Question

Which of the following statements are true about the magnetic susceptibility Xm of paramagnetic substance?

• A. Xm is positive at all temperature
• B. Value of Xm is proportional to the absolute temperature of the sample
• C. Value of Xm is inversely proportional to the absolute temperature of the sample
• D. Xm is zero at all temperature

Answer 1

Answer: (A), (C)

Xm is positive at all temperature, Value of Xm is inversely proportional to the absolute temperature of the sample

Answer 2

Paramagnetic substances are characterized by the presence of permanent magnetic dipoles due to unpaired electrons. When placed in an external magnetic field, these dipoles tend to align with the field, leading to a net magnetization in the direction of the applied field.

1. Nature of Magnetic Susceptibility ($\chi_m$): For paramagnetic substances, the magnetization (M) is in the same direction as the applied magnetic field (H). Magnetic susceptibility is defined as $\chi_m = \frac{M}{H}$. Since M and H have the same direction, $\chi_m$ is always positive for paramagnetic materials. This means the first statement, "Xm is positive at all temperature," is true.

2. Temperature Dependence of Magnetic Susceptibility (Curie's Law): The alignment of magnetic dipoles with the external field is opposed by random thermal motion. As the temperature increases, the thermal agitation increases, making it more difficult for the dipoles to align with the field. This results in a decrease in the net magnetization for a given field, and consequently, a decrease in the magnetic susceptibility. Conversely, as the temperature decreases, the alignment becomes more effective, increasing the susceptibility. This inverse relationship is described by Curie's Law for paramagnetic substances:

   $\chi_m = \frac{C}{T}$

   where C is the Curie constant (a positive constant specific to the material) and T is the absolute temperature in Kelvin. From Curie's Law, it is clear that the value of $\chi_m$ is inversely proportional to the absolute temperature of the sample. Therefore, the third statement, "Value of Xm is inversely proportional to the absolute temperature of the sample," is true.

3. Evaluating other statements:

   • "Value of Xm is proportional to the absolute temperature of the sample" is false, as it contradicts Curie's Law.
   • "Xm is zero at all temperature" is false, as paramagnetic substances have a positive susceptibility.

Hence, the correct statements are that $\chi_m$ is positive at all temperatures and is inversely proportional to the absolute temperature.