Q154 / 180 · KCET 2016 · Physics
\( x_{1} \) and \( x_{2} \) are susceptibility of a paramagnetic material at temperatures \( T_{1} K \) and \( T_{2} K \)
respectively, then
respectively, then
- A\( x_{1}=x_{2} \)
- Correct answerB\( x_{1} T_{1}=x_{2} T_{2} \)
- C\( \chi_{1} T_{2}=\chi_{2} T \)
- D\( x_{1} \sqrt{T_{1}}=x_{2} \sqrt{T_{2}} \)
Solution
Susceptibility is a dimensionless number. It is a measure of the extent to which a substance becomes magnetized.
Paramagnetic susceptibility \( \chi \) is given as
\[ \begin{array}{l} \chi=\frac{N g^{2} \beta^{2} S(S+1)}{3 K T} \\ \Rightarrow \chi \propto \frac{1}{T} \text { or } \chi T \propto 1 \end{array} \]
Therefore \( \chi_{1} T_{1}=\chi_{2} T_{2} \)
Paramagnetic susceptibility \( \chi \) is given as
\[ \begin{array}{l} \chi=\frac{N g^{2} \beta^{2} S(S+1)}{3 K T} \\ \Rightarrow \chi \propto \frac{1}{T} \text { or } \chi T \propto 1 \end{array} \]
Therefore \( \chi_{1} T_{1}=\chi_{2} T_{2} \)
Hence, the correct answer is option: 'B'.