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.
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=4r√3
→r=√34a