For a crystal of copper potassium sulphate,

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Quantum Mechanics · Symmetry, angular momentum and spin

The Boundary-Value Problem, Ch Diamagnetism, paramagnetism and magnetic susceptibility

Problem

\mathrm{CuK_2(SO_4)_2\cdot6H_2O}

, the

\mathrm{Cu^{2+}}

ion density is

N_v = 5.0\times10^{26}\,\mathrm{m^{-3}}

. A published Curie plot gives the reciprocal volume susceptibility

T = 2\,\mathrm{K}

1/\chi_m = 422

T = 10\,\mathrm{K}

1/\chi_m = 2111

((a)) Find the slope of

1/\chi_m

against

T

and hence the Curie constant

C

(in kelvin). ((b)) Extract the effective moment

m

per ion in Bohr magnetons and compare with

g_J\sqrt{S(S+1)}\,\mu_B

for

\mathrm{Cu^{2+}}

(

S = 1/2

L = 0

, quoted

g_J = 2.2

). ((c)) A sample of the same salt sits in

B = 0.5\,\mathrm{T}

T = 4.2\,\mathrm{K}

(liquid helium temperature). Evaluate

\mu_BB/k_BT

and decide whether this sample is close to saturation.