Question

Calculate the radius of tetrahedral void present in the unit cell of an atom X which crystallizes in fcc unit cell having an edge length $a=50\sqrt{2}pm$

• A. $5.62pm$
• B. $\sqrt{2}pm$
• C. $0.12pm$
• D. $\sqrt{3}pm$

Answer 1

The correct option is A $5.62pm$

In a fcc/ccp unit cell :
There are 8 tetrahedral voids, 2 at each body diagonals.
For fcc:
$\sqrt{2}a=4\times R$
Here R is the radius of the atom X
$\Rightarrow \sqrt{2}\times 50\sqrt{2}=4RR=25pm$

For a tetrahedral void :
$r=0.225R$
Here r is the radius of tetrahedral void and R is the radius of the atom X
$r=(0.225\times 25)pmr=5.625pm$