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Question

A crystal is made of particles X ,Y and Z. X forms fcc packing. Y occupies all the octahedral voids of X and Z occupies all the tetrahedral voids of X. If all the particles along one body diagonal are removed, then the formula of the crystal would be :

A
XYZ2
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B
X2YZ2
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C
X8Y4Z5
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D
X5Y4Z8
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Solution

The correct option is D X5Y4Z8
In fcc, a total of 4 octahedral and 8 tetrahedral voids are present.
So, it contains 4 Y, 4 Z and 4 X atoms but all the particles along one body diagonal are removed.
Number of Y atoms =41=3
Number. of X atoms =41/4=15/4and
No. of Z atoms =82=6 so
Compound is X15/4Y3Z6=X5Y4Z8

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