If the temperature of a black body is increased then the wavelength corresponding to the maximum emission will

Options

A. shift towards smaller wavelength
B. shift towards longer wavelength
C. not shift
D. shift in proportion to increase in temperature

Answer

To solve the question regarding the relationship between the temperature of a black body and the wavelength corresponding to maximum emission, we can use Wien's Displacement Law. Here is a step-by-step solution:

### Step-by-Step Solution:

1. **Understanding Wien's Displacement Law**:
Wien's Displacement Law states that the wavelength (\( \lambda_m \)) at which the emission of a black body spectrum is maximum is inversely proportional to the temperature (T) of the black body. Mathematically, it can be expressed as:
\[ \lambda_m \cdot T = B \]
where \( B \) is Wien's constant (approximately \( 0.288 \, \text{cm} \cdot \text{K} \)).

2. **Analyzing the Relationship**:
From the equation \( \lambda_m \cdot T = B \), we can rearrange it to find the wavelength:
\[ \lambda_m = \frac{B}{T} \]
This shows that as the temperature (T) increases, the wavelength (\( \lambda_m \)) must decrease in order to keep the product \( \lambda_m \cdot T \) constant.

3. **Conclusion**:
Therefore, if the temperature of a black body is increased, the wavelength corresponding to the maximum emission will decrease.

### Final Answer:
If the temperature of a black body is increased, the wavelength corresponding to the maximum emission will decrease.

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