Chemistry - Solid State Question with Solution | TestHub

For a face-centered cubic (fcc) unit cell, the atoms touch each other along the face diagonal.

The relationship between the edge length $a$ and the atomic radius $r$ is given by:

$4r=\sqrt{2}a$

$r=\frac{a}{2\sqrt{2}}$

Given $a=3.61\times 10^{-8}\text{cm}$.

Substituting the value of $a$:

$r=\frac{3.61\times 10^{-8}}{2\times 1.414}$

$r=\frac{3.61\times 10^{-8}}{2.828}$

$r=1.276\times 10^{-8}\text{cm}\approx 1.28\times 10^{-8}\text{cm}$

Answer: $1.28\times 10^{-8}\text{cm}$