Question

An element crystallises in fcc lattice having edge length $350pm$. Maximum radius of the atom which can be placed in the interstitial site without distorting the structure is

• A. $58.55pm$
• B. $117pm$
• C. $51.23pm$
• D. $83pm$

Answer 1

The correct option is C $51.23pm$

For fcc structure,

$\left(\frac{r+}{r-}\right)=0.414\text{for octahedral void}$

$=0.225\text{for tetrahedral void}$

Thus, maximum radius can be for octahedral void

$\therefore r_{+}=0.414r_{-}$

Also, $r_{-}=\frac{a}{2\sqrt{2}}$

$\therefore r_{+}=0.414\frac{a}{2\sqrt{2}}=0.414\times \frac{350}{2\sqrt{2}}=\frac{144.9}{2\sqrt{2}}=51.23pm$
Hence, (C) is the correct option.