Q.

The fraction of total volume occupied by the atoms present in a simple cube is

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a

π32

b

π42

c

π4

d

π6

answer is D.

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Detailed Solution

Volume of cube =a3Volume of unit cell =1×43πr3=43π(a2)3=πa36∴ packing fraction =πa36a3=π6                                                                                  ORIn simple cubic latticepacking fraction = volume occupied by one atomvolume of one cubic unit cell                    =43πr3(2r)3 =  43πr38r3                                           =  π6=0.524
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The fraction of total volume occupied by the atoms present in a simple cube is