A metal has a fcc lattice. The edge length of the unit cell is 404 pm. The density of the metal is `2.72 g cm^(-3)`? The molar mass of the metal is `(N_(A)" Avogadro's constant" = 6.02times10^(23) mol^(-1))`

Options

A. `40" g "mol^(-1)`
B. `30" g "mol^(-1)`
C. `27" g "mol^(-1)`
D. `20" g "mol^(-1)`

Answer

C

Explanation

`"Density " rho = (ZtimesM)/(a^(3)timesN_(A)times10^(-30))`
`therefore 2.72 = (4timesM)/((404^(3))times(6.02times10^(23))times10^(-30))`
`therefore M = (2.72times(404)^(3)times(6.02times10^(23))times10^(-30))/4`
=`27 g" " mol^(-1)`