Point out the best representation of relation between magnetic susceptibility `(Chi)` and temperature (T) for a paramagnetic material

Options

A.
B.
C.
D.

Explanation

To determine the best representation of the relationship between magnetic susceptibility (χ) and temperature (T) for a paramagnetic material, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Magnetic Susceptibility**:
- Magnetic susceptibility (χ) is a measure of how much a material will become magnetized in an applied magnetic field. For paramagnetic materials, this susceptibility varies with temperature.

2. **Recall Curie's Law**:
- According to Curie's Law, the magnetic susceptibility (χ) of a paramagnetic material is inversely proportional to its absolute temperature (T). This relationship can be expressed mathematically as:
\[ χ = \frac{C}{T} \]
where C is Curie's constant.

3. **Analyze the Inverse Relationship**:
- From the equation \(χ = \frac{C}{T}\), we can deduce that as the temperature (T) increases, the magnetic susceptibility (χ) decreases. This indicates an inverse relationship between χ and T.

4. **Graphical Representation**:
- In a graph representing this relationship, the y-axis would typically represent magnetic susceptibility (χ), and the x-axis would represent temperature (T).
- Since χ decreases as T increases, the graph should slope downwards from left to right.

5. **Evaluate Given Graphs**:
- Among the provided graphs, we need to identify which one shows a downward trend (decreasing χ with increasing T).
- The correct graph will show that as temperature increases, the value of susceptibility decreases.

6. **Select the Correct Option**:
- After evaluating the graphs, the first graph (option A) should depict the correct inverse relationship, where χ decreases as T increases.

### Conclusion:
The best representation of the relationship between magnetic susceptibility (χ) and temperature (T) for a paramagnetic material is the first graph (option A), which shows a decreasing trend.