In a simple model of paramagnetism, we can consider that some fraction f of the molecules have their magnetic moments aligned with the external magnetic field and that the rest of the molecules are randomly oriented and so do not contribute to the magnetic field.

(a) Use this model and Curie's law to show that at temperature T and external magnetic field B the fraction of aligned molecules is f = μB/3kT.

(b) Calculate this fraction for T = 300 K, B = 1 T, assuming μ to be 1 Bohr magneton.