Silver metal crysatllises with a face centred cubic lattice. The length of the unit cell is found to be `4.077xx10^(-8)cm`. Calulate the atomic radius and density of silver.

Explanation

Edge length of unit cell, `a = 4.077 xx 10^(-8) cm`
For fcc lattice, radius of an atom is related to edge length, a as :
`r = a/(2sqrt(2)) = (4.077 xx 10^(-8))/(2 xx 1.414) = 1.441 xx 10^(-8) cm`
Density, `rho = (Z xx M)/(a^3 xx N_A)`
`= (4 xx 108)/((4.077 xx 10^(-8))^(3)(6.02 xx 10^(23)))`
`( :. Z = 4 ` for fcc)
`= 10.58 g cm^(-3)`