The magnetic susceptibility of a paramagnetic substance at `- 173^(@)C` is `1.5 xx 10^(-2)` then its value at `-73^(@)C` will be?

Options

A. `7.5xx10^(-1)`
B. `7.5xx10^(-2)`
C. `7.5xx10^(-3)`
D. `7.5xx10^(-4)`

Explanation

To find the magnetic susceptibility of a paramagnetic substance at a different temperature, we can use Curie's Law, which states that the magnetic susceptibility (χ) is inversely proportional to the absolute temperature (T).

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Initial magnetic susceptibility, \( \chi_1 = 1.5 \times 10^{-2} \)
- Initial temperature, \( T_1 = -173^\circ C \)
- Final temperature, \( T_2 = -73^\circ C \)

2. **Convert Temperatures to Kelvin**:
- The absolute temperature in Kelvin is given by \( T(K) = T(°C) + 273 \).
- For \( T_1 \):
\[ T_1 = -173 + 273 = 100 \, K \]
- For \( T_2 \):
\[ T_2 = -73 + 273 = 200 \, K \]

3. **Apply Curie's Law**:
- According to Curie's Law:
\[ \frac{\chi_1}{\chi_2} = \frac{T_2}{T_1} \]
- Rearranging gives:
\[ \chi_2 = \chi_1 \cdot \frac{T_1}{T_2} \]

4. **Substitute the Values**:
- Substitute \( \chi_1 \), \( T_1 \), and \( T_2 \) into the equation:
\[ \chi_2 = (1.5 \times 10^{-2}) \cdot \frac{100}{200} \]

5. **Calculate \( \chi_2 \)**:
- Simplifying the fraction:
\[ \chi_2 = (1.5 \times 10^{-2}) \cdot 0.5 = 0.75 \times 10^{-2} = 7.5 \times 10^{-3} \]

6. **Final Result**:
- The value of magnetic susceptibility at \( -73^\circ C \) is:
\[ \chi_2 = 7.5 \times 10^{-3} \]

### Summary:
The magnetic susceptibility of the paramagnetic substance at \( -73^\circ C \) is \( 7.5 \times 10^{-3} \).