Assertion : For higher temperature, the peak emission wavelength of a black body shifts to lower wavelengths.
Reason : Peak emission wavelength of a black body is proportional to the fourth power of temperature.

Options

A. If both Assertion and Reason are correct but Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
C. If Assertion is true but Reason is false
D. If Assertion is false but Reason is true.

Explanation

To solve the question regarding the assertion and reason related to black body radiation, we will analyze both statements step by step.

### Step 1: Understanding the Assertion
The assertion states: "For higher temperature, the peak emission wavelength of a black body shifts to lower wavelengths."

- According to Wien's Displacement Law, the peak wavelength (λm) of radiation emitted by a black body is inversely proportional to its temperature (T). This can be expressed mathematically as:
\[ \lambda_m = \frac{b}{T} \]
where \(b\) is a constant (Wien's displacement constant).

- From this relationship, as the temperature (T) increases, the peak wavelength (λm) decreases. Therefore, the assertion is true.

### Step 2: Understanding the Reason
The reason states: "Peak emission wavelength of a black body is proportional to the fourth power of temperature."

- The reason is somewhat misleading. The correct relationship is that the total energy emitted per unit surface area of a black body (E) is proportional to the fourth power of its temperature:
\[ E = \sigma T^4 \]
where \(σ\) is the Stefan-Boltzmann constant.

- However, this statement does not directly relate to the peak emission wavelength. The peak emission wavelength is not proportional to the fourth power of temperature; it is inversely proportional to temperature.

### Step 3: Conclusion
- Both the assertion and the reason are true statements in their own right. However, the reason does not correctly explain the assertion. Therefore, the correct conclusion is that the assertion is true, the reason is true, but the reason is not the correct explanation of the assertion.

### Final Answer
The correct option is that both the assertion and reason are true, but the reason is not the correct explanation of the assertion.

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