Final answer:
In a solid metal sample, valence electrons are shared among many metal ions, forming a sea of electrons characteristic of metallic bonding.
Step-by-step explanation:
In a solid metal sample, valence electrons are not localized to individual atoms but are instead distributed among many metal ions. This is due to the nature of metallic bonding, where the metal atoms exist as cations arranged in a crystal lattice, with the valence electrons free to move about as a sea of electrons. This sea of electrons surrounds the metal cations and facilitates the conductivity and malleability of the metal.
Therefore, the correct answer to the question "In a solid metal sample, how are valence electrons distributed?" is option B) Valence electrons are shared among many metal ions. This sharing of electrons is characteristic of the metallic bond, which is distinctly different from covalent or ionic bonding where electrons are either shared between specific atoms or transferred to form ions.