Cameron Miranda
Planck's law, also known as Planck radiation law, is a mathematical relationship formulated by German physicist Max Planck in 1900. The law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature. Planck's law is based on the fact that electromagnetic radiation from heated bodies is made up of discrete units or quanta of energy, with the size of these units determined by a fundamental physical constant, known as Planck's constant. By applying Planck's law, we can calculate the energy of photons when their frequency is known, and it is particularly important when the material medium is in thermodynamic equilibrium.
| Characteristics | Values |
|---|---|
| Definition | A mathematical relationship formulated to explain the spectral-energy distribution of radiation emitted by a blackbody |
| Formula | \(P(\nu,T) = \frac{2 h {\nu}^3}{c^2} \frac{1}{e^\frac{h \nu}{kT}-1}\) |
| Variables | \(h\) (Planck's constant), \(c\) (speed of light), \(k\) (Boltzmann constant), \(T\) (absolute temperature), \(\nu\) (frequency of radiation) |
| Use Cases | Calculating the energy of photons when their frequency is known, describing the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium |
| Related Laws | Kirchhoff's law of thermal radiation, Wien's displacement law, Wien's law, Equation of radiative transfer |
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What You'll Learn
- The spectral-energy distribution of radiation emitted by a blackbody
- The spectral density of electromagnetic radiation emitted by a black body
- The spectral radiance of a body
- The relationship between the energy of photons and their frequency
- The energy radiated per time, per area, per frequency interval, per steradian
The spectral-energy distribution of radiation emitted by a blackbody
Planck's Law, also known as Planck Radiation Law, describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature. In other words, it explains the spectral-energy distribution of radiation emitted by a black body.
A black body is a hypothetical body that can absorb all electromagnetic radiation falling on it at every frequency. It reaches some equilibrium temperature and then re-emits that energy as quickly as it absorbs it. It is also known as a perfect absorber, as there is no reflected radiation, and its emission is independent of direction.
In 1896, Wien derived a distribution law of radiation, which was later used by Planck to base his quantum theory. Planck's law is a formula for the spectral radiance of an object at a given temperature as a function of frequency or wavelength. It has dimensions of power per solid angle per area per frequency or power per solid angle per area per wavelength.
The equation of radiative transfer describes how radiation is affected as it travels through a material medium. Planck's law is of special importance when the material medium is in thermodynamic equilibrium. Planck's law accurately predicts the spectral radiance of black bodies in a vacuum at any temperature.
The spectral distribution of the radiation emitted by a black body shifts with a change in temperature. The total radiated energy of a body increases with increasing temperature, and the peak of the emitted spectrum shifts to shorter wavelengths.
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The spectral density of electromagnetic radiation emitted by a black body
Planck's law, developed by Max Planck in 1900, describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature. It is a mathematical relationship that explains the spectral-energy distribution of radiation emitted by a black body, which is a hypothetical body that absorbs all electromagnetic radiation falling upon it, reaches equilibrium temperature, and then re-emits that energy.
The spectral radiance of a black body describes the spectral emissive power per unit area, per unit solid angle, and per unit frequency for particular radiation frequencies. Planck's law states that the spectral radiance can be expressed per unit wavelength or per unit frequency. The law can also be expressed in other terms, such as the number of photons emitted at a certain wavelength or the energy density in a volume of radiation.
The spectral radiance of radiation transmitted from the interior of a black body to its exterior through its surface is independent of direction due to the isotropy of the radiation in the body's interior. This is known as the Helmholtz reciprocity principle. Additionally, according to Kirchhoff's law of thermal radiation, the thermal radiation from a black body is always equal to the full amount specified by Planck's law.
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The spectral radiance of a body
Planck's law, also known as Planck radiation law, describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature. According to the law, as the temperature increases, the total radiated energy of a body increases, and the peak of the emitted spectrum shifts to shorter wavelengths.
Every physical body spontaneously and continuously emits electromagnetic radiation. The spectral radiance of a body, Bν, describes the spectral emissive power per unit area, per unit solid angle, and per unit frequency for particular radiation frequencies. The spectral radiance can also be expressed per unit wavelength λ instead of per unit frequency.
The equation of radiative transfer describes how radiation is affected as it travels through a material medium. Planck's law is of particular importance when the material medium is in thermodynamic equilibrium. In this case, the law describes the power per area per frequency or the power per area per wavelength. When these functions are multiplied by the total solid angle of a sphere, we get the spectral irradiance.
The spectral radiance can also be expressed in other terms, such as the number of photons emitted at a certain wavelength or the energy density in a volume of radiation. For example, Planck's law can be written in terms of the spectral energy density (u) by multiplying B by the appropriate form of the law. These distributions represent the spectral radiance of blackbodies—the power emitted from the emitting surface, per unit projected area of the emitting surface, per unit solid angle, per spectral unit (frequency, wavelength, wavenumber, or their angular equivalents, or fractional frequency or wavelength).
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The relationship between the energy of photons and their frequency
Planck's law, or Planck's radiation law, formulated by German physicist Max Planck in 1900, describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature. A black body is defined as one that completely absorbs all electromagnetic radiation falling on it at every frequency.
Planck's law is a formula for the spectral radiance of an object at a given temperature as a function of frequency or wavelength. It has dimensions of power per solid angle per area per frequency or power per solid angle per area per wavelength.
According to Planck's law, as the temperature of a body increases, the total radiated energy of the body increases, and the peak of the emitted spectrum shifts to shorter wavelengths. This law is independent of temperature, as stated by Wien's displacement law, and is important in the special case where the material medium is in thermodynamic equilibrium.
The energy of a photon is directly proportional to its frequency, as given by the equation E = hf, where E is the energy of the photon, h is Planck's constant, and f is the frequency of the photon. This relationship can be observed in the electromagnetic spectrum, where radio waves, with low frequency and low energy, are at the low end of the spectrum, while gamma rays, with high frequency and high energy, are at the high end.
The energy of a photon is also inversely proportional to its wavelength, which is the distance between two consecutive peaks or troughs of a wave. This relationship is described by the equation E = hc/λ, where c is the speed of light and λ is the wavelength of the photon. Thus, photons with shorter wavelengths (higher frequency) have more energy than those with longer wavelengths (lower frequency).
The relationship between the energy and frequency of photons has been studied experimentally through the photoelectric effect, where the kinetic energy of emitted electrons varies directly with the frequency of incident light. The energy of a photon is also related to its momentum, which follows the de Broglie equation, leading to practical applications such as optical tweezers.
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The energy radiated per time, per area, per frequency interval, per steradian
Planck's law, or Planck's radiation law, describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature. Planck's law is a formula for the spectral radiance of an object at a given temperature as a function of frequency or wavelength.
Every physical body spontaneously and continuously emits electromagnetic radiation. The spectral radiance of a body, Bν, describes the spectral emissive power per unit area, per unit solid angle, and per unit frequency for particular radiation frequencies.
Planck's law gives the energy radiated per unit time at frequency ν per unit frequency interval per unit solid angle into an infinitesimal cone from an element of the blackbody surface that is of unit area in projection perpendicular to the cone's axis. The monochromatic specific intensity Iν is:
> Iν = 2hc−2ν3/[exp(hν/kT− 1)]
Where h is Planck's constant, c is the speed of light, k is the Boltzmann constant, and T is the thermodynamic temperature of the black body. Iν has units of watts per square metre per steradian per hertz (W m−2 sr−1 Hz−1).
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Frequently asked questions
Planck's Law, or Planck Radiation Law, is a mathematical relationship formulated by German physicist Max Planck in 1900. It describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature.
We can use Planck's Law to calculate the spectral radiance of an object at a given temperature as a function of frequency or wavelength. It also helps us calculate the energy of photons when their frequency is known.
Planck's constant (h) is a fundamental physical constant that represents the size of discrete units or quanta of energy. The variable h holds the constant value of 6.63 x 10^-34 J.s in the International System of Units.
The equation commonly referred to as Planck's Law for radiation is:
> $P(\nu,T) = \frac{2 h {\nu}^3}{c^2}$ $\frac{1}{e^\frac{h \nu}{kT}-1}$
This equation represents the energy radiated per time, per area, per frequency interval, and per steradian.
