastering the layout and the underlying principles of the periodic table is considered crucial.