Question

Which of the following radiation laws describes the relation between peak wavelength and temperature of an emitting body?

• A. Kirchhoff's
• B. Planck's
• C. Stefan-Boltzmann's
• D. Wien's

Hint:

Wien's Law = Wavelength vs. Temperature.
Hotter body $\rightarrow$ Shorter wavelength (Blue/UV).
Cooler body $\rightarrow$ Longer wavelength (Red/Infrared).
This is why the Sun looks yellow/white and a heated iron rod looks red before it turns white.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question asks to identify the physical law that describes how the wavelength of maximum emission (peak wavelength) from a blackbody changes as its temperature changes.
Key Formula or Approach:
The law is expressed mathematically as:
\[ \lambda_{\text{max}} = \frac{b}{T} \]
Where \( \lambda_{\text{max}} \) is the peak wavelength, \( T \) is the absolute temperature (Kelvin), and \( b \) is Wien's displacement constant.

Step 2: Detailed Explanation:

• Wien's Displacement Law:
This law states that the wavelength at which the radiation intensity of a blackbody is maximum is inversely proportional to its absolute temperature.
As an object gets hotter, the peak of its radiation spectrum shifts toward shorter wavelengths (higher frequencies/energies).
Example: The Sun (approx. $6000$ K) emits peak radiation in the visible spectrum ($0.5$ $\mu$m), while the Earth (approx. $288$ K) emits peak radiation in the thermal infrared ($10$ $\mu$m).

• Comparison with other laws:
Stefan-Boltzmann Law: Relates the total energy emitted to the fourth power of temperature (\( E = \sigma T^4 \)).
Kirchhoff's Law: States that a good absorber is a good emitter at a given wavelength and temperature.
Planck's Law: Describes the entire spectral distribution of electromagnetic radiation from a blackbody.

Step 3: Final Answer:
Wien's Law specifically defines the "displacement" of the peak wavelength with respect to temperature.