If 'a' is the length of the side of the cube, the distance between the body centered atom and one corner atom

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Q. If 'a' is the length of the side of the cube, the distance between the body centered atom and one corner atom in the cube will be

(a)

\dfrac{2}{\sqrt{3}}a

(b)

\dfrac{4}{\sqrt{3}}a

(c)

\dfrac{\sqrt{3}}{4}a

(d)

\dfrac{\sqrt{3}}{2}a

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Step 1. The full body diagonal of a cube of edge a is $\sqrt{3}\,a$ (from $AG^2 = AC^2+CG^2 = 2a^2+a^2=3a^2$ , so $AG=\sqrt{3}a$ ).

Step 2. The body-centre atom sits at the exact midpoint of this body diagonal. …

Q.If 'a' is the length of the side of the cube, the distance between the body centered atom and one corner atom in the cube will be