Question

Which law relates the wavelength of maximum emission to the temperature of a blackbody?

• A. Stefan-Boltzmann Law
• B. Wien’s Displacement Law
• C. Planck’s Law
• D. Kirchhoff’s Law

Hint:

\textbf{Wien’s Law:} Hotter body → shorter wavelength.
Sun (hot) → shortwave, Earth (cool) → longwave.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
All objects emit electromagnetic radiation based on their temperature. The peak wavelength of this radiation shifts as temperature changes.
Step 2: Key Formula or Approach:
Wien's Displacement Law is expressed as:
\[ \lambda_{max} = \frac{b}{T} \] Where:
\( \lambda_{max} \) is the peak wavelength.
\( T \) is the absolute temperature (in Kelvin).
\( b \) is Wien's constant ($\approx 2898 \mu$m$\cdot$K).
Step 3: Detailed Explanation:
This law states that the wavelength at which a blackbody emits the maximum amount of radiation is inversely proportional to its absolute temperature.
- Higher temperature $\rightarrow$ Shorter peak wavelength (e.g., Sun).
- Lower temperature $\rightarrow$ Longer peak wavelength (e.g., Earth).
Step 4: Final Answer:
Wien's Displacement Law relates wavelength of maximum emission to temperature.