Question

Aluminium crystallises in a face-centred cubic lattice. The edge length of the unit cell of aluminium is 4.05 x 10^-10m. What is the density of aluminium? (Atomic mass of Al=27)

(a) 2700 kg m^-3

(b) 3000 kg m^-3

(c) 2400 kg m^-3

(d) 2100 kg m^-3

I have been asked this question by my college professor while I was bunking the class.

My doubt stems from Solid State topic in portion Solid State of Chemistry – Class 12

Answer 1

Right option is (a) 2700 kg m^-3

The explanation is: Given,

Atomic mass (M)=27 amu

For FCC structure, Z=4

Avogadro’s number (N0) = 6.02 x 10^23

Edge length of the Al unit cell (a)= 4.05 x 10^-10m

The density of aluminium (ρ) = (Z x M)/(a^3 X N0)

                                                      = (4 x 27)/((4.05 x 10^-10) ^3 x 6.02 x 10^23)

                                                      = 2700 kg m^-3.