calculate the avagadro number if iron crystallises as fcc and its density is 2.8g/cm^3 . if the volume of unit cell is 56.38 * 10^-24 cm^3/unit cell ( atomis mass = 56 )

1.Density= 2.8 g/cm³.

  As it crystallises in fcc lattice ,

  i.e.there are '8' Iron atoms at the corners and there contribution is 1/8.

      and 6 at 6 faces of the cube

     and atoms at the faces contribute=1/2.

    Therefore, total no. of Iron atoms per cube,(Z)=(8*1/8+6*1/2)=(1+3)=4 atoms.

 

Density=mass/volume

volume=(56.38*10^-24)cm³/unit cell.

mass of single = Z*(56)/N_A,  where N_{A=Avogadro's number.}

Therefore, density*volume=Z*(55.84)/N_A.

2.8*56.84=4*56/N_A.

N_A=4*56/2.8*56.84.