Silver metal crystallises with a face centred cubic lattice. The length of the unit cell is found to be `3.0xx10^(-8)`cm. Calculate atomic radius and density of silver.
Molar mass of Ag`=108 g mol^(-1), N_(A)=6.02xx10^(23)mol^(-1)`).

Explanation

`a=3xx10^(-8)cm, M=108g//mol `
`f.c.c.z =4Na=6.02xx10^(23)mol^(-1)`
For f.c.c. `a=2sqrt(2r)rArr r=(a)/(2sqrt(2))xx(sqrt(2))/(sqrt(2))`
`r=(asqrt2)/(4)`
`r=(3xx10^(-8) xx1.414)/(4)=1.06xx10^(-8) cm`
`d=(ZM)/(a^3xxNa)`
`d=(4xx108)/((3xx10^(-8))^(3)xx6.02xx10^(23))`
`d=2.66xx10^(1)`
`d=26.6g//cm^(3)`