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) \(1.8 \times 10^{-5}\)

Answer 2

Magnetic susceptibility (\(\chi\)) of a material is temperature dependent and can be approximated using the Curie-Weiss law for paramagnetic materials: \[ \chi = \frac{C}{T - \theta} \] where \(C\) is the Curie constant, \(T\) is the temperature in Kelvin, and \(\theta\) is the Curie-Weiss temperature. \\ Since we are given the magnetic susceptibility at two different temperatures and assuming the Curie constant remains the same, we can use the ratio of the susceptibilities at the two temperatures: \[ \frac{\chi_1}{\chi_2} = \frac{T_1}{T_2} \] Substituting the given values: \[ \frac{1.2 \times 10^{-5}}{\chi_2} = \frac{300}{200} \] Solving for \(\chi_2\): \[ \chi_2 = \frac{1.2 \times 10^{-5} \times 200}{300} = 1.8 \times 10^{-5} \] Thus, the susceptibility at 200 K is \(1.8 \times 10^{-5}\).