If $\mathrm{a}$ the length of the side of a cube, the distance between the body centered atom one corner atom in the cube will be

In a regular cube let the edge length be $\mathrm{a}$.

Then the face diagonal will be $\sqrt{2}\mathrm{a}$

Body diagonal is $\sqrt{3}\mathrm{a}$.

The distance between the center of the cube and the corner is the half distance of the body diagonal i.e $\frac{\sqrt{3}\mathrm{a}}{2}$.