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

Options

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

Answer

To determine which statements about the magnetic susceptibility \( \chi_m \) of paramagnetic substances are true, we can follow these steps:

### Step 1: Understand Magnetic Susceptibility
Magnetic susceptibility \( \chi_m \) is a measure of how much a material will become magnetized in an applied magnetic field. For paramagnetic substances, \( \chi_m \) is a key characteristic.

### Step 2: Identify Characteristics of Paramagnetic Substances
1. **Positive Susceptibility**: Paramagnetic substances have a positive magnetic susceptibility. This means they are attracted to magnetic fields.
2. **Temperature Dependence**: The susceptibility \( \chi_m \) of paramagnetic materials is inversely proportional to the absolute temperature \( T \). This can be expressed as:
\[ \chi_m \propto \frac{1}{T} \]

### Step 3: Analyze the Statements
Now, let's analyze the given statements one by one:

- **Option A**: "Value of \( \chi_m \) is respectively proportional to the absolute temperature."
- This is **false** because \( \chi_m \) is inversely proportional to temperature, not directly proportional.

- **Option B**: " \( \chi_m \) is positive at all temperatures."
- This is **true**. Paramagnetic substances have a positive susceptibility regardless of the temperature.

- **Option C**: " \( \chi_m \) is negative at all temperatures."
- This is **false**. \( \chi_m \) is not negative for paramagnetic substances; it is negative for diamagnetic substances.

- **Option D**: " \( \chi_m \) does not depend on the temperature of the sample."
- This is **false**. \( \chi_m \) does depend on temperature; it decreases as temperature increases.

### Conclusion
From the analysis, the only true statement regarding the magnetic susceptibility \( \chi_m \) of paramagnetic substances is **Option B**: \( \chi_m \) is positive at all temperatures.