Question

Iron crystallizes in a body-centered cubic unit. The edge of this cell is 287 pm. Calculate the density of iron

Answer 1

As we Know

Density = Mass/ Volume.

Therefore here

Mass is calculated for BCC unit cell i.e. for 2 atom.

Mass of One Atom = molar mass/ avogadro number.

= 55.845/6.023×10^23

=9.2720 × 10^-23 gram

Therefore for 2 atom I.e. for BCC unit cell

= 18.5440 × 10^-23 gram

Now volume = (edge)^3 I.e. (a)^3

Edge length =a= 287 pm = 287 ×10^-10 cm

a^3= (287×10^-10)^3

Volume =a^3=2.3640 × 10^-23 cm^3

Now density = Mass/ Volume

= (18.5440× 10^-23)/(2.3640×10^-23)

= 7.8443 gram / cm^3