Question

The length of the unit cell edge of a body-centered cubic metal crystal is $352$ pm. Calculate the radius (in pm) of an atom of the metal.

• A. $152.4$
• B. $15.2$
• C. $14.2$
• D. $182.0$

Answer 1

The correct option is A $152.4$

In a bcc unit cell, the atoms touch each other along the body diagonal.

So, if the radius of the atom is $r$, then body diagonal $=r+2r+r=4r$
From the geometry of a cube, body diagonal $=\sqrt{3}\times \text{edge length}=\sqrt{3}a$
Then, $4r=\sqrt{3}\times a$ or radius of metal atom $=\frac{\sqrt{3}}{4}\times a$
$r=\frac{\sqrt{3}}{4}\times a=\frac{\sqrt{3}}{4}\times 352=152.4$ pm