Question

Gold (atomic mass 197 u) crystallises in a face-centred unit cell. What is its atomic radius if the edge length of the gold unit cell is $0.407\times {10}^{-9}m$?

• A. 0.115 nm
• B. 0.144 nm
• C. 0.156 nm
• D. 0.235 nm

Answer 1

The correct option is B 0.144 nm

Edge length of the Gold unit cell $\left(a\right)=0.407\times {10}^{-9}m$
For FCC unit cell, the atomic radius $r=\frac{\sqrt{2}a}{4}$
$r=\frac{\sqrt{2}\times 0.407\times {10}^{-9}m}{4}$
$r=0.144nm.$