Explain why vanadium (radius = 134 pm) and copper (radius = 128 pm) have nearly identical atomic radii, even though the atomic number of copper is about 25% higher than that of vanadium. Predict the relative densities of these two metals. Look up the densities in a reference book, periodic table, or on the Internet to check if your predictions are correct.

Verified step by step guidance

1. Step 1: Understand that atomic radius is influenced by the number of electron shells and the effective nuclear charge. As you move across a period in the periodic table, the atomic number increases, but the additional electrons are added to the same shell, increasing the effective nuclear charge and pulling the electrons closer to the nucleus.
2. Step 2: Recognize that vanadium (V) and copper (Cu) are both transition metals. Transition metals have electrons filling the d subshell, which can lead to similar atomic radii due to the balance between increased nuclear charge and electron shielding.
3. Step 3: Consider that the atomic radius of copper is slightly smaller than that of vanadium, despite copper having a higher atomic number. This is due to the increased effective nuclear charge in copper, which pulls the electrons closer to the nucleus.
4. Step 4: Predict the relative densities of vanadium and copper. Density is mass per unit volume, and since copper has a higher atomic mass and a slightly smaller atomic radius, it is likely to have a higher density than vanadium.
5. Step 5: To verify the prediction, look up the densities of vanadium and copper in a reference book or online. Compare the actual densities to your prediction to see if they align.

Key Concepts

Atomic Radius

Atomic radius refers to the size of an atom, typically measured from the nucleus to the outermost electron shell. It can vary based on the number of electron shells and the effective nuclear charge experienced by the outer electrons. In transition metals like vanadium and copper, the presence of d-electrons influences the atomic radius, often leading to similar sizes despite differences in atomic number.

Effective Nuclear Charge

Effective nuclear charge (Z_eff) is the net positive charge experienced by an electron in a multi-electron atom. It accounts for the shielding effect of inner-shell electrons, which reduces the full nuclear charge felt by outer electrons. In the case of vanadium and copper, the increase in protons in copper is offset by increased electron shielding, resulting in similar atomic radii.

Density of Metals

The density of a metal is defined as its mass per unit volume and is influenced by both atomic mass and atomic structure. For metals, density can be predicted by considering the atomic mass and the arrangement of atoms in the crystal lattice. Although copper has a higher atomic number than vanadium, its density is also affected by its atomic packing and the mass of its atoms, leading to a comparison of their relative densities.