Wein's constant is `2892xx10^(-6)` MKS unit and the value of `lambda_(m)` from moon is 14.46 microns. What is the surface temperature of moon

Options

A. 100 K
B. 300 K
C. 400 K
D. 200 K

Answer

To find the surface temperature of the moon using Wien's law, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Wien's Law**:
Wien's law states that the wavelength at which the emission of a black body spectrum is maximized (λ_max) is inversely proportional to the temperature (T) of the body. The formula is given by:
\[ \lambda_{max} \cdot T = b \]
where \( b \) is Wien's constant.

2. **Given Values**:
- Wien's constant \( b = 2892 \times 10^{-6} \) m·K
- Wavelength from the moon \( \lambda_{m} = 14.46 \) microns \( = 14.46 \times 10^{-6} \) m

3. **Rearranging the Formula**:
We need to find the temperature \( T \). Rearranging the formula gives:
\[ T = \frac{b}{\lambda_{max}} \]

4. **Substituting the Values**:
Substitute the values of \( b \) and \( \lambda_{m} \) into the equation:
\[ T = \frac{2892 \times 10^{-6}}{14.46 \times 10^{-6}} \]

5. **Simplifying the Equation**:
The \( 10^{-6} \) terms cancel out:
\[ T = \frac{2892}{14.46} \]

6. **Calculating the Temperature**:
Now, perform the division:
\[ T \approx 200.0 \text{ K} \]

### Final Answer:
The surface temperature of the moon is approximately **200 K**.

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