Question

'$C$' represent the height of the HCP unit cell and '$a$' represent edge length of the hexagonal surface of the HCP unit cell. What is the value of $\frac{C}{a}$?

• A. $\sqrt{\frac{2}{3}}$
• B. $\sqrt{\frac{8}{3}}$
• C. $\sqrt{\frac{32}{3}}$
• D. $\sqrt{\frac{3}{2}}$

Answer 1

The correct option is B $\sqrt{\frac{8}{3}}$

In HCP unit cell, the relationship between height and radius is
$C=4r\sqrt{\frac{2}{3}}$
$a=2r$
$\therefore \frac{C}{a}=2\sqrt{\frac{2}{3}}=\sqrt{\frac{8}{3}}$