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.

Answer

r = `1.44xx10^(8)cm; rho=10.58"g cm"^(-3)`

Explanation

Step I. Calculation of atomic radius
For b.c.c. lattice, `r=(sqrt2)/(4)a=(sqrt2)/(4)xx(4.077xx10^(-8)cm)=1.44xx10^(-8)cm`
Step II. Calculation of density of silver
Density `(rho)=(ZxxM)/(a^(3)xxN_(0)xx10^(-30)cm^(3))`
Z = 4 , M = 108 g `mol^(-1)`, a = `4.077xx10^(-8)cm, 407.7"pm", N_(0)=6.022xx10^(23)mol^(-1)`
`(rho)=(4xx("108g mol"^(-1)))/((407.7)^(3)xx(6.022xx10^(23)"mol"^(-1))xx(10^(-30)xx"cm"^(3)))=10.58"g cm"^(-3)`