An element with molar mass `2.7 xx 10^(2) kg mol^(-1)` forms a `2.7 xx 10^(3) kg^(-3)`, what is the nature of the cubic unit cell?

Explanation

We know that `rho=(ZxxM)/(a^(3)xxN_(0)xx10^(-30))orZ=(rhoxxa^(3)xxN_(0)xx10^(-30))/(M)`
Edge length of unit cell (a) = 405 pm = `405xx10^(-12)m=4.05xx10^(-10)m` ltbRgt Molar mass of unit cell (M) = `2.7xx10^(-2)"kg mol"^(-1)`
Density of the unit cell `(rho)=2.7xx10^(3)"kg m"^(-3)`
Avogadro's No. `(N_(0))=6.022xx10^(23)"mol"^(-1)`
`Z=((2.7xx10^(3)"kg m"^(-3))xx(4.05xx10^(-10)m)^(3)xx(6.022xx10^(23)"mol"^(-1)))/((2.7xx10^(-2)"kg mol"^(-1)))=3.99~=4`
Since there are four atoms per unit, the cubic unit cell must be face centred (fcc) or cubic close packed (ccp).