Silver having atomic mass 107.87 crystallizes in faces centred cubic structure. If density is `10.76"gcm"^(-3)` calculate the edge length of unit cell.

Explanation

Molar mass of silver, `M=107.87"g mol"^(-1)`
`d=10.75"g cm"^(-3)`
`N_(A)=6.002xx10^(23)"mol"^(-1)`
z(f.c.c. lattice) = 4
`d=(ZxxM)/(a^(3)xxN_(A))`
`a^(3)=(ZxxM)/(d xxN_(A))`
`=(4xx107.87"g mol"^(-1))/(10.75"g cm"^(-3)xx6.022xx10^(23)"mol"^(-1))`
`=6.667xx10^(-23)"cm"^(3)=66.65xx10^(-24)"cm"^(3)`
`a=(66.65)^(1//3)xx10^(-8)"cm"`
`{:[("Let"x=(66.65)^(1/(3))),("log"x="log"(66.65)^(1/3)=1/(3)"log"66.65),("log"x=1/(3)xx1.8238=0.6079),(x="antilog"0.6079=4.05)]:}`
`a=4.05xx10^(-8)"cm"`
`=4.05xx10^(-8)xx10^(10)"pm"`
`a=405"pm"`