The density ( ρ ) of a simple cubic unit cell is calculated using: ρ=
Z⋅M
a3⋅NA
Where: Z= Number of atoms per unit cell (1 for simple cubic) M= Molar mass of the metal (g∕mol) a= Edge length of the unit cell (cm ) NA= Avogadro's Number (6.022×1023mol−1) Finding the Edge Length (a): a3=
21.5cm3mol−1
NA
a3=
21.5cm3mol−1
6.022×1023mol−1
a3=3.57×10−23cm3 a=3.29×10−8cm Calculating Density (ρ) :
ρ=
1.210gmol−1
(3.29×10−8cm)3⋅(6.022×1023mol−1)
ρ=9.77gcm−3 Answer: The density of the metal is 9.77g∕cm3.