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Calcium has a cubic closest packed structure as a solid. Assuming that calcium has an atomic radius of \(197 \mathrm{pm}\), calculate the density of solid calcium.

Nickel has a face-centered cubic unit cell. The density of nickel is \(6.84 \mathrm{~g} / \mathrm{cm}^{3}\). Calculate a value for the atomic radius of nickel.

A certain form of lead has a cubic closest packed structure with an edge length of \(492 \mathrm{pm} .\) Calculate the value of the atomic radius and the density of lead.

Iridium (Ir) has a face-centered cubic unit cell with an edge length of \(383.3 \mathrm{pm}\). Calculate the density of solid iridium.

A metallic solid with atoms in a face-centered cubic unit cell with an edge length of \(392 \mathrm{pm}\) has a density of \(21.45 \mathrm{~g} / \mathrm{cm}^{3}\). Calculate the atomic mass and the atomic radius of the metal. Identify the metal.

Barium has a body-centered cubic structure. If the atomic radius of barium is \(222 \mathrm{pm}\), calculate the density of solid barium.

The radius of gold is \(144 \mathrm{pm}\), and the density is \(19.32 \mathrm{~g} / \mathrm{cm}^{3}\). Does elemental gold have a face-centered cubic structure or a body-centered cubic structure?

The radius of tungsten is \(137 \mathrm{pm}\) and the density is \(19.3 \mathrm{~g} / \mathrm{cm}^{3}\). Does elemental tungsten have a face-centered cubic structure or a body-centered cubic structure?

What fraction of the total volume of a cubic closest packed structure is occupied by atoms? (Hint: \(V_{\text {sphere }}=\frac{4}{3} \pi r^{3}\).) What fraction of the total volume of a simple cubic structure is occupied by atoms? Compare the answers.

Iron has a density of \(7.86 \mathrm{~g} / \mathrm{cm}^{3}\) and crystallizes in a bodycentered cubic lattice. Show that only \(68 \%\) of a body-centered lattice is actually occupied by atoms, and determine the atomic radius of iron.