Assertion: Red star is at lower temperature than blue star.
Reason: According to Wien's displacement law, `lamda_m prop 1/T`

Options

A. If both assertion and reason are correct and reason is a correct explanation of the assertion.
B. If both assertion and reason are correct but reason is not the correct explanation of assertion.
C. If assertion is correct but reason is incorrect.
D. If assertion is incorrect but reason is correct.

Answer

To solve the question, we will analyze the assertion and the reason provided, using Wien's displacement law.

### Step 1: Understand the Assertion
The assertion states that "Red star is at lower temperature than blue star." This implies that the temperature of the red star is less than that of the blue star.

### Step 2: Understand the Reason
The reason provided is based on Wien's displacement law, which states that the wavelength of the peak emission (λm) of a black body is inversely proportional to its absolute temperature (T). Mathematically, this can be expressed as:
\[ \lambda_m \propto \frac{1}{T} \]
This means that as the temperature increases, the peak wavelength decreases.

### Step 3: Apply Wien's Displacement Law
According to the assertion, if the red star has a lower temperature than the blue star, then:
- The temperature of the red star (T_red) < Temperature of the blue star (T_blue).
- According to Wien's law, if T_red < T_blue, then λm_red > λm_blue (the peak wavelength of the red star is greater than that of the blue star).

### Step 4: Compare Wavelengths
We know that:
- Red light has a longer wavelength than blue light.
- Therefore, if λm_red > λm_blue, it confirms that the red star emits light at a longer wavelength compared to the blue star, which is consistent with the assertion that the red star is at a lower temperature.

### Step 5: Conclusion
Both the assertion and the reason are correct. The reason provided (Wien's displacement law) correctly explains the assertion.

### Final Answer:
Both the assertion and reason are correct, and the reason is the correct explanation of the assertion.

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