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))`

Answer

`19.41 g cm^(-3)`

Explanation

Density, `rho = (Z xx M)/(a^3 xx N_A)`
For fxx unit cell, `r = a/(2sqrt(2))`
`a = 2sqrt(2) r = 2 xx 1.414 xx 0.144`
`= 0.407 nm = 0.407 nm = 0.407 xx 10^(-7) cm`
`rho = (4 xx (197 g mol^(-1)))/((0.407 xx 10^(-7) cm)^(3) xx (6.022 xx 10^(23) mol^(-1)))`
`= 19.41 g cm^(-3)`.