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Worksheet: Packing Efficiency


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


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

  • AArsenic (density 5.73 g/cm3)
  • BSilicon (density 2.33 g/cm3)
  • CRed phosphorus (density 2.34 g/cm3)
  • DGermanium (density 5.32 g/cm3)
  • ECadmium (density 8.65 g/cm3)


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


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

  • AAAA
  • BABC
  • CABB
  • DABA


A metal has an atomic packing density of 6 8 % . Which type of lattice do the metal atoms form?

  • ASimple cubic
  • BFace-centered cubic
  • CHexagonal close-packed
  • DBody-centered cubic
  • EDiamond cubic


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

  • ABody-centered cubic
  • BSimple cubic
  • CFace-centered cubic
  • DDiamond cubic
  • EHexagonal close-packed


In a face-centred 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 ?

  • A42.9%
  • B74.9%
  • C60.0%
  • D59.9%
  • E49.9%