An element with molar mass `2.7 xx 10^(-2)" kg mol"^(-1)` forms a cubic unit cell with edge length 405 pm. If the density is `2.7 xx 10^(3)" kg m"^(-3)`, what is the nature of the cubice unit cell?

Explanation

`"Density, d"=(zxxM)/(a^(3)xxN_(A))" "(rho)=(nM)/(a^(3)N_(A))`
`therefore" "n=(rhoxxa^(3)xxN_(A))/(M)=((2.7xx10^(3)"kg m"^(-3))(4.05xx10^(-10)m)^(3)(6.022xx10^(23)mol^(-1)))/(2.7xx10^(-2)" kg mol"^(-1))`
`=3.99=4`
Thus, there are 4 atoms of elements present per unit cell, hence, the cubic unit cell must be face - centred or cubic close - packed (ccp).