block elements can exhibit variable number of oxidation states.

Oxidation states or oxidation numbers are numbers assigned to individual atoms within a compound. These numbers represent the number of electrons an atom can lose, gain, or share when forming a chemical bond with another atom. It helps us keep track of electron transfers in chemical reactions, especially oxidation-reduction (redox) reactions.

Block elements are classified based on the type of atomic orbitals that are being filled with electrons. There are four types of block elements: s-block, p-block, d-block, and f-block. 1. S-block elements: These elements have their outermost electrons in the s orbitals. Examples are alkali metals (Group 1) and alkaline earth metals (Group 2). 2. P-block elements: These elements have their outermost electrons in the p orbitals. Examples include elements in Groups 13 to 18. 3. D-block elements: These elements have their outermost electrons in the d orbitals, and are also known as transition metals. They belong to Groups 3 to 12. 4. F-block elements: These elements have their outermost electrons in the f orbitals. They are also known as inner transition metals, which include the lanthanides and actinides series.

Block elements exhibit variable oxidation states due to three main factors: 1. Atomic size: A larger atomic size allows the atom to accommodate more electrons; thus, resulting in multiple oxidation states. 2. Energy levels: The difference in energy levels between the atomic orbitals can impact the stability of the electrons, affecting their ability to be involved in chemical reactions. 3. Shielding effect: The shielding effect refers to the ability of inner electrons to shield outer electrons from the attractive force of the nucleus. This effect influences the ease with which the atom can lose or gain electrons to form chemical bonds, leading to variable oxidation states.

D-block and f-block elements are particularly prone to having variable oxidation states due to their electron configurations. The d and f orbitals are close in energy levels, leading to multiple possible electron configurations and, subsequently, different oxidation states. For example, iron (Fe) is a d-block element, specifically a transition metal. It has an electron configuration of [Ar] 3d^6 4s^2, where [Ar] represents the configuration of the noble gas Argon (18 electrons). Iron can lose two electrons from the 4s orbital, forming Fe^(2+), or it can lose two more from the 3d orbital, forming Fe^(3+). Thus, iron can exhibit multiple oxidation states (Fe^(2+) and Fe^(3+)).

To summarize, block elements can exhibit variable oxidation states due to factors such as atomic size, energy levels, and shielding effect. The d-block and f-block elements, in particular, demonstrate multiple oxidation states because of their electron configurations that involve closely spaced energy levels in d and f orbitals.