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 = 27 g mol ^(-1)`
Edge length `(alpha) = 4. -5 xx 10 ^(-8) cm`
Density, d=2.7 g `cm^(-3)`
Apply the relation,
`d = ( Z xx M)/( alpha ^(2) 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 alpha ^(3) xx N _(A))/( M)`
`= ( 2.7 g cm ^(-3) xx ( 4. 05 xx 10 ^(-8) cm ) ^(3) xx 6. 0 22 xx 10 ^(25) mol ^(-1))/( 27 g mol ^(-1))`
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.