Profile
Settings
Refer your friends
Sign out
Wien’s law of radiation, also known as Wien’s displacement law, is concerned with the temperature of a black body (an ideal substance that emits and absorbs all frequencies of light) and the wavelength at which it emits the most light. This law is named after German physicist Wilhelm Wien who discovered it. He was awarded the Nobel Prize in Physics in 1911.
Wien’s law of radiation states that
The blackbody radiation curve for different temperatures will peak at different wavelengths inversely proportional to the temperature.
Mathematically
λₘT = b
where λₘ is the maximum wavelength corresponding to maximum intensity
T is the absolute temperature
b is the Wein’s Constant = 0.288 cm-K
Wien’s displacement law explains that objects emit different wavelengths from the spectrum at different temperatures. For example, hotter objects emit shorter wavelengths, so they appear red, while cooler objects emit longer wavelengths, so they appear blue.
In the early days of quantum mechanics, the biggest challenge physicists faced was explaining the wave nature of atoms. Blackbody radiation plays an important role in quantum mechanics. A black body is an object that absorbs all radiation at absolute zero temperature. That is, there is no transmission or emission of radiation. Many scientists have contributed to this explanation.
Max Planck described quantum blackbody radiation mechanically, while Wien’s law and Rayleigh-Jeans law were derived from Planck’s law. Wien’s law was developed for shorter wavelengths, while Rayleigh-Jeans law was for longer wavelengths.
Wien described the blackbody wavelength distribution in terms of short wavelength energy, but it was not a good approximation for long wavelengths. Planck’s law later modified it to give it universality of acceptance at longer wavelengths. Therefore, the Wien transposition law is considered a special case of Planck’s law.
Analysis
Electromagnetic radiation is emitted by all living things, and it comes in a variety of wavelengths. Radiation that strikes an item is absorbed in part and reflected in part. When an object is in thermodynamic equilibrium, the rate at which it absorbs and emits radiation is the same. As a result, a good radiation absorber (anything that absorbs radiation) can also be a good emitter. A perfect absorber, also known as a blackbody, absorbs all electromagnetic energy that strikes it.
Although the blackbody is an idealisation because no physical object absorbs 100% of the received radiation, we can create a close representation of one in the shape of a small hole in the wall of a sealed enclosure, known as a cavity radiator.
Any radiation that enters through a tiny hole in the hollow wall is trapped inside the cavity. Hence, the interior walls of a cavity radiator are rough and blackened. The hollow walls absorb exactly as much radiation as they emit at thermodynamic equilibrium (temperature T). Furthermore, the radiation entering the hole is balanced by the radiation leaving it inside the hollow. The light emitted from the hole can be used to determine the emission spectrum of a blackbody. Blackbody radiation can be defined as the electromagnetic waves released by it.
The wavelength of emitted radiation and the temperature T of the blackbody determine the intensity of blackbody radiation. At the end of the 19th century, the intensity distribution of radiation emitted by cavities was investigated experimentally. In general, radiation released by materials follows the blackbody radiation curve only roughly. Nevertheless, the spectra of typical stars nearly match the blackbody radiation curve.
Each curve corresponds to a different blackbody temperature, starting from low temperature (the lowest curve) to high temperature (the highest curve).
Two important laws summarising the experimental results of blackbody radiation are Wien’s displacement law and Stefan’s law. Wien’s displacement law is represented by a curve connecting the maximum values of the intensity curve. The hotter the body, the shorter the wavelength corresponding to the emission peak of the radiation curve. Quantitatively, according to Wien’s law, the temperature of a distant star can be estimated by measuring the wavelength of the radiation emitted by it.
Importance of Wien’s Law
We can determine the temperature of astronomical objects using Wien’s displacement law.
It is used in the design of remote sensors.
The peak emission per nanometres of the sun with a wavelength of 500 nm in the green spectrum which is in the human eye sensitive range.
Conclusion
Wien’s law tells us where (that is, at what wavelength) the star’s luminosity is the greatest. As the surface temperature increases, this maximum intensity (brightness) shifts towards the blue end of the spectrum. As surface temperature decreases, peak intensity/brightness shifts more towards the red end of the spectrum.
