If `lambda_(m)` denotes

Options

A. `lambda_(m) prop T`
B. `lambda_(m) prop T^(-1)`
C. `lambda_(m) prop T`
D. `lambda_(m)` is independent on T

Explanation

To solve the question regarding the relationship between the wavelength of maximum intensity (denoted as \(\lambda_m\)) and temperature (T) as described by Wien's Displacement Law, we can follow these steps:

### Step-by-Step Solution

1. **Understanding Wien's Displacement Law**:
Wien's Displacement Law states that the wavelength of maximum intensity (\(\lambda_m\)) of radiation emitted by a black body is inversely proportional to the absolute temperature (T) of the black body. Mathematically, this can be expressed as:
\[ \lambda_m \propto \frac{1}{T} \]

2. **Expressing the Proportionality**:
From the proportionality, we can write:
\[ \lambda_m = \frac{b}{T} \]
where \(b\) is a constant known as Wien's displacement constant.

3. **Rearranging the Equation**:
Rearranging the equation gives us:
\[ \lambda_m \cdot T = b \]
This shows that the product of the wavelength of maximum intensity and the absolute temperature is constant.

4. **Identifying the Relationship**:
From the equation \(\lambda_m \propto \frac{1}{T}\), we can also express this in terms of powers:
\[ \lambda_m \propto T^{-1} \]
This indicates that as the temperature increases, the wavelength of maximum intensity decreases.

5. **Conclusion**:
Therefore, we conclude that the wavelength of maximum intensity (\(\lambda_m\)) is inversely proportional to the absolute temperature (T). This confirms that \(\lambda_m\) is independent of T in terms of direct proportionality, but rather it is inversely related.

### Final Answer:
According to Wien's Displacement Law, \(\lambda_m \propto T^{-1}\).