Predict the number of valence electrons present in each of the following atoms (include the outermost d-electrons): (a) Bi; (b) Ba; (c) \(\mathrm{Mn}\); (d) Zn.

Transition metals are elements that occupy groups 3 to 12 on the periodic table. These metals are characterized by their unique ability to use the electrons in their d-orbital for bonding, which is not commonly observed in other elements. When calculating the number of valence electrons for transition metals, both the electrons in the outermost s subshell and the d-electrons from the penultimate shell are considered. This inclusion of d-electrons gives transition metals a variety of oxidation states and the capacity for complex chemical bonding.

For example, manganese (Mn), a transition metal, has a total of 7 valence electrons — 2 from the 4s subshell and 5 from the 3d subshell. The d-electrons play a vital role in forming metallic bonds and allow transition metals to act as catalysts in many chemical reactions due to their variable oxidation states.

The periodic table is a chart that organizes all known chemical elements based on their atomic number, electron configuration, and recurring chemical properties. Elements are listed in order of increasing atomic number in rows called periods. Columns, known as groups or families, contain elements with similar chemical behaviors due to their similar valence electron configurations.

Understanding the periodic table is crucial when predicting valence electrons. For main group elements, the group number can indicate the number of valence electrons. However, this rule does not always apply to transition metals. The periodic table also reveals trends in electronegativity, atomic size, and several other important chemical properties that are essential for understanding chemical bonding and reactions.

Electron configuration refers to the distribution of electrons in an atom's orbitals. Electrons fill subshells (s, p, d, f) in a manner that minimizes the energy of the atom. The way electrons are distributed among the orbitals of an atom explains the atom's chemical properties, including the types of bonds it can form and its reactivity.

For example, the electron configuration of zinc (Zn) is written as (4s² 3d¹⁰). The '4s' and '3d' describe quantum numbers that indicate the shell and subshell. The superscript shows that there are two electrons in the 4s subshell and ten electrons in the 3d subshell. When discussing valence electrons, these are the exterior and partially filled subshells that get involved in chemical bonding.

Chemical bonding is the force that holds atoms together in compounds. This bonding allows for the creation of stable molecules from atoms. The type and number of bonds that an atom can form largely depend on its valence electrons. The main types of chemical bonds include ionic, covalent, and metallic bonds.

Covalent bonding occurs when atoms share valence electrons, ionic bonding arises from the electrical attraction between positively and negatively charged ions, and metallic bonding is characterized by a 'sea' of shared electrons amongst metal cations. The valence electrons in transition metals, including both their s and d electrons, allow these elements to form a variety of bond types, leading to the vast array of compounds and materials we see around us.