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 2.7g `cm^(-3)`, what is the nature of the cubic unit cell?

Explanation

Density,
`d=(Z xx M)/(a^3 xx N_A)` or `Z=(d xx a^3 xx N_A)/(M)` ...(i)
According to the given data,
`M = 27 g mol^(-1), a=4.05 xx 10^(-8)` cm, `d = 2.7 g cm^(-3), N_A = 6.022 xx 10^(23) mol^(-1)`
Substituting these values in expression (i), we get
`Z=(2.7 g cm^(-3) xx (4.05 xx 10^(-8) cm)^3 xx 6.022 xx 10^(23) mol^(-1))/(27 g mol^(-1))` = 3.99 = 4
Since, there are 4 atoms of the element present per unit cell, the cubic unit cell must be face centred.