The compound CuCl has Zns structure. Its density is 3.4 g `cm^(-3)`. What is the length of the edge of the unit cell ?

Answer

578 pm

Explanation

We know that `a^(3)=(ZxxM)/(rhoxxN_(0))`
According to available data,
Formula mass of CuCl (M) `=63.5+35.5="99 g mol"^(-1)`
No. of atoms per unit cell`(Z) = 4" "(because` ZnS has fcc structure)
Avogadro's number `(N_(0))=6.022xx10^(23)"mol"^(-1)`
Density of unit cell `(rho)=3.4"g cm"^(-3)`
`a^(3)=(4xx("99 g mol"^(-1)))/((3.4gcm^(-3))xx(6.022xx10^(23)mol^(-1)))=193.3xx10^(-24)cm^(3)`
`a=(193.3xx10^(-24)cm^(3))^(1//3)=5.78xx10^(-8)cm = "578 pm."`