Aluminium crystallizes in a cubic lattice with an edge of 404 pm and density of metal is 2.70 g/ `cm^(3)`. What type of cubic is formed by aluminium ?

Explanation

If there is "n" aluminium atoms per unit cell :
`Density (rho)=(nM)/(N_(A)a^(3))`
`implies`2.70=`(nxx270)/(6.023xx10^(23)(4.04xx10^(-8)cm))^(3)`
`impliesn=6.023xx10^(22)(4.04xx10^(-8))^(-3)= 3097~~4`
Hence, Al forms face-centred cubic (FCC) lattice. the coordination number of Al in FCC is 12 i.e., each Al atom has twelve other Al atoms in its nearest neighbour.

An atom of aluminium (solid black) present on the centre of middle vertical face is equidistant from the twelve adjoining atoms, hence, coordination number of an atom in FCC arrangement is twelve.