The unit cell of rhenium oxide is a cube with atoms touching along the edges. Since the O atoms are positioned along the edges, the length of the unit cell (a) can be found by adding the radius of an oxygen atom (73 pm) to the radius of a rhenium atom (137 pm) twice:
a = 2(73 pm + 137 pm) = 420 pm
Converting to cm, we have:
a = 420 pm × (1 cm/10⁻¹² m) = 4.2 × 10⁻⁵ cm
The volume of the unit cell can be found by taking the cube of the edge length:
V = a³ = (4.2 × 10⁻⁵ cm)³ = 7.62 × 10⁻¹⁴ cm³
Therefore, the volume of a unit cell in this crystal is 7.62 × 10⁻¹⁴ cm³.