Question

The empty space left in hcp in three-dimensions is__________.

• A. $26$%
• B. $74$%
• C. $52.4$%
• D. $80$%

Answer 1

The correct option is A $26$%

The space left in hcp in three-dimensions is 26%.
The space occupied by spheres in the hcp arrangement is 74%.

Packing fraction is

$\frac{6\times \frac{4}{3}\pi r^3}{a^{2}csin{60}^o}=0.74$

i.e. 74 %

The space left in hcp in three-dimensions is 26 %

a=2r, c=$2\sqrt{\frac{2}{3}}a$

Hence, the correct option is $\text{A}$