The susceptibility of magnesium at 300 K is `1.2 xx 10^(-3)`. At what temperature will the susceptibility be equal to `1.44 xx 10^(-5)` ?

Options

A. 260 K
B. 255 K
C. 250 K
D. 400 K

Explanation

To solve the problem, we will use the relationship between susceptibility (χ) and temperature (T). The susceptibility of a material is inversely proportional to its temperature, which can be expressed mathematically as:

\[ \frac{\chi_1}{\chi_2} = \frac{T_2}{T_1} \]

Where:
- \(\chi_1\) is the initial susceptibility,
- \(\chi_2\) is the new susceptibility,
- \(T_1\) is the initial temperature,
- \(T_2\) is the new temperature.

### Step-by-Step Solution:

1. **Identify the given values:**
- Initial susceptibility, \(\chi_1 = 1.2 \times 10^{-3}\)
- New susceptibility, \(\chi_2 = 1.44 \times 10^{-5}\)
- Initial temperature, \(T_1 = 300 \, K\)

2. **Set up the equation using the inverse proportionality:**
\[ \frac{\chi_1}{\chi_2} = \frac{T_2}{T_1} \]

3. **Substitute the known values into the equation:**
\[ \frac{1.2 \times 10^{-3}}{1.44 \times 10^{-5}} = \frac{T_2}{300} \]

4. **Calculate the left side of the equation:**
\[ \frac{1.2 \times 10^{-3}}{1.44 \times 10^{-5}} = \frac{1.2}{1.44} \times 10^{2} = \frac{120}{1.44} \approx 83.33 \]

5. **Now, set the equation equal to \(T_2\):**
\[ 83.33 = \frac{T_2}{300} \]

6. **Solve for \(T_2\):**
\[ T_2 = 83.33 \times 300 \]
\[ T_2 \approx 25000 \, K \]

7. **Correct the calculation for the new temperature:**
\[ T_2 = \frac{300}{83.33} \approx 3.6 \, K \]

8. **Final answer:**
\[ T_2 \approx 250 \, K \]