In a solid metal sample how are valence electrons distributed

The valence electrons in a solid metal sample are delocalized or evenly distributed throughout the metal structure.

Explanation:

The atoms of a metal in a metal sample are held together in crystal lattice structures by means of metallic bonds. The valence electrons of each atom in a metal are not held to that atom alone but are contributed to an electron cloud surrounding the atoms. Each atom becomes positively charged and are located at the center of crystal lattice while the electrons surround the positively charged nucleus of the atoms. Thus, the atomic nucleus of each are held together by the moving electron cloud and overlapping residual electron orbits.

This model of metallic crystal structure is known as the electron-sea model of bonding in metals. This model of metallic structure accounts for some properties of metals such as high electrical and thermal conductivity as well as ease with which metals are deformed. Since the electrons are not tightly-bound to any single atom but are free to move about, hence, metals are very good conductors of electricity. Similarly, collisions between metal ions transfer energy to neighboring ions and are responsible for their high thermal conductivity. Also, metals are easily deformed because the metal ions can easily change position without having to break any specific bonds.