Wien's constant is `2892 xx10^(-6)` SI unit and the value of `lambda_(m)` for Moon is 14.46 micron.The surfece temperature of Moon is :

Options

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

Explanation

To find the surface temperature of the Moon using Wien's Displacement Law, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Wien's Displacement Law**:
Wien's Displacement Law states that the product of the maximum wavelength (λ_m) and the absolute temperature (T) of a black body is a constant. Mathematically, it is given by:
\[ \lambda_m \cdot T = b \]
where \( b \) is Wien's constant.

2. **Identify the Given Values**:
- Wien's constant \( b = 2892 \times 10^{-6} \) m·K (SI units)
- Maximum wavelength for the Moon \( \lambda_m = 14.46 \) microns = \( 14.46 \times 10^{-6} \) m

3. **Rearranging the Formula**:
To find the temperature \( T \), we rearrange the formula:
\[ T = \frac{b}{\lambda_m} \]

4. **Substituting the Values**:
Now, substitute the values of \( b \) and \( \lambda_m \):
\[ T = \frac{2892 \times 10^{-6}}{14.46 \times 10^{-6}} \]

5. **Calculating the Temperature**:
- First, simplify the equation:
\[ T = \frac{2892}{14.46} \]
- Now, perform the division:
\[ T \approx 200 \text{ K} \]

6. **Conclusion**:
The surface temperature of the Moon is approximately \( 200 \) Kelvin.

### Final Answer:
The surface temperature of the Moon is \( 200 \) K.

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