Worksheet: Packing Efficiency

In this worksheet, we will practice calculating the packing efficiencies of crystal lattices from the atomic or ionic radii and the Bravais lattice type.

Q1:

Which of the following elemental materials contains the fewest atoms per unit volume?

• AGermanium (density 5.32 g/cm3)
• BArsenic (density 5.73 g/cm3)
• DSilicon (density 2.33 g/cm3)
• ERed phosphorus (density 2.34 g/cm3)

Q2:

A metal has an atomic packing density of . What type of lattice do the metal atoms form?

• ASimple cubic
• BFace-centered cubic
• CBody-centered cubic
• DDiamond cubic
• EHexagonal close-packed

Q3:

Calculate to the nearest percent the packing density of the carbon atoms in diamond.

Q4:

Which of the following lattice structures has the lowest packing density?

• AFace-centered cubic
• BSimple cubic
• CBody-centered cubic
• DDiamond cubic
• EHexagonal close-packed

Q5:

In a face-centered cubic ionic lattice, cations of element occupy half of the octahedral holes between anions of element . The mass of the ion is ‎ less than the mass of the ion. As a percentage of the total mass, how much of the material is made up of element ?

Q6:

In a close-packed system, what percentage of the unit cell is occupied by holes?

Q7:

Fill in the blank: In a hexagonal close-packed system, the metal atom caps are arranged in an pattern.

• ABBB
• BABC
• CABB
• DABA
• EAAA