Worksheet: Density of a Cubic Lattice

In this worksheet, we will practice calculating the density of a cubic lattice using the molecular formula, lattice parameters, and Bravais lattice type.

Q1:

Thallium(I) iodide crystallises with the same type of cubic lattice as cesium chloride. The edge length of the unit cell is 4.20 Å and the radius of the iodide ion is 2.16 Å.

Calculate the radius of a thallium ion in this structure.

Calculate the density of thallium(I) iodide.

Q2:

Lithium hydride crystallises with the same type of cubic lattice as sodium chloride. The edge length of the unit cell is 4.083 Å. Assume that there is contact between the hydride ions along the face diagonal of the unit cell.

Calculate to 3 significant figures the radius of a hydride ion in this structure.

  • A 1.82 Å
  • B 1.36 Å
  • C 1.02 Å
  • D 1.44 Å
  • E 1.76 Å

Calculate to 3 significant figures the density of lithium hydride.

  • A 0.776 g/cm3
  • B 0.652 g/cm3
  • C 0.727 g/cm3
  • D 0.741 g/cm3
  • E 0.582 g/cm3

Q3:

Magnesium oxide crystallises with the same type of cubic lattice as sodium chloride. The edge length of the unit cell is 4.212 Å. Assume that there is contact between the oxide ions along the face diagonal of the unit cell.

Calculate the radius of an oxide ion in this structure.

  • A 1.40 Å
  • B 1.88 Å
  • C 2.11 Å
  • D 1.49 Å
  • E 1.82 Å

Calculate the density of magnesium oxide.

  • A 3.58 g/cm3
  • B 2.87 g/cm3
  • C 3.63 g/cm3
  • D 3.42 g/cm3
  • E 2.69 g/cm3

Q4:

Barium has a body-centred cubic unit cell with an edge length of 5.025 Å.

Calculate the radius of a barium atom in this structure.

Calculate the density of barium.

Q5:

Tungsten has a body-centred cubic unit cell with an edge length of 3.165 Å.

Calculate the radius of a tungsten atom in this structure.

Calculate the density of tungsten to 3 significant figures.

Q6:

L i C l and K C l both have face-centred cubic unit cells. The unit cell of L i C l has an edge length of 0.514 nm, while the unit cell of K C l has an edge length of 6.28 Å. There is contact between the potassium and chloride ions along the edge of the K C l cell, and between the chloride ions along the face diagonal of the L i C l cell. Assume that chloride ions have the same radii in the two salts.

Calculate the radius of a chloride ion in L i C l .

Calculate the radius of a potassium ion in K C l .

Calculate the density of L i C l .

Calculate the density of K C l .

Q7:

Silver has a face-centred cubic unit cell with an edge length of 409 pm.

Calculate the radius of a silver atom in this structure.

Calculate the density of silver.

Q8:

Calcium has a face-centred cubic unit cell with an edge length of 558.8 pm.

i) Calculate the radius of a calcium atom in this structure.

ii) Calculate the density of calcium.

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