The magnetic susceptibility of a paramagnetic material at `-73^(@)C "is" 0.0075`, its value at `-173^(@)C` will be

Options

A. 0.045
B. 0.03
C. 0.015
D. 0.0075

Explanation

To solve the problem, we will use the relationship between magnetic susceptibility and temperature for paramagnetic materials. The formula we will use is:

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

where:
- \(\chi_1\) is the magnetic susceptibility at temperature \(T_1\),
- \(\chi_2\) is the magnetic susceptibility at temperature \(T_2\).

### Step 1: Convert the temperatures from Celsius to Kelvin
We need to convert the given temperatures from Celsius to Kelvin using the formula:

\[ T(K) = T(°C) + 273 \]

For \(T_1 = -73°C\):
\[ T_1 = -73 + 273 = 200 \, K \]

For \(T_2 = -173°C\):
\[ T_2 = -173 + 273 = 100 \, K \]

### Step 2: Substitute the known values into the formula
We know:
- \(\chi_1 = 0.0075\),
- \(T_1 = 200 \, K\),
- \(T_2 = 100 \, K\).

Now we can substitute these values into the equation:

\[ \frac{0.0075}{\chi_2} = \frac{100}{200} \]

### Step 3: Simplify the equation
The right side simplifies to:

\[ \frac{100}{200} = \frac{1}{2} \]

So the equation becomes:

\[ \frac{0.0075}{\chi_2} = \frac{1}{2} \]

### Step 4: Solve for \(\chi_2\)
Cross-multiplying gives:

\[ 0.0075 \cdot 2 = \chi_2 \]

Calculating this gives:

\[ \chi_2 = 0.015 \]

### Final Answer
The magnetic susceptibility of the paramagnetic material at \(-173°C\) is \(0.015\).

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