Which of the following statements are ture about the magnetic susceptibility `chi(m)` of paramagnetic substance?

Options

A. Value of `chi_(m)` is inversely proportional to the absolute temperatuty of the sample
B. `chi_(m)` is positive at all temperature
C. `chi_(m)` is negative at all temperature
D. `chi_(m)` does not depend on the temperature of the sample

Answer

To determine which statements are true about the magnetic susceptibility \(\chi_m\) of paramagnetic substances, we can analyze the properties of paramagnetic materials and their susceptibility.

### Step-by-Step Solution:

1. **Understanding Magnetic Susceptibility**:
- Magnetic susceptibility (\(\chi_m\)) is a measure of how much a material will become magnetized in an applied magnetic field. It is defined as the ratio of the magnetization (\(M\)) of the material to the applied magnetic field strength (\(H\)):
\[ \chi_m = \frac{M}{H} \]

2. **Characteristics of Paramagnetic Materials**:
- Paramagnetic materials have a positive magnetic susceptibility. This means that they are attracted to magnetic fields and can be magnetized in the direction of the applied magnetic field.
- Therefore, we can state:
\[ \chi_m > 0 \quad \text{(for paramagnetic materials)} \]

3. **Temperature Dependence**:
- The magnetic susceptibility of paramagnetic materials is inversely proportional to the absolute temperature (\(T\)). This relationship can be expressed as:
\[ \chi_m \propto \frac{1}{T} \]
- As the temperature increases, the susceptibility decreases, indicating that the material becomes less magnetized at higher temperatures.

4. **Conclusion**:
- Based on the properties of paramagnetic materials, we can conclude that:
- Paramagnetic materials have positive magnetic susceptibility.
- The magnetic susceptibility of paramagnetic materials is inversely proportional to temperature.

### Final Statements:
- Both statements regarding the magnetic susceptibility \(\chi_m\) of paramagnetic substances are true:
- **Statement A**: Paramagnetic materials have positive magnetic susceptibility.
- **Statement B**: The magnetic susceptibility of paramagnetic materials is inversely proportional to temperature.