Which among the following options give the correct relationship between the edge

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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.

Options:

A . a=√34r

B . r=a2√2

C . r=√34a

D . r=a2

Answer: Option C
:
C
In

△ E F D

,
b = a + a = 2a
Now in

△ A F D

c^{2} = a^{2} + b^{2} = a^{2} + 2 a^{2} = 3 a^{2}

\to c = \sqrt{3 a}

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,

\sqrt{3 a} = 4 r

a = \frac{4 r}{\sqrt{3}}

\to r = \frac{\sqrt{3}}{4} a

Which Among The Following Options Give The Correct Relations...

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