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Question
Calculate the percentage efficiency of packing in case of simple cubic cell.
Solution
Simple cubic unit cell:
a. In a simple cubic lattice, the atoms are located only on the corners of the cube. The particles touch each other along the edge.
b. Thus, the edge length or side of the cube ‘a’, and the radius of each particle, ‘r’ are
related as a = 2r
c. The volume of the cubic unit cell = a3 = (2r)3 = 8r3
d. Since a simple cubic unit cell contains only 1 atom,
The volume of one atom (occupied space) = `4/3pir^3`
e. Packing efficiency = `"Volumeof oneatom"/"Volumeof cubicunit cell"xx100%`
`=(4/3pir^3)/(8r^3)xx100=pi/6xx100`
`=52.36%~~52.4%`
f. The packing efficiency of simple cubic metal crystal is 52.4 %.
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