Anaya Nolan
Wien's displacement law, also known as Wien's law, is a fundamental concept in the study of radiation. It describes the relationship between the temperature of an object and the wavelength of its maximum emission of radiation. The law was discovered by German physicist Wilhelm Wien, who won the Nobel Prize for Physics in 1911 for his work. Wien's displacement law can be used to determine the peak radiation output at a specific wavelength, and it has various applications in the study of black-body radiation and incandescent light bulbs. However, it is important to note that the law has limitations and does not apply to longer-wavelength blackbody radiations.
| Characteristics | Values |
|---|---|
| Definition | States that the black-body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature |
| Formula | B(ν, T) = (2hν3/c2) / (e^(hν/kbT) – 1) |
| Constant | 2.878 × 10^-3 mK or 2898 μm⋅K |
| Use Case | Used to determine the peak radiation output at a wavelength of 500 nm for the surface of the sun (5700 K) |
| Limitations | Fails in the case of longer wavelength blackbody radiations; a continuous Wein curve cannot be obtained when the body's temperature is reduced |
| Temperature Units | Kelvin (K); convert from oC if the temperature is given in degrees |
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What You'll Learn
Relationship between temperature and wavelength
In physics, Wein's displacement law, also referred to as Wein's law, describes the relationship between the temperature of an object and the wavelength of its maximum emission of radiation. The law is a fundamental concept in the study of radiation.
According to Wein's displacement law, the black-body radiation curve for different temperatures peaks at a wavelength that is inversely proportional to the temperature. In other words, as the temperature increases, the wavelength of the peak emission decreases, and vice versa. This relationship is described by the equation:
{displaystyle d\nu }* (in hertz)
Where the peak wavelength is given by:
Λpeak = b/T
Where "b" is the Wein's displacement constant, and "T" is the absolute temperature in Kelvin. The value of the Wein's displacement constant in SI units is approximately 2.8977719 x 10^-3 m·K or 2898 μm·K in micrometers.
The law is relevant to everyday experiences, such as the colour change in an incandescent light bulb when the temperature of the filament drops due to a voltage drop. It is also used to estimate the temperature of objects, such as the Sun's surface, lava, or any hot body, by measuring the peak wavelength of its thermal emission spectrum.
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Peak emission at optical frequency
Wein's displacement law, also known as Wein's Law, is a fundamental concept in the study of radiation. It describes the relationship between the temperature of an object and the wavelength of its maximum emission of radiation. In other words, it states that the higher the temperature, the lower the wavelength (λmax) for which the radiation curve reaches its maximum. This shift to shorter wavelengths corresponds to photons of higher energy.
The law is particularly useful when considering the peak of black body emission per unit frequency or per proportional bandwidth. In these cases, a different proportionality constant must be used, but the form of the law remains the same: the peak wavelength is inversely proportional to temperature, and the peak frequency is directly proportional to temperature. This relationship can be expressed mathematically using Wein's displacement constant, represented by 'b' in the equation and calculated to be approximately 2.878 x 10^-3 mK in SI units.
Wein's displacement law can be used to estimate the temperature of an object based on the peak wavelength or frequency of its thermal emission spectrum. For example, it can be applied to calculate the temperature of the Sun's surface by finding the peak wavelength of a solar spectrum. The law also has applications in understanding the behaviour of incandescent light bulbs, where the heat produced by the filament is directly proportional to the voltage, and the temperature of the filament drops with any voltage drop.
Additionally, Wein's displacement law has been derived from Planck's law for the spectrum of black-body radiation. While Planck's more general equation did not explicitly include Wein's constant, it introduced Planck's constant 'h'. However, by combining Planck's constant with the Boltzmann constant 'k', Wein's constant can be obtained. This demonstrates the interconnectedness of these laws in describing the behaviour of black-body radiation.
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Black-body radiation
Wien's displacement law, also known as Wien's law, describes the relationship between the temperature of a black body and the wavelength at which it emits the most light or radiation. The law is named after German physicist Wilhelm Wien, who received the Nobel Prize for Physics in 1911 for his discovery. Wien's law states that the blackbody radiation curve for different temperatures peaks at a wavelength that is inversely proportional to the temperature. In other words, as the temperature of a black body increases, the wavelength of its peak emission decreases, and vice versa.
Wien's law can be applied to various scenarios, such as determining the peak radiation output of the sun's surface at a given temperature. It also explains the colour appearance of objects at different temperatures. For example, hotter objects emit shorter-wavelength radiation, appearing blue, while cooler objects emit longer-wavelength radiation, appearing reddish.
However, Wien's displacement law has limitations. It fails in the case of longer-wavelength blackbody radiations, and a continuous Wien curve cannot be obtained when the body's temperature is reduced. Planck's law for black-body radiation, formulated by Max Planck, provides a more general equation that includes Wien's constant implicitly through Planck's constant. Planck's law specifies the spectral brightness or intensity of black-body radiation as a function of wavelength at any given temperature and is responsible for the shift in the peak wavelength observed in Wien's law.
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Planck's Law
The law is closely related to Wien's displacement law, which describes the relationship between the temperature of an object and the wavelength at which it emits radiation most intensely. Wien's displacement law is derived from Planck's law and can be used to numerically evaluate the constant relating temperature and peak parameter values.
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Incandescent light bulbs
In 1893, Wilhelm Wien developed a law that described the relationship between the temperature of a black body and the wavelength at which it emits maximum radiation. Wien's displacement law states that the black-body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature.
Wien's displacement law can be applied to incandescent light bulbs. An incandescent light bulb has a filament that produces light through thermal radiation. As the temperature of the filament changes, the colour of the light emitted by the bulb shifts. When the filament's temperature decreases, longer wavelengths are emitted, and the bulb appears dimmer with a reddish tinge. Conversely, as the filament's temperature increases, the emitted wavelengths become shorter, and the bulb appears brighter with a whiter tinge.
Wien's displacement law can be used to determine the temperature of the filament in an incandescent light bulb. The law is expressed mathematically as:
Λpeak = b/T
Where λpeak is the peak wavelength of the spectral density, T is the temperature of the filament, and b is Wien's displacement constant, approximately equal to 2.897771955 x 10^-3 m·K.
There are demonstrations that use an incandescent light bulb to illustrate Wien's displacement law. In one such demonstration, the light bulb is attached to a Variac autotransformer. By adjusting the voltage on the Variac, the temperature of the filament can be controlled, resulting in observable changes in the colour of the light emitted by the bulb.
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Frequently asked questions
Wien's Displacement Law, also known as Wien's Law, describes the relationship between the temperature of an object and the wavelength at which it emits the most radiation.
You can use Wien's Displacement Law when studying radiation, particularly when dealing with blackbody radiation. It helps determine the peak wavelength of radiation emitted by an object at a given temperature.
A blackbody is an ideal body that can absorb all incident electromagnetic radiation, regardless of frequency or angle. It must also be a good emitter of radiation to maintain thermal equilibrium.
Wien's Displacement Law has limitations when dealing with longer wavelength blackbody radiations. It fails to provide a continuous Wien curve when the body's temperature is reduced.
Wien's Displacement Law is derived from Planck's Law, which describes the spectral brightness or intensity of black-body radiation as a function of wavelength at a given temperature. Planck's Law predicts Wien's Displacement Law and can be used to evaluate the constant relating temperature to the peak parameter value.
