Question

The packing efficiency of the two dimensional unit cell show below is

• A. 39.27%
• B. 68.02%
• C. 74.05%
• D. 78.54%

Answer 1

The correct option is D

78.54%

$P.E=\frac{\text{Area occupied by effective atoms}}{\text{Area of square}}\times 100$

The relationship here is that the diagonal = 4r, or $2a^2=16r^2;a=2\sqrt{2}r$

$=\frac{2\times \pi r^2}{(2\sqrt{2}r{)}^2}\times 100=\frac{2\pi r^2}{8r^2}\times 100$

$=\frac{\pi }{4}\times 100=78.54\%$