Question

Packing efficiency by arrangement of atoms in two dimensional hexagonal close packing is

• A. 60.43
• B. 65.78
• C. 59.78
• D. 68.76

Answer 1

Answer: (A)

Let radius of the sphere $=r$
Area occupied by sphere in hexagonal close packing
$\pi r^2+6\times \left(\frac{1}{6}\times \pi r^2\right)=2\pi r^2$
Area of hexagonal $=6\times \left[\frac{\sqrt{3}}{4}\times (2r{)}^2\right]$
$6\times \frac{\sqrt{3}}{4}\times 4r^2=6\sqrt{3}\times r^2$
$\%$ occupied by $=\frac{2\pi r^2}{6\times \sqrt{3}\times r^2}\times 100$
$=\frac{2\times 3.14}{6\times \sqrt{3}}\times 100=60.43\%$