Wien’s Displacement Law

Wien’s law is a relation between the temperature of a blackbody (an ideal substance that emits and absorbs all frequencies of light) and the wavelength at which it emits the most light. It is named after German scientist Wilhelm Wien, who discovered the rule and earned the Nobel Prize in Physics in 1911.

In the 1890s, Wien addressed the wavelength or frequency distribution of blackbody radiation. It was his idea to use an oven with a small hole as a suitable approximation for the perfect blackbody. Any radiation that enters the small hole is dispersed and reflected so often off the inside walls of the oven that practically all incoming radiation is absorbed and the possibility of some of it making its way out of the hole again is extremely minimal.

Wien’s Displacement Law 

Definition

Wien’s displacement law suggests that for various temperatures, the black-body radiation curve will peak at distinct wavelengths that are inversely proportional to the temperature.

Max Planck used quantum mechanics to explain black body radiation, while Rayleigh-Jeans and Wein’s provide specific examples for Planck’s law. Wein’s law was created for shorter wavelengths, and Rayleigh-Jeans’ law was described for longer wavelengths. However, Wein’s law existed long before Max Planck’s explanation.

Wein’s described the distribution of black body wavelengths with respect to energies for shorter wavelengths, but it did not provide adequate estimates for longer wavelengths. Later, Planck’s law rectified this, resulting in a universal that was acceptable even for longer wavelengths. As a result, Wein’s displacement law is regarded as a subset of Planck’s law.

What is Black Body?

A blackbody is a body that emits the maximum heat for its absolute temperature. A blackbody is a physical body that has been idealised and has particular characteristics. A black body in thermal equilibrium has an emissivity of = 1.0 by definition. Real-world objects do not release as much heat as a totally black body. 

Gray bodies release less heat than black bodies and are so referred to as such. At room temperature, a blackbody’s surface emits around 448 watts per square metre of thermal radiation. Real-world things with emissivities less than 1.0 (such as copper wire) emit radiation at a slower pace. A blackbody absorbs all incident electromagnetic radiation regardless of frequency or angle of incidence. As a result, its absorptivity equals unity, the highest attainable value. In other words, a blackbody is an excellent absorber.

Wien’s Displacement Law  Formula

λmax = b/T

Where,

λmax – Maximum Wavelength, T – Absolute Temperature, b – Wein’s Constant and value = 2.88 x 10-3 m-K or 0.288 cm-K

The above equation is referred to as the Wien’s law formula or Wien’s displacement law formula. With increase in absolute temperature, the maximum wavelength corresponding to maximum emission will decrease. The Wien’s constant (b) is a physical constant that determines the relation between the thermodynamic absolute temperature of the black body and the maximum wavelength. It is represented by the symbol b. It is a result of the black body’s temperature and wavelength, which becomes shorter as the wavelength increases with temperature.

Wien’s displacement constant (b)

Wien’s constant is a physical constant that establishes the relation between the thermodynamic temperature and wavelength of a black substance. It is a combination of temperature and the wavelength of the black body, which becomes shorter as the temperature rises and the wavelength approaches its maximum.

Application of Wien’s Displacement Law

• A 1500K hot wood fire generates peak radiation at 2000 nm, which is easily calculated. As a result, the vast majority of the radiation released by the wood fire is invisible to the naked eye. As a result, while a bonfire is a wonderful source of warmth, it is a poor source of light.
• The temperature at the surface of the sun is 5700 K. And we can calculate the peak radiation output at a wavelength of 500 nm. by using the Wien displacement law. This colour refers to the green portion of the visible light spectrum. Our eyes, it turns out, are super vulnerable to visible light at this wavelength. We should be delighted that a disproportionately large fraction of the sun’s energy falls within a relatively limited visible spectrum.
• When a piece of metal is heated, it turns red hot at first. This is the longest visible wavelength. After additional heating, the colour shifts from red to orange, then yellow. When the metal is at its hottest, it emits a white light. The radiation is dominated by shorter wavelengths.

Conclusion 

Wien’s law is a relation between the temperature of a blackbody (an ideal substance that emits and absorbs all frequencies of light) and the wavelength at which it emits the most light. Any radiation that enters the small hole is dispersed and reflected so often off the inside walls of the oven that practically all incoming radiation is absorbed and the possibility of some of it making its way out of the hole again is extremely minimal. A blackbody is a body that emits the maximum heat for its absolute temperature. As a result, the vast majority of the radiation released by the wood fire is invisible to the naked eye. And we can calculate the peak radiation output at a wavelength of 500 nm. by using the Wien displacement law.