Which among the four `chi` versus T graphs shown in the following figure is the correct one for a paramagnetic substsnace will look like ?

Options

A.
B.
C.
D.

Answer

To determine the correct graph of magnetic susceptibility (χ) versus temperature (T) for a paramagnetic substance, we need to understand the behavior of paramagnetic materials with respect to temperature.

### Step-by-Step Solution:

1. **Understand Paramagnetism**:
- Paramagnetic substances have unpaired electrons, which give rise to a net magnetic moment. This means that they are attracted to magnetic fields.

2. **Behavior with Temperature**:
- The magnetic susceptibility (χ) of paramagnetic materials is inversely proportional to temperature (T). As temperature increases, the thermal agitation causes the alignment of magnetic moments to decrease, leading to a decrease in susceptibility.

3. **Mathematical Representation**:
- The relationship can be expressed as:
\[ \chi = \frac{C}{T} \]
where \(C\) is the Curie constant. This indicates that as \(T\) increases, \(χ\) decreases.

4. **Graph Characteristics**:
- The graph of χ versus T for a paramagnetic substance will show a hyperbolic decline. It will start from a positive value at low temperatures and approach zero as the temperature increases.

5. **Identifying the Correct Graph**:
- Look for a graph that starts at a certain positive value on the y-axis (χ) when T is low and slopes downwards towards the x-axis (T) as T increases. This behavior is characteristic of paramagnetic substances.

### Conclusion:
The correct graph for the magnetic susceptibility (χ) versus temperature (T) of a paramagnetic substance will show a hyperbolic decline, starting from a positive value and approaching zero as temperature increases.