Copper has fcc crystal structure. Assuming an atomic radius of 130 pm for copper atom (Cu = 63.54) :
(a) What is the length of unit cell of Cu ?
(b) what is the volume of the unit cell ?
(c ) How many atoms belong to the unit cell ?
(d) Find the density of Cu.

Explanation

As we know
`rho = (n xx M_(m))/(N_(o)xx a^(3))`,
(a) For FCC structure
`4r = sqrt(2)a`
`a = 2sqrt(2)r`
`= 2sqrt(2)xx130 p m= 367.64 p m`
(b) Volume of unit cell `= a^(3)=(n xxM_(m))/(N_(o)xx rho)=(3.67xx10^(-8))^(3)=4.94xx10^(-23)cm^(3)`
(c ) n = 4
(d) `rho = (4xx63.54)/(6.023xx10^(23)xx(3.67xx10^(-8))^(3))=8.54 gm//cm^(3)`