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)`)

Explanation

For fcc , Z = 4 , Atomic mass (M) = 63.554 , r = 127.8 pm , d = ? ?
Avogardo number `N_(A) = 6.02 xx 10^(23) g mol^(-1)`
`d = (Z xx M)/(a^(3) xx N_(A)) " " [ because` In Fc.c. structure `sqrt2` a = 4 r]
`a = (4 xx r)/(sqrt2) = (4 xx 127.8)/(1.414) = 361. 52` pm
`d = (4 xx 63.55)/(6.02 xx 10^(23) xx (3.61 xx 10^(-8))^(3))`
`d = 0.89 xx 10^(1) = 8.9 gm cm^(-3)`