Gold (atomic mass = 197 u) has atomic radius = 0.144 nm. It crystallises in face centred unit cell. Calculate the density of gold. (No = `6.022xx10^(23)mol^(-1))`

Explanation

Step-I. Calculate of edge length of unit cell.
For face centred cubic unit cell (f.c.c)
Edge length `(a)=2sqrt2r=2xx1.414xx144"pm"=407.23"pm"`
Step-II. Calculation of density of unit cell.
Density of unit cell `(rho)=(ZxxM)/(a^(3)xx"No"xx10^(-30))`
Edge length (a) = 407.21 pm=407.23
No. of atoms per unit cell (Z) = 4
Atomic mass of gold (M) = 197 u = `"197 g mol"^(-1)`
Avogadro's No. (No)=`6.022xx10^(23)mol^(-1)`
`"Density of unit cell"=(4xx("197 g mol"^(-1)))/((407.23)^(3)xx(6.022xx10^(23)"mol"^(-1))xx(10^(-30)"cm"^(3)))="19.38 g cm"^(-3)`