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 :

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

Here, Z = number of atoms in a unit cell

M = atomic mass

`$N_0$` = Avogadro's number =
`$6.022 * 10^(23)$`

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 =
`$3.52 * 10^(-8)$` cm

From (i),

`$\rho = (ZM)/(a^3N_0) $`

`$\rho = (4 * 55.84)/((3.52 * 10^(-8))^3 * 6.022 * 10^(23)) $`

`$= 8.51 \ \ g \ cm ^(-3)$`

Therefore, the density of Iron β is
`$ 8.51 \ \ g \ cm ^(-3)$`.