Question

Magnetic susceptibility of Mg at 300 K is \( 1.2 \times 10^{-5} \). What is its susceptibility at 200 K?

• A. \( 18 \times 10^{-5} \)
• B. \( 180 \times 10^{-5} \)
• C. \( 1.8 \times 10^{-5} \)
• D. \( 0.18 \times 10^{-5} \)

Answer 1

The Correct Option is C

Magnetic susceptibility of most materials tends to decrease as temperature increases. This relationship is typically governed by the Curie-Weiss law, which approximates susceptibility \( \chi \) at a different temperature using the formula:
\( \chi_T = \chi_0 \left( \frac{T_0}{T} \right) \) where:
- \( \chi_T \) is the susceptibility at temperature \( T \), 
- \( \chi_0 \) is the susceptibility at a reference temperature \( T_0 \), 
- \( T \) is the new temperature. 

Given \( \chi_{300K} = 1.2 \times 10^{-5} \) and \( T_0 = 300 \, \text{K} \), \( T = 200 \, \text{K} \), the susceptibility at 200 K is:
\( \chi_{200K} = 1.2 \times 10^{-5} \times \left( \frac{300}{200} \right) = 1.8 \times 10^{-5} \)