Question

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

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

Answer 1

Answer: (B)

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