Question

In face centred cubic unit cell edge length is:

• A. $\frac{4}{\sqrt{3}}r$
• B. $\frac{4}{\sqrt{2}}r$
• C. $2r$
• D. $\frac{\sqrt{3}}{2}r$

Answer 1

Answer: (B)

In face centred cubic unit cell the spheres occupy all the eight comers of the cube and also the centre of the six faces of the cube. A sphere at the centre of the face is shared by two unit cells and therefore makes a contribution of only 1/2 to a particular unit cell. The radius of the atom $(r)=\frac{a}{2\sqrt{2}}$ a (edge length) $=2\sqrt{2}r$ $r=\frac{2\sqrt{2}r\times \sqrt{2}}{\sqrt{2}}$ $=\frac{4r}{\sqrt{2}}$