The correct graph which shows the variation of paramagnetic susceptibility S with temperature T is

Options

A.
B.
C.
D.

Answer

To solve the problem of determining the correct graph that shows the variation of paramagnetic susceptibility \( S \) with temperature \( T \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: According to the Curie law, the paramagnetic susceptibility \( S \) is inversely proportional to the temperature \( T \). This can be mathematically expressed as:
\[ S \propto \frac{1}{T} \]

2. **Express the Relationship Mathematically**: We can write the relationship as:
\[ S = \frac{C}{T} \]
where \( C \) is the Curie constant.

3. **Identify the Type of Graph**: The equation \( S = \frac{C}{T} \) can be rearranged to show that as \( T \) increases, \( S \) decreases. This indicates a hyperbolic relationship.

4. **Graph Characteristics**: The graph of \( S \) versus \( T \) will show a downward curve, starting from a higher value of \( S \) when \( T \) is low and approaching zero as \( T \) increases.

5. **Select the Correct Option**: Among the given options, we need to identify the graph that depicts this inverse relationship. The correct graph will show a hyperbolic decline of \( S \) with increasing \( T \).

6. **Conclusion**: After analyzing the options, we find that the graph corresponding to the equation \( S = \frac{C}{T} \) is the one that correctly represents the variation of paramagnetic susceptibility with temperature.

### Final Answer:
The correct graph showing the variation of paramagnetic susceptibility \( S \) with temperature \( T \) is **Option 3**.