Question

The magnetic susceptibility of a paramagnetic material at \( -73^\circ \text{C} \) is \( 0.0075 \). Its value at \( -173^\circ \text{C} \) will be

• A. \( 0.0075 \)
• B. \( 0.0045 \)
• C. \( 0.0150 \)
• D. \( 0.0030 \)

Hint:

For paramagnetic materials, the magnetic susceptibility is inversely proportional to the absolute temperature, as per Curie’s law.

Answer 1

The Correct Option is C

Step 1: Curie’s Law.
The magnetic susceptibility \( \chi \) of a paramagnetic material is inversely proportional to the temperature, according to Curie's law: \[ \chi = \frac{C}{T} \] where \( C \) is the Curie constant and \( T \) is the absolute temperature.
Step 2: Applying Curie’s law.
Using the values at \( T_1 = -73^\circ C \) and \( T_2 = -173^\circ C \), the temperature in Kelvin is: \[ T_1 = 200 \, \text{K}, \quad T_2 = 100 \, \text{K} \] Thus, the ratio of the magnetic susceptibility is: \[ \frac{\chi_2}{\chi_1} = \frac{T_1}{T_2} = \frac{200}{100} = 2 \] Hence, \( \chi_2 = 2 \times 0.0075 = 0.0150 \).
Step 3: Conclusion.
The magnetic susceptibility at \( -173^\circ C \) is \( 0.0150 \), so the correct answer is (C).