Wien's Law

Wien's law of displacement describes the relationship between the temperature of a black body and the wavelength at which it emits the most radiation. This means that the hotter an object, the shorter the wavelength of its peak radiation becomes.

Formula of Wien's law

$$\lambda_{\text{max}}$$ = \frac{b}{T}

whereby:

• $\lambda_{\text{max}}$ = the wavelength (in meters) at which the intensity of the emitted radiation is maximum
• $b$ = Wien's constant ≈ 2.897 × 10⁻³ m·K
• $T$ = absolute temperature of the object (in Kelvin, K)

This means that at higher temperatures the maximum emitted light is blue-shifted (shorter wavelength, higher frequency), while at lower temperatures the light is red-shifted (longer wavelength, lower frequency).

Practical applications of Wien's law

1. Stars and their colors

   • Blue stars (~10,000 K) radiate primarily in ultraviolet and blue.
   • The Sun (~5,778 K) has a peak in the yellow-green part of the spectrum (~500 nm).
   • Red dwarfs (~3,000 K) emit more in the infrared .

2. Thermal cameras & Infrared measurement

   • Low-temperature objects (such as humans, ~300 K) emit infrared radiation with a peak around 10 μm (invisible to the human eye).
   • Hot objects (>1000 K) begin to glow visibly red.

3. Incandescent light bulbs and LED technology

   • A classic light bulb (~2500-3000 K) radiates mainly in the infrared, which means energy loss.
   • LEDs and fluorescent lighting are designed to generate more visible light without unnecessary heat radiation.

4. Cosmology and the cosmic microwave background

   • The cosmic microwave background (CMB) radiation has a temperature of ~2.7 K , which gives a peak wavelength in the microwave region (~1 mm) .

Summary

• Hot object? → Short wavelength (blue, UV)
• Cold object? → Long wavelength (red, IR, microwaves)
• Wien's law helps in stellar analysis, thermography and lighting technology.