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A two dimensional lattice of closest pac...

A two dimensional lattice of closest packed identical circles , indicating a suitable unit cell is represent as follows then the fractional void area is

A

`0.93`

B

`0.093`

C

`0.17`

D

`0.017`

Text Solution

Verified by Experts

The correct Answer is:
B
Let r be the radius of a circle. The unit cell shown in the figure is composed of two equilateral triangles, ABC and BCD, each with side 2r and s=32r, the area of the unit cell is `2(3r,r^(3))^(1//2)=2r^(2)sqrt(3)`.
The unit cell contains `(1)/(6)+(1)/(3)+(1)/(6)+(1)/(3)=1` circle of area `pir^(2)`. The fractional void area is
`(2r^(2)sqrt(3)-pir^(2))/(2r^(2)sqrt(3))=0.093`
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