Chromium metal crystallizes as a body-centered cubic lattice. If the atomic radius of Cr is 1.25 angstroms, what is the density of Cr metal in grams per cubic centimeter? A) 2.76 g/cm³ B) 5.52 g/cm³ C) 7.18 g/cm³ D) 3.59 g/cm³ E) 7.81 g/cm³

Question

Quizplus · Accepted Answer

In a body-centered cubic (BCC) lattice, the relation between the atomic radius (r) and the edge length (a) is a = 4r/√3. For Cr, r = 1.25 Å, so a = 4(1.25)/√3 Å. The volume of the unit cell is a³. The BCC unit cell contains 2 atoms. The molar mass of Cr is 51.996 g/mol, and Avogadro's number is 6.022 x 10²³ atoms/mol. Density = (mass of atoms in unit cell)/(volume of unit cell). Calculating this gives approximately 7.18 g/cm³.

Chromium Metal Crystallizes as a Body-Centered Cubic Lattice