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Question

An atom Y crystallizes in fcc unit cell having an edge length a=2002 pm . What would be the radius of octahedral void present in the unit cell at the body centre?

A
100 pm
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B
141.4 pm
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C
73.2 pm
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D
22.5 pm
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Solution

The correct option is C 73.2 pm
For fcc:
2a=4×R
Here R is the radius of the atom Y
2×2002=4RR=100 pm

For a octahedral void :
r=0.414 R
Here r is the radius of tetrahedral void and R is the radius of the atom Y
r=(0.414×100) pmr=41.4 pm


In a fcc/ccp unit cell :
Octahedral Voids location :
1 at body centre and 12 voids at edge centres .
Contribution for voids at edges is 112
Contribution for body centre void is 1

Total octahedral voids :1+4×112=4
There are 4 octahedral voids per unit cell


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