Solid State

Given Values:
The edge length a=288pm. The density (ρ) is 7.2g∕cm3. The mass given is 208 g .
Step 1: Find volume of one unit cell
The edge length must be changed to centimeters: 1pm=10−10cm. So: a=288×10−10cm.
The volume of one unit cell is: V=a3=(288×10−10)3cm3=2.389×10−23cm3
Step 2: Find total volume that 208 g will occupy
V‌total ‌=‌

m

ρ

=‌

208

7.2

=28.89cm3
Step 3: Find the number of unit cells in 208g
‌ Number of unit cells ‌=‌

V‌total ‌

V‌unit cell ‌

=‌

28.89

2.389×10−23

=1.209×1024
Step 4: Find the total number of atoms
A body centered cubic (bcc) unit cell has 2 atoms per unit cell.
So, Total atoms = Number of unit cells ×2=1.209×1024×2=2.42×1024 which is the same as 24.2×1023.