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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
a=34r
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B
r=a22
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C
r=34a
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D
r=a2
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Solution

The correct option is C r=34a

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


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