Question

How does the magnetic susceptibility (\(\chi\)) of paramagnetics change with respect to absolute temperature (T) ?

• A. \(\chi \propto\) T
• B. \(\chi \propto\) T\(^{-1}\)
• C. \(\chi\) = constant
• D. \(\chi \propto\) e\(^T\)

Hint:

Remember the temperature dependence for different magnetic materials: - {Paramagnetic:} \(\chi \propto 1/T\) (Curie's Law). - {Diamagnetic:} \(\chi\) is small, negative, and independent of temperature. - {Ferromagnetic:} \(\chi \propto 1/(T-T_c)\) for T>T\(_c\) (Curie-Weiss Law), where T\(_c\) is the Curie temperature.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question is about the behavior of paramagnetic materials in a magnetic field at different temperatures. Magnetic susceptibility (\(\chi\)) is a measure of how much a material becomes magnetized in an applied magnetic field.
Step 2: Key Formula or Approach:
The relationship between magnetic susceptibility and absolute temperature for paramagnetic materials is described by Curie's Law.
Curie's Law states that the magnetization of a paramagnetic material is directly proportional to the applied magnetic field and inversely proportional to the absolute temperature. This implies that the magnetic susceptibility (\(\chi\)) is inversely proportional to the absolute temperature (T).
\[ \chi = \frac{C}{T} \] where C is the Curie constant.
Step 3: Detailed Explanation:
From Curie's Law, we have the relationship: \[ \chi \propto \frac{1}{T} \] This can also be written using a negative exponent as: \[ \chi \propto T^{-1} \] This means that as the temperature of a paramagnetic substance increases, its ability to be magnetized decreases. This is because the random thermal motion of the atoms at higher temperatures opposes the alignment of their magnetic dipoles with the external field.
Step 4: Final Answer:
The magnetic susceptibility (\(\chi\)) of a paramagnetic substance is inversely proportional to the absolute temperature (T), so \(\chi \propto T^{-1}\).