What physical property depends on the ability of a material's electrons to move freely?

The correct answer is the property that describes how well a material can conduct electricity, which is directly related to the freedom of movement of its electrons. When electrons in a material can move freely, they can carry an electric charge, leading to higher electrical conductivity.

In metals, for instance, the structure of the atoms allows electrons to be less tightly bound to their respective nuclei, enabling them to flow easily when an electric field is applied. This is why metals are typically good conductors of electricity, as they have a high density of free electrons.

In contrast, other properties like thermal conductivity, optical clarity, and viscosity do not rely primarily on the movement of electrons. Thermal conductivity relates to how well heat energy is transferred through a material, which can involve vibrations of atoms as well as the movement of free electrons, but is not solely dependent on electron mobility. Optical clarity pertains to how light passes through a material and is influenced by its molecular structure rather than electron movement. Viscosity, on the other hand, is a measure of a fluid's resistance to flow, which is related to intermolecular forces rather than the behavior of electrons.

Thus, the ability of a material's electrons to move freely is most accurately reflected in its electrical conductivity.