AIIMS 2007 Physics Black Body Radiation Assertion Reason Question

To tackle the question regarding black body radiation, let's analyze the assertion and the reason provided:

Assertion:

A hollow metallic closed container maintained at a uniform temperature can act as a source of black body radiation.

Reason:

All metals act as black bodies.

Evaluation of the Assertion:

1. Black Body Definition: A black body is an idealized physical object that absorbs all incoming radiation, regardless of frequency or angle. It also emits radiation in a characteristic spectrum determined solely by its temperature, described by Planck's law.

2. Hollow Metallic Container: A hollow metallic container, while it may emit radiation when heated, does not qualify as a perfect black body. Metals generally reflect rather than absorb radiation, meaning they do not absorb all wavelengths effectively. Therefore, a hollow metallic container cannot be considered a true black body source.

Evaluation of the Reason:

1. Metals and Black Bodies: The statement that "all metals act as black bodies" is incorrect. While metals can radiate energy when heated, they do not absorb all incident radiation and therefore do not exhibit the characteristics of a black body.

Conclusion:

• Since neither the assertion nor the reason is true, the correct answer is D) Both Assertion and Reason are false.

Clarification of Incorrect Options:

• Option A: Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

  • This is incorrect because both the assertion and the reason are false. A hollow metallic container cannot act as a black body, and not all metals act as black bodies.

• Option B: Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion.

  • This is incorrect for the same reasons as Option A. Both statements are false.

• Option C: Assertion is true but Reason is false.

  • This is also incorrect. The assertion is false; hence this option cannot be true.

Relevant Concepts:

• Black Body Radiation: Described by Planck's law, which states the spectral radiance of a black body at thermal equilibrium is given by:

$$B( u, T) = \frac{2h u^3}{c^2} \cdot \frac{1}{e^{\frac{h u}{kT}} - 1}$$

where:

• $B( u, T)$ = spectral radiance,
• $h$ = Planck's constant ($6.626 \times 10^{-34} \, \text{J s}$),
• $u$ = frequency of the radiation,
• $c$ = speed of light in a vacuum ($3 \times 10^8 \, \text{m/s}$),
• $k$ = Boltzmann's constant ($1.38 \times 10^{-23} \, \text{J/K}$),
• $T$ = absolute temperature in Kelvin.

In conclusion, it is crucial to differentiate between idealized concepts such as a black body and real materials, which often do not meet these criteria. Understanding these distinctions is key in thermodynamics and the study of radiation.