Question

The height of a $HCP$ unit cell is $5.715$ $\text{Å}.$ What is the volume of the unit cell in ${\text{Å}}^3$ ?

• A. $91$
• B. $182$
• C. $273$
• D. $82.5$

Answer 1

Answer: (B)

The height of the $HCP$ unit cell $=4\sqrt{\frac{2}{3}}.r=5.715$
$\text{r}=\frac{5.715\times \sqrt{3}}{\sqrt{2}\times 4}=1.75\text{Å}$
The base area of the unit cell $=6\sqrt{3}{r}^2$
The volume of the unit cell $=basearea\times$ $\text{height}=24\sqrt{2}{\text{r}}^3=181.8$ ${\text{Å}}^3$