If the temperature of a black body is increased, then the maximum of the spectrum will

Options

A. shift towards shorter wavelength
B. shift towards shorter frequency
C. shift towards shorter or longer wavelength depending on the nature of the black body
D. no shift

Answer

To solve the problem, we need to understand the relationship between the temperature of a black body and the wavelength of the maximum intensity of its emitted spectrum. This relationship is described by Wien's Displacement Law.

### Step-by-Step Solution:

1. **Understanding Wien's Displacement Law**:
Wien's Displacement Law states that the wavelength (λ) at which the intensity of radiation is maximum is inversely proportional to the temperature (T) of the black body. Mathematically, it can be expressed as:
\[ \lambda_{\text{max}} \cdot T = b \]
where \( b \) is a constant (Wien's displacement constant).

2. **Analyzing the Effect of Temperature Increase**:
If the temperature (T) of the black body increases, according to the law, we can rearrange the equation to show the relationship:
\[ \lambda_{\text{max}} = \frac{b}{T} \]
Here, if T increases, the value of \( \lambda_{\text{max}} \) will decrease because \( b \) is a constant.

3. **Conclusion on Wavelength Shift**:
Since \( \lambda_{\text{max}} \) decreases with an increase in temperature, this means that the maximum of the spectrum will shift towards shorter wavelengths.

4. **Final Answer**:
Therefore, if the temperature of a black body is increased, the maximum of the spectrum will shift towards shorter wavelengths.