Answer
The percentage change in the unit cell is 97.6%.
Work Step by Step
Given $R_{bcc}=0.12584 nm$ and $R_{fcc}=0.12894 nm$
unit cell length: $a_{bcc}=\frac{4}{\sqrt{3}}R_{bcc}$
$a_{bcc}=\frac{4}{\sqrt{3}}\times 0.12584 $
unit cell length: $a_{fcc}=\frac{4}{\sqrt{2}}R_{bcc}$
$a_{fcc}={2\sqrt{2}}\times 0.12894 $
volume of bcc unit cell
$(a_{bcc})^3=(\frac{4}{\sqrt{3}}\times 0.12584)^3 nm^3$
$(a_{bcc})^3=0.024545 nm^3$
volume of fcc unit cell
$(a_{fcc})^3=(\frac{4}{\sqrt{3}}\times 0.12894)^3 nm^3$
$(a_{bcc})^3=0.048506 nm^3$
percentage change=$\frac{(a_{fcc})^3-(a_{bcc})^3}{(a_{bcc})^3}\times 100$
percentage change=$\frac{0.048506-0.024545}{0.024545}\times 100=97.6$
The percentage change in the unit cell is 97.6%.
