Solid State - Result Question 20

####20. The packing efficiency of the two-dimensional square unit cell shown below is

(2010)

(a) 39.27

(b) 68.02

(c) 74.05

(d) 78.54

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Answer:

Correct Answer: 20. (d)

Solution:

  1. Contribution of circle from corner of square =14

Effective number of circle per square

=14×4+1( at centre )=2

Area occupied by circle =2πr2,r= radius.

Also, diagonal of square 4r=2L, where L= side of square.

Packing fraction = Area occupied by circles  Area of square 

=2πr2L2=2πr28r2=π4=0.785

packing efficiency =78.5.



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