Question

The susceptibility of tungsten is $6.8 \times 10^{-5}$ at temperature $300\,\text{K}$. The susceptibility at temperature $400\,\text{K}$ is

• A. $5.1 \times 10^{-5}$
• B. $6.8 \times 10^{-5}$
• C. $3.4 \times 10^{-5}$
• D. $4.8 \times 10^{-5}$

Hint:

Paramagnetic susceptibility decreases with increase in temperature according to Curie’s law.

Answer 1

The Correct Option is A

Step 1: Temperature dependence of susceptibility.
For paramagnetic substances, susceptibility follows Curie’s law:
\[ \chi \propto \frac{1}{T} \]

Step 2: Write ratio of susceptibilities.
\[ \frac{\chi_1}{\chi_2} = \frac{T_2}{T_1} \]

Step 3: Substitute given values.
\[ \chi_2 = \chi_1 \frac{T_1}{T_2} = 6.8 \times 10^{-5} \times \frac{300}{400} \] \[ \chi_2 = 5.1 \times 10^{-5} \]

Step 4: Conclusion.
The susceptibility at $400\,\text{K}$ is $5.1 \times 10^{-5}$.