Which periodic trend is partially responsible for the observation that the maximum oxidation state of the transition-metal elements peaks near groups 7 \(\mathrm{B}\) and 8 \(\mathrm{B} ?\) (a) The number of valence electrons reaches a maximum at group 8 \(\mathrm{B} .\) (b) The effective nuclear charge increases on moving left across each period. (c) The radii of the transition-metal elements reach a minimum for group \(8 \mathrm{B},\) and as the size of the atoms decreases it becomes easier to remove electrons.

The concept of an oxidation state is integral to understanding how elements interact in chemical reactions. In essence, the oxidation state reflects the degree of oxidation of an atom within a compound. It's denoted by integers, which can be positive, negative, or zero, and represents the hypothetical charge that the atom would have if all bonds to unlike atoms were 100% ionic.

Consider water (H2O) as an example: the oxygen has an oxidation state of -2, while each hydrogen has an oxidation state of +1. This illustrates how electrons are unequally shared, with the more electronegative oxygen atom having a greater share of the electrons.

Oxidation states also play a crucial role in redox reactions, which involve the transfer of electrons between species. An increase in the oxidation state corresponds to oxidation, while a decrease corresponds to reduction. Therefore, recognizing how oxidation states change helps predict the chemical behavior and reaction pathways of elements.

The effective nuclear charge (often symbolized as Z_eff) is a concept used to explain how strongly electrons are held in an atom. It's the net positive charge experienced by electrons in the valence shell, after accounting for the shielding effect of other electrons. As a basic rule, the effective nuclear charge increases from left to right across a period in the periodic table. This occurs because as protons are added to the nucleus, the overall positive charge increases, but the added electrons mainly populate the same shell, providing minimal additional shielding.

Understanding Z_eff is crucial because it affects atomic radius, ionization energy, and an element's ability to attract electrons in chemical bonds (its electronegativity). Higher effective nuclear charges result in tighter hold on the electrons, higher ionization energies, and generally increase an atom's tendency to assume higher oxidation states, which are often required for the formation of certain compounds.

The atomic radius is a measure of the size of an atom. It can be thought of as the distance from the nucleus to the outer boundary of the electron cloud. Atomic radius generally decreases across a period on the periodic table as Z_eff increases—and vice versa: it increases down a group as additional electron shells are added, which are further from the nucleus and less tightly bound due to the shielding effect.

The size of atoms has a profound impact on their chemical properties, including their oxidation states. Smaller atoms can achieve higher oxidation states more easily than larger ones. For transition metals, this is partly because the electrons are closer to the nucleus and held more tightly, which stabilizes the higher oxidation states. Additionally, smaller atomic radii facilitate the overlap of orbitals during bond formation, which is essential in polyatomic ions and complex compounds where transition metals often exhibit their maximum oxidation states.