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Question

Which among the following options give the correct relationship between the edge lengths ‘a’ and the radius of a sphere ‘r’ in a body-centered cubic structure.


A
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B
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C
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D
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Solution

The correct option is B

In EFD
b = a + a = 2a
Now in AFD
c2=a2+b2=a2+2a2=3a2
c=3a
The length of the body diagonal 'c' is equal to 4r, where r is the radius of the sphere (atom), as the three spheres along the diagonal touch each other.
Therefore, 3a=4r
a=4r3
r=34a


Chemistry

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