The correct answer is option 2: Atomic number.

To understand why atomic number is the most fundamental characteristic of an element, let`s analyze the other options.

Melting point (option 1) is the temperature at which a substance transitions from a solid to a liquid state. While melting point can vary for different elements, it is not a fundamental characteristic as it depends on factors like molecular structure and intermolecular forces.

Color (option 3) is not a fundamental characteristic of an element as it can vary depending on the chemical compounds that the element is involved in.

Atomic weight (option 4) is the average weight of the isotopes of an element, taking into account their abundances. While atomic weight provides useful information, it is not as fundamental as atomic number.

On the other hand, atomic number (option 2) represents the number of protons in the nucleus of an atom, which determines the element`s identity. Each element has a unique atomic number that differentiates it from other elements. Atomic number also determines the arrangement of electrons and the element`s position in the periodic table. Therefore, atomic number is considered the most fundamental characteristic of an element.