What is Planck's law?

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- GoPhotonics

Sep 22, 2023

Planck's law, also known as Planck radiation law, is a fundamental principle that describes the electromagnetic radiation emitted by a black body in thermal equilibrium at a definite temperature. A blackbody is a perfect object which absorbs or emits radiation that falls on it at all frequencies over all angles of incidence. In 1900, German physicist Max Planck proposed the equation to find a relation between the radiation emitted by a blackbody, its temperature and wavelength.

Classical physics assumes that radiation is emitted continuously by matter, with a smooth spectrum of energy levels, yet it could not explain the observed spectrum of black body radiation.

According to Planck, atoms and molecules can only emit or absorb energy in specific, discrete quantities known as quanta. The smallest amount of energy that can be emitted or absorbed in the form of electromagnetic radiation is known as quantum.

The law describes the spectral density of electromagnetic radiation emitted at all wavelengths from a black body in thermal equilibrium at a given temperature T, when there is no net transfer of matter or energy between the black body and its surroundings.

Based on this hypothesis, Planck demonstrated that the spectral radiance of a body at an absolute temperature T, for a specific frequency ν, can be expressed as follows:

Here, B(ν,T) = measure of spectral radiance density, h = Planck’s constant, c = velocity of light, ν = frequency of electromagnetic radiation, T = absolute temperature of the body and kB = Boltzmann Constant. 

The spectral radiance density of a body, denoted as Bν, characterizes the energy it emits as radiation across various frequencies. It is measured as the power emitted per unit area of the body, per unit solid angle over which the radiation is measured, and per unit frequency.

Later, Albert Einstein showed that the energy of the radiation absorbed or emitted is directly proportional to the frequency of the radiation.

Where h is the Proportionality constant, Planck's constant = 6.626×10−34J−s

The Planck law illustrates the connection between the total radiated energy of a body and the peak of its emitted spectrum.

The amount of radiation emitted from a body's surface is referred to as Planck radiation. The ratio of the actual radiance to the theoretical Planck radiance is known as the emissivity. It is influenced by factors such as the body's chemical composition, temperature, wavelength, angle of passage, and polarization. For a natural interface, the emissivity always falls within the range of 0 to 1.

At low frequencies, Planck’s law tends to be Rayleigh-Jeans formula, which is a good approximation of the spectral radiance of blackbody radiation, hν <<kT and hν/kT <<1, the formula becomes:

It describes the spectral radiance of blackbody radiation as the temperature increases.

At high frequencies, Wien’s law describes the temperature (T) of a blackbody and the wavelength at which its emission spectrum peaks. In order to find λmax, take the derivative of 

Take derivative of the equation:

For λ = λmax,

It tends to the Wien approximation, which is valid for describing the spectral radiance of blackbody radiation at extremely high temperatures.