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What is the packing efficiency of a two dimensional square unit cell? Ans-78.54% how??

What is the packing efficiency of a two dimensional square unit cell?


Ans-78.54%


how??

Grade:12

3 Answers

Saurabh Anand
38 Points
10 years ago

in 2 dimensional.....a unit cell square contains 4 circles each having 1/4 contribution to the unit cell(we are talking about circle bcoz it is the case of 2-D not 3-D)....so effective no of circle will be 1 and area of circle is πr2 ....and 2r=a where a is the side of unit square cell....now use packing efficiency formula and u will get the answer..

kamlesh
13 Points
5 years ago
Area of square=L²
4R=√2L
R=L/2√2
% packing fraction=area of circle*100/area of square
2*πR²/L²
= 78.5%
Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

The diagonal is given as 4r, where r is the radius of an atom.
Diagonal = √L^2 + L^2 ​= √2L​
4r = √2L​or L = ​4r/√2​
Total area = L^2
or(​4r/√2​)^2 = 8r2
Number of spheres inside the square is
1 + 4(0.25​) = 2
Area of each sphere = πr^2
Total area of spheres = 2×πr^2
Packing fraction = Totalareaofspheres/Totalarea​
= 2×πr2​/8r^2
= π/4
​= 0.785
So, the percentage fraction is 78.5%

Thanks and Regards

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