Lustre, electrical and thermal conductivity of metals can be explained by the theory of:

Sea of free electrons

The lustre, electrical and thermal conductivity of metals can be explained by the theory of sea of free electrons. So the answer is (3) Sea of free electrons.

In the sea of free electrons model, the valence electrons of metal atoms are delocalized and free to move throughout the metal. These free electrons are responsible for the metallic properties of metals, including their lustre, electrical and thermal conductivity.

When light hits a metal surface, the free electrons are excited and absorb the light energy. This causes the electrons to oscillate at the same frequency as the light wave. The oscillating electrons then emit light of the same frequency, which is reflected back to the observer. This is why metals have a shiny lustre.

Free electrons are also responsible for the electrical conductivity of metals. When an electric field is applied to a metal, the free electrons are forced to move in the direction of the electric field. This creates a current flow through the metal.

Free electrons are also responsible for the thermal conductivity of metals. When heat is applied to one end of a metal, the free electrons at that end absorb the heat energy and begin to move faster. This causes the electrons to collide with other electrons and transfer the heat energy to them. The process continues until the heat energy is distributed evenly throughout the metal.

Other types of forces, such as dipole-dipole interactions, Coulombic forces and London forces, are not able to explain the metallic properties of metals.