Question

Chromium crystallizes with a body-centered cubic unit cell. The radius of a chromium atom is 125 pm . Calculate the density of solid crystalline chromium in grams per cubic centimeter. Express the density in grams per cubic centimeter to three significant figures.

Answer 1

Begin by finding the mass of the unit cell. Obtain the mass of an chromium atom from its molar mass. Since the BCC unit cell contains 2 atoms per unit cell, multiply the mass of chromium by 2 to get the mass of a unit cell.

m (Cr atom) = 51.99 x 1 / 6.023 x 10²³ = 8.63 x 10^-23

m (unit cell) = 8.63 x 10^-23 x 2 atoms = 17.26 x 10^-23

compute the edge length (l) of the unit cell (in m) from the atomic radius of aluminum. For the face-centered cubic structure, d = 4r/ √3 = 4x 125 x 10^-12 / √3 = 2.886 x 10^-10 m        

Compute the volume of the unit cell (in cm) by converting the edge length to cm and cubing the edge length. (We use centimeters because we want to report the density in units of g/cm3.)

V = l³

   = (2.886 x 10^-10/10^-2)³

   = 2.437 x 10^-23

Density = m(unit cell) / V = 17.26 x 10^-23  /2.437 x 10^-23   = 7.082478 g/cm3