Copper crystallises with face centred cubic unit cell . If the radius of copper atom is 127.8 pm , calculate the density of copper metal.
(Atomic mass of Cu = 63.55 u and Avogadro's number `N_(A) = 6.02 xx 10^(23) mol^(-1)`) Multiply the answer with 100

Answer

894

Explanation

For a fcc unit cell, edge length (a) is related to radius of atom as :
`r = a/(2sqrt(2))`
or `" " a = 2sqrt(2).r = 2 xx 1.414 xx 127.8`
`= 361.42 p m`
or `" " = 361.42 xx 10^(-10) cm`
Since the lattice is fcc, the number of copper atoms per unit cell, Z = 4
Density, `rho = (Z xx M)/(a^3 xx N_A)`
`M = 63.55 u, N_A = 6.02 xx 10^(22)`
`:. rho = (4 xx 63.55)/((361.42 xx 10^(-10))^(3) xx (6.02 xx 10^(23)))`
`= 8.94 g cm^(-3)`.