1. Tardigrade
  2. Question
  3. Chemistry
  4. The edge lengths of the unit cells in terms of the radius of spheres constituting fcc, bcc and simple cubic unit cell are respectively

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

The Solid State

Solution:

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, $\sqrt{2} a =4 r$
$
\Rightarrow a =2 \sqrt{2} r
$
In bcc: The atoms at the body diagonal touch each other.
So, $\sqrt{3} a=4 r$
$
\Rightarrow a =\frac{4}{\sqrt{3}} r
$
In simple cubic: The atoms at the corners touch each other. So, $a=2 r$