Question

The Wien’s Displacement Law relates the wavelength at which maximum emission occurs to:

• A. Emissivity of the surface
• B. Absolute temperature of the blackbody
• C. Surface area of the emitter
• D. Stefan-Boltzmann constant

Hint:

Use Wien’s Law: $\lambda_{\text{max}} T = b$ to find the peak wavelength of radiation for a given temperature. As temperature rises, peak shifts to lower wavelengths.

Answer 1

The Correct Option is B

Wien’s Displacement Law describes the relationship between the temperature of a blackbody and the wavelength at which it emits radiation most intensely.
Mathematically, it is given as:
\[ \lambda_{\text{max}} T = b \]
Where:
$\lambda_{\text{max}}$ = wavelength at maximum emission (in meters)
$T$ = absolute temperature of the blackbody (in Kelvin)
$b$ = Wien’s constant $\approx 2.897 \times 10^{-3}$ m·K
This equation shows that as the temperature increases, the peak of the emitted spectrum shifts toward shorter wavelengths (i.e., higher energy radiation).
Now, evaluating the options:
Option 1: Emissivity affects intensity, not wavelength shift — incorrect.
Option 2: Correct, since Wien’s Law directly relates peak wavelength to absolute temperature.
Option 3: Surface area influences total emitted energy, not peak wavelength — incorrect.
Option 4: Stefan-Boltzmann constant is used in a different law for total emissive power — incorrect.
Hence, Wien’s Displacement Law specifically links wavelength of maximum emission to the absolute temperature of the blackbody.