An atom X crystallizes in fcc unit cell having an edge length $a=100\sqrt{2}pm$ . What would be the radius of tetrahedral void present in the unit cell?

The correct option is C $11.25pm$
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
$\Rightarrow \sqrt{2}\times 100\sqrt{2}=4RR=50pm$

For a tetrahedral void :
$r=0.225R$
Here r is the radius of tetrahedral void and R is the radius of the atom X
$r=(0.225\times 50)pmr=11.25pm$