Question

Calculate the ratio between C and a, if $‘C^{\prime }$ represent the height of the HCP unit cell and $‘a^{\prime }$ represent edge length of the hexagonal surface of the $HCP$ unit cell.

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

Answer 1

Answer: (B)

HCP is ABAB... type of structure, in which height of lattice means distance between two A A type layer.
As we know distance between two layers of ABAB... or ABCABC... type structure is $2\sqrt{\frac{2}{3}}r$ . where r is radius of atom and for HCP structure $a=2r$
so distance between 1st and 3rd layer will be
$C=2\sqrt{\frac{2}{3}}a=\sqrt{\frac{8}{3}}aso,\frac{C}{a}=\sqrt{\frac{8}{3}}$