Question

Copper crystal has a face -centred cubic lattice structure. Atomic radius of copper atom is 128 pm. Calculate the density of copper . Atomic mass of copper = 63.5
or Copper crystallises into a fcc lattice, its edge length is ` 3.62 xx 10^(-8)` cm. Calculate the dinsity of copper (atomic mass of Cu= 63.5 u, ` N_(A) = 6.022 xx 10^(23) "mol"^(-1)`)

Answer 1

Correct Answer - `10.71 " g cm"^(-3)`
For fcc , `r= a/sqrt2 or a = 2sqrt2r = 2xx 1.414 xx 128"pm"` = 362 pm
`p = (Z xx M)/(a^(3) xx N_(0)) = ( 4xx 63.5 "g mol"^(-1))/((362xx10^(-10)"cm")^(3) xx (6.02 xx 10^(23)"mol"^(-1)))= 8.9"cm"^(-3)`
Alternatively, `p = ( "mass of unit cell")/("volume of unit cell") = ( 4xx(63.5 "g mol"^(-1)//6.02xx10^(23)"mol"^(-1)))/((362xx 10^(-10)"cm")^(3))= 8.9 "g cm"^(-3)`