Packing Efficiency

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chemistry 12th class cbse notes

Packing efficiency is defined as the percentage of total space filled by the constituent particles in a crystal.

Packing efficiency in hcp and ccp structures:

Let us consider the unit cell of ccp in which sphere ABCDEFGH are occupied at corner. And sphere a,b,c,d,e,f are placed at centre of face.

Packing efficiency

Let the unit cell edge length be ‘a’ and face diagonal AC = b.

For calculation of packing efficiency consider the right angle triangle ABC. In triangle ABC

calculation of packing efficiency

Putting the value of AB, BC and AB in above eq..(1) we get

calculation of packing efficiency

If r is the radius of the sphere, we find

calculation of packing efficiency

By equating eq..(2) and (3) we get

calculation of packing efficiency

Number of atom per unit cell in ccp = 4

calculation of packing efficiency

Volume of cube = a3

Therefore,

calculation of packing efficiency

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