The conductivity of metals is indeed attributed to the mobility of their valence electrons, which are relatively loosely bound compared to inner-shell electrons. While it is true that in heavier metals the valence electrons are farther from the nucleus, other factors come into play that contribute to the higher conductivity of silver compared to heavier metals.
Electron Mobility: In metals, the valence electrons form a "sea" of delocalized electrons that are free to move throughout the metal lattice. Silver has a relatively high electron mobility due to its crystal structure and the strength of the metallic bonding. The valence electrons in silver experience less scattering and are more mobile, facilitating the flow of electric current.
Electron Density: Silver has a high electron density, meaning it has a relatively large number of valence electrons per unit volume. The presence of a higher number of mobile electrons enhances the conductivity because there are more electrons available to participate in the conduction process.
Band Structure: The electronic band structure of metals also plays a role in their conductivity. In the case of silver, the energy bands that correspond to the valence and conduction electrons overlap, allowing easy movement of electrons. This overlapping of energy bands is favorable for conducting electricity.
Ionization Energy: The ionization energy required to remove a valence electron from an atom also influences the conductivity of a metal. While the valence electrons in heavier metals may be further from the nucleus, they may also experience stronger effective nuclear charges due to increased atomic number. This results in higher ionization energies, making it more difficult for the valence electrons to become mobile and participate in electrical conduction.
Overall, while the distance between valence electrons and the nucleus is a factor to consider, other factors such as electron mobility, electron density, band structure, and ionization energy collectively contribute to the higher conductivity of silver compared to heavier metals.