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Question

A body centred cubic lattice is made up of hollow spheres of B. Spheres of solid A are present inside the hollow spheres of B. If the radius of A is half the radius of B, what is the ratio of the total volume of spheres of B unoccupied by A in a unit cell and the volume of the unit cell?

A
7π364
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B
73128
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C
7π24
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D
None of these
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Solution

The correct option is A 7π364
Volume of A spheres in the unit cell = 4πr33
Volume of B spheres in the unit cell = 4πr3×83
Hence, unoccupied volume = VolumeBVolumeA = 7×4πr33
For BCC, 3a=4R, here R=2r
Total volume of unit cell = a3=(4(2r)3)3
Hence, ratio = unoccupied volumevolume of unit cell = 7π364

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