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 1: Understand the relationship between susceptibility and temperature
Paramagnetic susceptibility (S) is known to be inversely proportional to the absolute temperature (T). This means that as the temperature increases, the susceptibility decreases.

### Step 2: Write the mathematical expression
From the relationship, we can express this as:
\[ S \propto \frac{1}{T} \]
This can also be written as:
\[ S = \frac{k}{T} \]
where \( k \) is a constant.

### Step 3: Analyze the graph of the relationship
The equation \( S = \frac{k}{T} \) indicates that the graph of S versus T will be a hyperbola. Specifically, it will be a rectangular hyperbola that approaches the axes but never touches them.

### Step 4: Identify the characteristics of the graph
In a graph of S versus T:
- As T increases, S decreases.
- The graph will not intersect the axes, indicating that S approaches zero as T approaches infinity.

### Step 5: Select the correct graph
Given the options available, we need to identify which graph represents a rectangular hyperbola. The correct graph will show a curve that decreases as T increases, demonstrating the inverse relationship.

### Conclusion
After analyzing the options, we find that the third option represents the correct graph, which is a rectangular hyperbola showing the variation of paramagnetic susceptibility (S) with temperature (T).

### Final Answer
The correct option is **C**.

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