The strength of metallic bonding generally decreases with an increase in the number of valence electrons. This is because the presence of more valence electrons leads to increased electron-electron repulsion, which weakens the metallic bond.
In a metallic bond, valence electrons are free to move within a "sea" of electrons shared among the metal atoms. These delocalized electrons create a strong attractive force between the positive metal ions and hold the metallic lattice together.
When the number of valence electrons increases, there are more electrons available in the electron cloud. As a result, the repulsive forces between these electrons become stronger. The increased electron-electron repulsion weakens the metallic bonding and reduces the overall strength of the bond.
Furthermore, an increase in the number of valence electrons also leads to an increase in the electron cloud's electron density. This increased electron density can cause greater electron-electron repulsion and reduce the ability of the metal ions to attract and hold onto the delocalized electrons.
Therefore, as the number of valence electrons increases, the strength of the metallic bond decreases due to increased electron-electron repulsion and a decrease in the effective attraction between the metal ions and the delocalized electrons.