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Question

A body centered cubic lattice is made up of hollow shere of B. Sphere of solid A are present in hollow sphere of B. Radius of A is half of the radius of B. What is the ratio of total volume of sphere B unoccupied by A in unit cell and volume of unit cell?

A
29π364
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B
7π364
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C
19π364
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D
2π364
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Solution

The correct option is B 7π364
Effective number of atoms of B present in a unit cell=2
Total volume of B uncoupied by A in a unit cell=2×43(R3r3)×π=73πR3 (r=R2)
Volume of unit cell=a3
Again, in body centered cubic lattice, 3a=4R
a3=(4R3)3=6433R3
Ratio of total volume of sphere B unoccupied by A in unit cell and volume of unit cell
=73πR36433R3=7π364

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