Question

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 Round your answer to 3 significant digits. cm

Answer 1

8.60 g/cm³

Step-by-step explanation:

In the lattice structure of iron, there are two atoms per unit cell. So:

`(2)/(a^(3) ) = (N_(A) )/(V_(molar) )` where
`V_(molar) = (A)/(\rho )` an and A is the atomic mass of iron.

Therefore:

`(2)/(a^(3) ) = (N_(A) * p )/(A)`

This implies that:

`A = (\frac{2A}{N_(A) * p)^{(1)/(3) } }`

=
`(4)/(√(3) )r`

Assuming that there is no phase change gives:

`\rho = (4A)/(N_(A)(2√(2r))^(3) )`

= 8.60 g/m³