AIIMS 2005 Physics Blackbody Radiation Assertion Reason Question

To analyze the given question effectively, we need to break down both the assertion and the reason, and evaluate their truthfulness and relationship.

Assertion

Assertion: For higher temperatures, the peak emission wavelength of a black body shifts to lower wavelengths.

This statement is true. According to Wien's Displacement Law, the wavelength at which the emission of a black body spectrum peaks is inversely proportional to the temperature. Mathematically, this can be expressed as:

$$\lambda_{\text{max}} = \frac{b}{T}$$

where:

• $\lambda_{\text{max}}$ is the peak wavelength,
• $T$ is the absolute temperature in Kelvin,
• $b$ is Wien's displacement constant (approximately $2898 \, \mu m \cdot K$).

As the temperature $T$ increases, the peak wavelength $\lambda_{\text{max}}$ decreases, thus confirming the assertion.

Reason

Reason: Peak emission wavelengths of a blackbody is proportional to the fourth-power of temperature.

This statement is false. The peak wavelength is not proportional to the fourth power of temperature; rather, it is inversely proportional to the temperature, as shown in Wien's Displacement Law. The Stefan-Boltzmann Law states that the total energy radiated per unit surface area of a black body is proportional to the fourth power of its absolute temperature $T$:

$$j^* = \sigma T^4$$

where $j^*$ is the total power radiated per unit area and $\sigma$ is the Stefan-Boltzmann constant. However, this relates to total emitted energy, not the peak emission wavelength.

Conclusion

Based on the analysis above, the correct answer is B: Both assertion and reason are true but reason is not the correct explanation of assertion. The assertion is true, while the reason is false, as it incorrectly describes the relationship between wavelength and temperature.

Clarification of Other Options

• Option A: Incorrect because while the assertion is true, the reason is false.
• Option C: Incorrect as it states that the assertion is true (which it is), but the reason is false.
• Option D: Incorrect because the assertion is true.

Thus, the correct option is B because the assertion stands correct while the reason fails to accurately explain the assertion, despite both being related to the concepts of blackbody radiation.