Question
A sample of paramagnetic salt contains 2.0 x 1024 atomic dipoles each of dipole moment 1.5 x 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)
Solution
Given,
Number of atomic dipoles, n = 2.0 x 1024
Magnetic dipole moment of each dipole = 1.5 x 10–23 J T–1
∴ Total possible magnetic dipole moment of the sample, M = 1.5 x 10–23 x 2.0 x 1024
= 30 J T–1
Magnetic field, B1 = 0.64 T
At temperature of 4.2 K, the magnetic saturation is 15%.
∴ Dipole moment achieved at 4.2 K = 15% of M
Hence,
According to Curie's law,
Here,
and
is the magnetic dipole moment at 0.92 K .
