The graph between `chi` and 1/T for paramagnetic material will be represented by

Options

A.
B.
C.
D.

Answer

To solve the question regarding the graph between susceptibility (χ) and 1/T for a paramagnetic material, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept**:
- For paramagnetic materials, the susceptibility (χ) is related to temperature (T) through Curie's Law, which states that χ is inversely proportional to T.

2. **Write the Equation**:
- According to Curie's Law, we can express this relationship mathematically as:
\[ \chi = \frac{C}{T} \]
- This can also be rewritten as:
\[ \chi = C \cdot \frac{1}{T} \]
- Here, C is Curie's constant.

3. **Identify Variables**:
- In this equation, we can identify:
- y-axis: χ (susceptibility)
- x-axis: \( \frac{1}{T} \)

4. **Determine the Type of Graph**:
- The equation \( \chi = C \cdot \frac{1}{T} \) is in the form of \( y = mx \), where m (slope) is equal to C.
- This indicates a linear relationship between χ and \( \frac{1}{T} \).

5. **Graph Characteristics**:
- Since the equation is linear, the graph will be a straight line.
- The line will pass through the origin (0,0) because when \( T \) approaches infinity (1/T approaches 0), χ approaches 0.

6. **Select the Correct Graph**:
- From the options provided, we need to identify which graph is a straight line passing through the origin.
- After evaluating the options, we find that only option D represents a straight line that passes through the origin.

### Conclusion:
- The correct answer is option D, which represents the graph of susceptibility (χ) versus \( \frac{1}{T} \) for a paramagnetic material.