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Question
Calculate the efficiency of packing in case of a metal crystal for simple cubic
Solution
Simple cubic - In a simple cubic lattice, the particles are located only at the corners of the cube and touch each other along the edge.
Let the edge length of the cube be ‘a’ and the radius of each particle be r.
So, we can write:
a = 2r
Now, volume of the cubic unit cell = a3
= (2r)3
= 8r3
We know that the number of particles per unit cell is 1.
Therefore, volume of the occupied unit cell = `4/3pir^3`
Hence, packing efficiency = `"Volume of one particle"/"Volume of cubic unit cell"xx100%`
= `(4/3pir^3)/8r^3xx100%`
= `1/6pixx100%`
=`1/6xx22/7xx100%`
= 52.4%
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