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Show in case of body centered cube only 68% the space is occupied and rest is unoccupied.

Asked by Topperlearning User 16th June 2016, 3:54 PM
Answered by Expert
Answer:

Atom in the body diagonal will be in touch with other two atoms diagonally. 

In Δ EFD ,

b2 = a2 +a2= 2a2,

b= √2a

Now in ΔAFD

c2 = a2+b2 = a2 + 2a2  = 3a2

c =  √3a

√3a = 4r

r = √3/4 x a

Volume of the cube = a3 will be equal to a3 = [4/√3 x r]3.

Packing efficiency = volume occupied by two spheres in the unit cell x 100 / total volume of the unit cell   %

= 2 x (4/3) Πr3 x 100/ [(4/√3)r]3  %

=(8/3) Πr3  x100 / 64/(3√3)r3  %  =  68%.

Answered by Expert 16th June 2016, 5:54 PM
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