1.

Calculate the efficiency [percentage of volume occupied and unoccupied] of packing in case of a metal crystal for simple cubic.

Answer»

Solution :For simple cubic `a=2r`.
`"Efficiency "=("Volume OCCUPIED by all spheres")/("Total volume of cube")XX100`
`"Efficiency "=((4)/(3)PIR^(3))/((2r)^(3))xx100 =(4xxpixxr^(3))/(3xx8xxr^(3))xx100=(pi)/(6)xx100=(22)/(7xx6)xx100=(2200)/(42)=52.4%`
Percentage of volume occupied `=52.4%`.
Percentage of volume UNOCCUPIED `=47.6%`.


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