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 the Asseration and Reason are true and reason explains the Assertion :
B. If both the Assertion and Reason are true but reason does ot explain the Assertion :
C. If Assertion is true but reason false
D. If Assertion is false but reason is true

Answer

To solve the problem, we need to analyze both the assertion and the reason provided in the question.

### Step 1: Understanding the Assertion
The assertion states that for higher temperatures, the peak emission wavelength of a black body shifts to lower wavelengths. This is based on Wien's Displacement Law, which states that the wavelength at which the emission of a black body spectrum is maximized (λ_max) is inversely proportional to the temperature (T) of the black body.

**Mathematical Representation:**
\[ \lambda_{max} \propto \frac{1}{T} \]
This means as the temperature (T) increases, the peak wavelength (λ_max) decreases.

### Step 2: Analyzing the Reason
The reason states that the peak emission wavelength of a black body is proportional to the fourth power of temperature. This statement is incorrect. Instead, the peak emission wavelength is inversely proportional to the temperature, as stated above.

**Correct Relationship:**
\[ \lambda_{max} \cdot T = b \]
where \( b \) is a constant (Wien's displacement constant). This indicates that as temperature increases, the peak wavelength decreases, not that it is proportional to the fourth power of temperature.

### Step 3: Conclusion
From the analysis:
- The assertion is **true**: Higher temperature leads to lower peak emission wavelength.
- The reason is **false**: The peak emission wavelength is not proportional to the fourth power of temperature; it is inversely proportional to temperature.

### Final Answer:
- **Assertion**: True
- **Reason**: False