Question

An element has a bcc structure having unit cells $12.08\times {10}^{23}$. Find the total number of atoms in these unit cells.

• A. $24.16\times {10}^{23}$
• B. $12.08\times {10}^{23}$
• C. $36.24\times {10}^{23}$
• D. $6.02\times {10}^{23}$

Answer 1

The correct option is A $24.16\times {10}^{23}$

Each bcc unit cell has a total of 2 atoms - one from the eight corner atoms contribting 1/8 each and one from the atom sitting at the cube centre.
$\text{No. of atoms at corners}=\frac{1}{8}\times 8=1\text{No. of atoms at centre}=\frac{1}{1}\times 1=1\text{No. of atoms per unit cell}=1+1=2$

$\text{Total number of atoms}=2\times \text{Total number of unit cells}=2\times 12.08\times {10}^{23}=24.16\times {10}^{23}$