Silver metal crystallises with a face centred cubic lattice. The length of unit cell is formed to be `4.077 xx 10^(-8)` cm. Calculate atomic radius and density of silver.
(Atomic mass of Ag = 108 u, `N_(A) = 6.023 xx 10^(23) mol^(-1)`).

Explanation

Given : `a = 4.077 xx 10^(-8)` cm, Z = 4, M = 108 g `mol^(-1)`
`N_(A) = 6.023 xx 10^(23)`
`d = (Z xx M)/(a^(3) xx N_(A))`
`= (4 xx 108)/((4.077 xx 10^(-8))^(3) xx 6.023 xx 10^(23))`
`= 6.22 g//cm^(3)`
For fcc `r = (a)/(2 sqrt(2))`
`= (4.077 xx 10^(-8) cm)/(2 sqrt(2))`
`= 1.44 xx 10^(-8)` cm