An element with molar mass2.7 xx 10^(-2) "mol"^(-1)forms a cubic unit cell with edge length 405 pm. If its density is 2.7xx10^3 kg m^(-3),what is the nature of the cubic unit cell ?

An element with molar mass2.7 xx 10^(-2) "mol"^(-1)forms a cubic unit

1.	An element with molar mass2.7 xx 10^(-2) "mol"^(-1)forms a cubic unit cell with edge length 405 pm. If its density is 2.7xx10^3 kg m^(-3),what is the nature of the cubic unit cell ?
Answer» Solution :Density , `rho=(ZxxM)/(a^3xxN_0) "or" Z=(rhoxxa^3xxN_A)/M` Here, M (MOLAR mass of the element )=`2.7xx10^(-2)"kg MOL"^(-1)` a (edge length) =405 pm =`405xx10^(-12) m =4.05xx10^(-10) m` `rho` (density) =`2.7xx10^3 "kg m"^(-3)` `N_A` (AVOGADRO's number )=`6.022xx10^23 "mol"^(-1)` Substituting these values in expression (i), we GET `Z=((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 3 atoms of the element present per unit cell. Hence, the cubic unit cell must be face-centred or cubic close packed (ccp)