In a solid material, such as a metal, the conduction band refers to the range of energy levels available for electrons to move freely and participate in electrical conduction. The conduction band is typically formed by the overlap or delocalization of atomic orbitals in the crystal lattice.
In the case of a metal with the electronic configuration 1s2 2s2 2p6 3s1, the valence electron is indeed the 3s1 electron. Valence electrons are the outermost electrons that participate in chemical bonding and are typically involved in determining the material's properties.
The 2s2 and 2p6 electrons, being in lower energy levels, will still be present in their respective atomic orbitals within the metal. However, these electrons are not directly involved in conduction. Instead, they contribute to the overall stability of the metal lattice and are responsible for the metallic bonding that holds the metal atoms together.
In metallic bonding, the valence electrons are delocalized and can move freely throughout the lattice, creating a "sea" of mobile electrons. When an electric field is applied, these delocalized electrons can move in response, leading to electrical conduction. Therefore, it is the 3s1 electron in this case that would be in the conduction band and contribute to the metal's conductivity.