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 cubic unit cell ?

Explanation

We shell apply the relation :
`d=(zM)/(a^(3)N_(A)) or z=(da^(3)N_(A))/(M)`
Here, `d=2.7gcm^(-3), a=4.05xx10^(-8)cm, M="27 g mol"^(-1) and N_(A)=6.022xx10^(23)" atoms mol"^(-1)`
Substituting the values in the equation, we have
`z=("2.7 g cm"^(-3)xx(4.05xx10^(-8))^(3)cm^(3)xx6.022xx10^(23)" atoms mol"^(-1))/("27 g mol"^(-1))`
`=(2.7xx(4.05)^(3)xx10^(-24)xx6.022xx10^(23))/(27)" atoms = 4 atoms"`
The element has a face - centred cubic cell.