5.23 A sample of paramagnetic salt contains 2.0 × 1024 atomic dipoles each of dipole moment 1.5 × 10–23 J T–1. The sample is placed under a homogeneous magnetic field of 0.64 T, and cooled to a temperature of 4.2 K. The degree of magnetic saturation achieved is equal to 15%. What is the total dipole moment of the sample for a magnetic field of 0.98 T and a temperature of 2.8 K? (Assume Curie’s law)

Number of atomic dipoles, $n=2.0×{10}^{24}$
Dipole moment of each atomic dipole,
When the magnetic field,
The sample is cooled to temperature, ${T}_{1}=4.2°K$
Total dipole moment of the atomic dipole,

Magnetic saturation is achieved at 15%.
15
Hence, effective dipole moment,
When the magnetic field,
Temperature, ${T}_{2}=2.8°K$
ts total dipole moment = M2
According to Curie's law,
we have the ratio of two magnetic dipoles as:
$\begin{array}{rl}\frac{{M}_{2}}{{M}_{1}}& =\frac{{B}_{2}}{{B}_{1}}×\frac{{T}_{1}}{{T}_{2}}\\ \therefore {M}_{2}& =\frac{{B}_{2}{T}_{1}{M}_{1}}{{B}_{1}{T}_{2}}\\ & =\frac{0.98×4.2×4.5}{2.8×0.64}=10.336{\mathrm{JT}}^{-1}\end{array}$
Therefore,  Is the total dipole moment of the sample for a magnetic field of 0.98 T and a temperature of 2.8K.