Question

Magnetic susceptibility of Mg at 300 K is 5 1.2x10^-5 . What is its susceptibility at 200 K ?

• A. 18x10^-5
• B. 180x10^-5
• C. 1.8x10^-5
• D. 0.18x10^-5

Answer 1

The Correct Option is C

For paramagnetic substances, magnetic susceptibility \(\chi\) is inversely proportional to temperature \(T\) (Curie’s Law): \[ \chi \propto \frac{1}{T} \] Let \(\chi_1 = 1.2 \times 10^{-5}\) at \(T_1 = 300\,K\) We are to find \(\chi_2\) at \(T_2 = 200\,K\) Using Curie’s Law: \[ \frac{\chi_1}{\chi_2} = \frac{T_2}{T_1} \Rightarrow \frac{1.2 \times 10^{-5}}{\chi_2} = \frac{200}{300} = \frac{2}{3} \] \[ \chi_2 = \frac{1.2 \times 10^{-5} \times 3}{2} = 1.8 \times 10^{-5} \times 3 = 5.4 \times 10^{-5} \] Wait! There’s a mistake above — let's redo the correct way: \[ \chi_2 = \chi_1 \times \frac{T_1}{T_2} = 1.2 \times 10^{-5} \times \frac{300}{200} = 1.2 \times 10^{-5} \times 1.5 = 1.8 \times 10^{-5} \] Correction: The correct value is: \[ \chi_2 = 1.8 \times 10^{-5} \] So the correct answer is: (3) \(1.8 \times 10^{-5}\)