Question

Iron is a solid phase of iron still unknown to science. The only difference between it and ordinary iron is that Iron forms a crystal with an fcc unit cell and a lattice constant . Calculate the density of Iron.

Answer 1

The question is incomplete. The complete question is :

Iron β is a solid phase of iron still unknown to science. The only difference between it and ordinary iron is that Iron β forms a crystal with an fcc unit cell and a lattice constant, a = 0.352 nm. Calculate the density of Iron β.

Solution :

The density is given by :

$\rho = \frac{ZM}{a^3N_0} \ \ g/cm^3$         ..................(i)

Here, Z = number of atoms in a unit cell

         M = atomic mass

         $N_0$ = Avogadro's number = $6.022 \times 10^{23}$

          a = edge length or the lattice constant

Now for FCC lattice, the number of atoms in a unit cell is 4.

So, Z = 4

Atomic mass of iron, M = 55.84 g/ mole

Given a  = 0.352 nm = $3.52 \times 10^{-8}$ cm

From (i),

$\rho = \frac{ZM}{a^3N_0}$      

$\rho = \frac{4 \times 55.84}{(3.52 \times 10^{-8})^3 \times 6.022 \times 10^{23}}$

  $= 8.51 \ \ g \ cm ^{-3}$

Therefore, the density of Iron β is $8.51 \ \ g \ cm ^{-3}$.