Chemistry - Solid State Question with Solution | TestHub

For a face-centered cubic (fcc) unit cell, the relationship between the edge length $a$ and the atomic radius $r$ is given by:

$a=2\sqrt{2}r$

Given $r=128\text{ pm}$.

$a=2\times 1.414\times 128\text{ pm}$

$a=361.984\text{ pm}\approx 362\text{ pm}$

Converting the edge length into cm:

$a=362\times 10^{-12}\text{ m}=362\times 10^{-10}\text{ cm}=3.62\times 10^{-8}\text{ cm}$

Answer: $3.62\times 10^{-8}\mathrm{cm}$