Silver metal crystallizes with a face centred cubic lattice. The length of the unit cell is found to be `4.077 xx 10^(-8)` cm. Calculate atomic radius and density of silver. (Atomic mass of Ag = 108 u, `N_A = 6.02 xx 10^(23) mol^(-1)`)

Explanation

(i) `d = (Z xx M)/(a^3 xx N_A)" "...(1)`
According to the given data:
`a =4.077 xx 10^(-8)` cm, Z=4, M = 108 g `mol^(-1)`, `N_A=6.02 xx 10^(23) g mol^(-1)`
Substituting these values in the expression (1), we get
`d=(4 xx 108 g mol^(-1))/((4.077 xx 10^(-8) cm)^3 xx 6.022 xx 10^(23) mol^(-1))`
= 10.58 g `cm^(-3)`
`r=(a)/(2sqrt2)=(4.077 xx 10^(-8) cm)/(2sqrt2) = 1.44 xx 10^(-8) cm`