Short Answer

Wien’s displacement law states that the wavelength at which a blackbody emits maximum radiation is inversely proportional to its absolute temperature. This means that as the temperature of a blackbody increases, the peak wavelength of its emitted radiation shifts toward shorter wavelengths.

Mathematically, the law is written as λmax T = constant, where λmax is the wavelength of maximum emission and T is the temperature in Kelvin. This law helps explain why hotter objects appear more bluish and cooler objects appear more reddish.

Detailed Explanation :

Wien’s Displacement Law

Wien’s displacement law is a fundamental concept in the study of blackbody radiation. It explains how the color or the peak wavelength of the radiation emitted by a blackbody changes with temperature. A blackbody emits radiation of different wavelengths, but one particular wavelength has the highest intensity. Wien’s law states that this dominant wavelength moves toward shorter wavelengths as the temperature increases.

The mathematical form of the law is:

λmax T = b

Where:

λmax = wavelength at which radiation is maximum
T = absolute temperature in Kelvin
b = Wien’s constant (2.898 × 10⁻³ mK)

This law clearly shows an inverse relationship between temperature and peak wavelength.

Meaning of Wien’s Displacement Law

Wien’s displacement law tells us:

If the temperature increases, the maximum emission shifts to shorter wavelengths (toward blue or ultraviolet).
If the temperature decreases, the maximum emission shifts to longer wavelengths (toward red or infrared).

This shift explains the color changes in heated objects. For example, when metal is heated, it first glows red, then orange, then yellow, and finally white as temperature keeps rising. Each color corresponds to radiation of different wavelengths.

Why Wien’s Law Is Important

Wien’s displacement law helps us:

Understand how objects emit radiation at different temperatures
Predict the color of stars
Estimate the temperature of distant objects in space
Explain the glow of heated metals
Analyze radiation curves of blackbodies

The law is used widely in astronomy, physics, engineering, and climate science.

Behavior of Blackbody Curves

A blackbody emits radiation across a wide range of wavelengths. However, not all wavelengths are emitted with the same intensity. The spectral distribution forms a curve that has a peak.

Wien’s law tells us where this peak lies. As temperature increases:

The entire curve rises
The peak moves leftward, toward shorter wavelengths
The object emits more energy at every wavelength

As temperature decreases, the curve lowers and shifts toward longer wavelengths.

Examples Explained Through Wien’s Law

To understand Wien’s law better, consider some everyday and scientific examples:

Heated Objects Changing Color

A piece of iron glows dull red at lower temperatures. As temperature increases, it becomes orange, yellow, and then white.
This is because the peak wavelength moves toward shorter wavelengths with increasing temperature.

Temperature of Stars

Stars appear different colors depending on their temperature.

Red stars → cooler
Yellow stars → moderate temperature
Blue stars → very hot

Astronomers use Wien’s law to calculate the surface temperature of stars, including the Sun.

Infrared Cameras

Warm bodies emit infrared radiation with peaks in the infrared region.
Wien’s law helps design sensors that detect these wavelengths.

Earth’s Radiation

Earth emits radiation mostly in the infrared region because its temperature is low compared to stars.
This concept helps in climate studies and satellite observations.

Wien’s Constant (b)

The constant in the equation λmax T = b is known as Wien’s constant:

b = 2.898 × 10⁻³ mK

This value helps calculate peak wavelength precisely.

Wien’s Law and Temperature Measurement

Wien’s displacement law is used in:

Pyrometers (non-contact thermometers)
Astronomy (measuring star temperatures)
Furnace temperature monitoring
Lava and molten metal temperature analysis

Since the law only needs the wavelength and not the material, it is very useful.

Relation to Blackbody Radiation Laws

Wien’s displacement law is part of the complete study of radiation:

Planck’s law describes the full radiation spectrum.
Stefan–Boltzmann law describes total emitted energy.
Wien’s law describes the peak wavelength.

Together, they explain blackbody emission completely.

Conclusion

Wien’s displacement law states that the wavelength of maximum radiation emitted by a blackbody is inversely proportional to its temperature. As temperature increases, the peak wavelength shifts toward shorter wavelengths, making objects appear brighter and bluer. This law is essential for understanding blackbody curves, star temperatures, heated object colors, and various scientific measurements. It plays a key role in thermodynamics, astronomy, and heat radiation studies.