Derive a relationship between molar mass, density of the substance and unit cell edge length.(b) Define - paramagnetic solids.

Answer:

(a) Let the edge length of a cubic unit cell be \(a\), the number of atoms (formula units) per unit cell \(n\), molar mass \(M\) and Avogadro’s number \(N_A\).

Volume of unit cell \(= a^3\). Mass of one atom \(= M/N_A\), so mass of the unit cell \(= n\,M/N_A\).

Density \(\rho = \dfrac{\text{mass of unit cell}}{\text{volume of unit cell}} = \dfrac{nM}{a^3 N_A}\), hence \(M = \dfrac{\rho\, a^3 N_A}{n}\).

(n = 1 for simple cubic, 2 for bcc, 4 for fcc.)

(b) Paramagnetic solids: solids containing atoms, ions or molecules with unpaired electrons, which are weakly attracted by an external magnetic field but lose their magnetism when the field is removed, e.g. O₂, Cu²⁺ and Fe³⁺ salts.