An element with molar mass 27 g `"mol"^(-1)` forms a cubic unit cell with edge length `4.05 xx 10^(-8)` cm. If its density is 2.7 g `cm^(-3)`, what is the nature of the cubic unit cell?

Explanation

Given, molar mass of the given element
M = 27g `"mol"^(-1)`
Edge length `(a)= 4.05 xx 10^(-8)` cm
Density, `d=2.7"g cm"^(-3)`
Apply the relation, `d=(Z xx M)/(a^(3)xx N_(A))`
where, Z is the number of atoms in the unit cell and `N_(A)` is the Avogadro.s number,
Thus, `Z=(d xx a^(3) xx N_(A))/(M)`
`=(2.7g cm^(-3) xx (4.05 xx 10^(-8)cm)^(3)xx6.022 xx 10^(23) "mol"^(-1))/(27"g mol"^(-1))=4`
Since, the number of atoms in the unit cell is four, the given, cubic unit cell has a face-centred cubic (fcc) or cubic-closed packed (ccp) structure.