Question

	An electron spin can adopt either of two orientations in a magnetic field, and its energies are ±μB, where μ = 9.274 x 10-24 J/T is the Bohr magneton and B is the intensity of the magnetic field (often reported in teslas, T). Calculate the relative populations of upper to lower energy spin states at 4 K, the temperature of liquid helium. Take B = 1 T. Find the numerical value.

Answer 1

Population of a particular state at a particular temperature is given by the Boltzmann Distribution. For the upper energy spin state we can write this as

Whre n_u = number of electron in higher energy spin state

N = total number of electron

E_u =

k = Boltzmann constant

Similary we can write this for the electrons in lower energy spin state

E_l =

Given that T = 4 K

B = 1 Tesla

and

hence, the ratio of population of upper energy state to lower eneergy state is

Hence, the ratio of the populations in upper and lower energy state of electron spin at 4K is 0.4637.