Question

The edge lengths of the unit cell in terms of the radius of spheres constituting fcc, bcc and simple cubic unit cell are respectively:

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

Answer 1

The correct option is A $2\sqrt{2r},\frac{4r}{\sqrt{3}},2r$

In FCC: The atoms at the face diagonals touch each. If $a$ is the edge length of cube and $r$ is the radius of the atom.

So, $\sqrt{2}a=4r$

$\Rightarrow a=2\sqrt{2}r$

In bcc: The atoms at the body diagonal touch each other.

So, $\sqrt{3}a=4r$

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

In simple cubic: The atoms at the corners touch each other.

So, $a=2r$