Explain why vanadium (radius =134 pm ) and copper (radius =128 pm ) have nearly identical atomic

step 1 So now we'll work on problem 102. In this problem, we're asked to explain why vanadium radius of

Explain why vanadium (radius =134 pm ) and copper (radius...

Explain why vanadium (radius $=134 \mathrm{pm}$ ) and copper (radius =128 $\mathrm{pm}$ ) have nearly identical atomic radii, even though the atomic number of copper is about 25$\%$ higher than that of vanadium. What would you predict about the relative densities of these two metals? Look up the densities in a reference book, periodictable, or on the Internet. Are your predictions correct?

Key Concepts

Atomic Radius

Atomic radius refers to the size of an atom, typically defined by the distance from the nucleus to the outermost electrons. In transition metals, even though more electrons are added as the atomic number increases, the overall size does not increase dramatically because additional electrons often enter inner orbitals or d subshells that do not contribute as strongly to the outer boundary of the electron cloud. This leads to only a modest change in radius even when the number of protons and electrons increases noticeably.

Effective Nuclear Charge and Electron Shielding

Effective nuclear charge is the net positive charge experienced by outer electrons after accounting for the repulsion from inner electrons. In transition metals, the electrons added to d orbitals do not shield each other very effectively. As a result, even though a metal like copper has a higher atomic number than vanadium, the increase in effective nuclear charge (owing to poor shielding by the d electrons) tends to pull the outer electrons closer, resulting in an atomic radius that is very similar to that of vanadium.

Metallic Crystal Structure and Density

Metal density is determined by both the mass of individual atoms and how these atoms are packed together in the solid state. While copper and vanadium have similar atomic sizes due to their effective nuclear charge and electron shielding characteristics, copper’s atoms are heavier because of its higher atomic mass. With a crystal structure that permits similar packing efficiencies, the increased mass per atom in copper results in a higher density compared to vanadium. This prediction aligns with experimental values, where copper is observed to be denser.

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