Question

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The wavelength of radiation is displaced as temperature changes, but the product of wavelength and temperature remains constant. Reason (R) : Wien's Law is a special case of Planck's radiation law in the region of longer wavelength. In the light of the above statements, choose the most appropriate answer from the options given below :

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

Remember the "W" in Wien's for "Wave" (Short Wave). Wien's law fails at long wavelengths, which led to the "Ultraviolet Catastrophe" that Planck eventually solved.

Answer 1

The Correct Option is C

Concept:
• Wien's Displacement Law: $\lambda_{max} T = b$ (constant). This states that the peak wavelength is inversely proportional to temperature.
• Planck's Law: Describes the spectral density of electromagnetic radiation at all wavelengths.

Step 1: Evaluate Assertion (A).
The statement correctly describes Wien's Displacement Law: as $T$ increases, $\lambda_{max}$ decreases (displaces), but the product $\lambda_{max}T$ is constant. Thus, (A) is correct.

Step 2: Evaluate Reason (R).
Wien's Law is derived from Planck's Law in the region of short wavelengths (or high frequencies). In contrast, the Rayleigh-Jeans Law is the special case for longer wavelengths. Since the reason specifies "longer wavelength" for Wien's Law, (R) is incorrect.