Question

Percentage of free space in a body-centred cubic unit cell is:

• A. $34$
• B. $28$
• C. $30$
• D. $32$

Answer 1

The correct option is D $32$

Packing fraction = $\frac{\text{Volume occupied by atoms in a unit cell}}{\text{Volume of the unit cell}}$

For Body centered cubic cell , Packing fraction = $\frac{2\times \frac{4}{3}\pi \times r^3}{{\left(\frac{4r}{\sqrt{3}}\right)}^2}$ = $\frac{\sqrt{3}\pi }{8}=0.68$

where ,edge length a= $\frac{4r}{\sqrt{3}}$

Therefore, volume occupied = $68\%$

Hence vacant volume = $32\%$

So correct answer is option $D$.