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)
  • CCadmium (density 8.65 g/cm3)
  • DSilicon (density 2.33 g/cm3)
  • ERed phosphorus (density 2.34 g/cm3)

Q2:

A metal has an atomic packing density of 68%. 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 M occupy half of the octahedral holes between anions of element L. The mass of the L ion is 66.57% less than the mass of the M ion. As a percentage of the total mass, how much of the material is made up of element M?

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

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