38. Plot the densities of the second row transition metals (Y to Cd) as a function of Z. Explain the trend in terms of metallic bonding.
Based on the simple mass to volume ratio, the density is expected to increase from Y to Cd (mass increases and atomic size decreases because of increasing Z*). Clearly this is only true up to Ru. The role of metallic bonding is to change the internuclear distance between atoms, thereby affecting the volume portion of the density. The valence orbitals used to fill bands are the 5s and 4d, for a total of 6 orbitals creating 6 energy bands. Up to Mo, these bands will be half-filled and all filled orbitals will be bonding or nonbonding in character. This decreases the distance between atoms and increases the density. For Tc and Ru, the electrons are filling mainly nonbonding orbitals, so the density continues to increase because of the increased mass of the atoms. From Rh to Cd antibonding orbitals are being filled, which decreases the net bonding and increases the internuclear distance, thereby leading to a decrease in density.