According to Wien's law

Options

A. `lambda_mT`= constant
B. `lambda_m/T`= constant
C. `lambda_msqrtT` = constant
D. `lambda_m/sqrt7` = constant

Answer

To solve the question based on Wien's law, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Wien's Law**:
Wien's law states that the wavelength at which the emission of a black body spectrum is at its maximum (λ_max) is inversely proportional to the absolute temperature (T) of the black body.

2. **Mathematical Expression**:
The relationship can be expressed mathematically as:
\[ \lambda_{\text{max}} \cdot T = b \]
where \( b \) is Wien's displacement constant.

3. **Rearranging the Equation**:
From the above equation, we can express the peak wavelength in terms of temperature:
\[ \lambda_{\text{max}} = \frac{b}{T} \]
This shows that as the temperature increases, the peak wavelength decreases, which is consistent with Wien's law.

4. **Identifying the Correct Option**:
Given the options (A, B, C, D), we need to identify which option correctly represents the relationship derived from Wien's law. Based on the derived equation, we can conclude that the correct option will reflect the inverse relationship between \( \lambda_{\text{max}} \) and \( T \).

5. **Final Conclusion**:
After evaluating the options, we find that option B correctly represents the relationship stated by Wien's law.