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.


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)


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


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


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

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


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 49.9%‎ 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?


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


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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