Question

An element crystallizes in FCC lattice of edge length $400$pm. Calculate the maximum diameter which can be placed in interstitial sites without distorting the structure.

• A. $125$pm
• B. $117$pm
• C. $102$pm
• D. $139$pm

Answer 1

The correct option is B $117$pm

We know that octahedral void is the largest void present in the FCC lattice.

If $R$ is the radius of octahedral void and $r$ is the radius of lattice sphere

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

$a$ is edge length.

$\Rightarrow r=\frac{400}{2\sqrt{2}}pm=141.12pm$ (Given $a=400pm$)

Now, for octahedral void,

$a=2(r+R)$

$\Rightarrow 2R=a-2r=400–2\times 141.12=171.16pm$

So, maximum diameter $=117.16pm$