Question

Gold has a face centered cubic unit cell and has the density 𝟏𝟗. 𝟑 𝒈 𝒄𝒎−𝟑 . Calculate the length along an edge. (𝐴𝑢 = 197 𝑔 𝑚𝑜𝑙 −1 ) 

Answer 1

For FCC crystal structure $n=\frac{1}{8}\cdot8+\frac{1}{2}\cdot6=4$ atoms per unit cell and $V=a^3$ .

$\rho=\frac{n\cdot M}{V\cdot N_A}=\frac{n\cdot M}{a^3\cdot N_A}\to a=(\frac{n\cdot M}{\rho\cdot N_A})^{1/3}=$

$=(\frac{4\cdot 0.197}{19300\cdot 6.023\cdot10^{23}})^{1/3}=4.077\cdot10^{-10}\ (m)$ . Answer