Question

If the susceptibility of a paramagnetic substance at a temperature of \(23^\circ C\) is \(2.3\times10^{-5}\), then its susceptibility at a temperature of \(467^\circ C\) is:

• A. \(2.3\times10^{-6}\)
• B. \(6.9\times10^{-6}\)
• C. \(9.2\times10^{-6}\)
• D. \(4.6\times10^{-6}\)

Hint:

For paramagnetic substances: \[ \chi \propto \frac{1}{T}. \] Always convert temperature into Kelvin before applying Curie's law.

Answer 1

The Correct Option is C

Concept: According to Curie's law, \[ \chi=\frac{C}{T}. \] Therefore, \[ \chi T=\text{constant}. \]

Step 1: Convert temperatures into Kelvin.
\[ T_1=23+273=296K. \] \[ T_2=467+273=740K. \]

Step 2: Apply Curie's law.
\[ \chi_1T_1 = \chi_2T_2. \] \[ (2.3\times10^{-5})(296) = \chi_2(740). \] \[ \chi_2 = 2.3\times10^{-5} \left(\frac{296}{740}\right). \] \[ = 2.3\times10^{-5}\times0.4. \] \[ = 9.2\times10^{-6}. \] Hence, \[ \boxed{9.2\times10^{-6}}. \]