Chromium has a body-centered cubic unit cell How many atoms of rm Cr are present in each unit cell?

Answer 1

1) Use the Pythagorean Theorem to calculate d, the edge length of the unit cell:d2 + (d√2)2 = (4r)2

3d2 = 16r2

d2 = (16/3) (1.25 x 10-8 cm)2

d = 2.89 x 10-8 cm

2) Calcuate the volume of the unit cell:(2.89 x 10-8 cm)3 = 2.41 x 10-23 cm3

3) Calcuate the mass inside the unit cell:each atom: 52g mol-1 / 6.022 x 1023 mol-1 = 8.64 x 10-23g two atoms/unit cell: 8.64 x 10-23g x 2 = 1.73 10-23g

4) Density = mass/volume = 1.73 10-23g / 2.41 x 10-23 cm3 = 7.17g/cm3

Answer 2

There is one chromium atom at each corner of the cube, contributing 1/8 of an atom to the unit cell. Additionally, there is one chromium atom in the center of the cube, which contributes 1 whole atom. Therefore, there are 2 atoms of chromium in a body-centered cubic unit cell.

Answer 3

(8/8)+1=2

Answer 4

2