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a sample of paramagnetic salt contains 2 0 x 1024...

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)

Answer:

Number of atomic dipoles, n= 2.0 × 10²⁴

Dipole moment of each atomic dipole, M= 1.5 × 10 ^{- 23}J T^{- 1}

When the magnetic field, B₁= 0.64 T

The sample is cooled to a temperature, T₁= 4.2°K

Total dipole moment of the atomic dipole, M_tot= n × M

= 2 × 10²⁴× 1.5 × 10 ^{- 23}

= 30 J T^{- 1}

Magnetic saturation is achieved at 15%.

Hence, effective dipole moment,

When the magnetic field, B₂= 0.98 T

Temperature, T₂= 2.8°K

Its total dipole moment = M₂

According to Curie's law, we have the ratio of two magnetic dipoles as:

Therefore, 10.336 J T^-1 is the total dipole moment of the sample for a magnetic field of 0.98 T and a temperature of 2.8 K.

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