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The **Rayleigh-Jeans law** is a formula that approximates
black-body radiation at longer wavelengths, i.e.,
approximates one of the two tails of the spectrum,
which is precisely specified by the Planck function.
The Raleigh-Jeans law has the advantage of being a simpler function,
easier to manipulate algebraically and incorporate into
formulae describing astronomical phenomena.

B_{λ}(T) = 2cK_{B}T/λ^{4}

- λ - wavelength.
- T - temperature.
- B
_{λ}(T) - spectral energy distribution (SED): density of energy radiated at the given temperature and wavelength. - c - speed of light.
- K
_{B}- Boltzmann constant.

Or, based upon frequency, giving a SED according to frequency-differentials:

B_{ν}(T) = 2ν²K_{B}T/c²

- ν - frequency.
- B
_{ν}(T) - analogous SED, for frequency instead of wavelength.

Being a good approximation of the spectrum's longer-wavelength tail,
it is useful in radio astronomy. The region of the spectrum
where it is a useful approximation is called the
**Rayleigh-Jeans regime** or **Raleigh-Jeans region**.
The this regime's location depends upon the temperature-regime: the
hotter the type of objects, the more the Rayleigh-Jeans regime
extends toward shorter wavelengths.

The *Rayleigh-Jeans law* was devised before the Planck function
was known and was derived from classical (pre-quantum mechanics)
physical principles by Lord Rayleigh and James Jeans. However, it
was clearly wrong: it says that the shorter the wavelength, the
more electromagnetic radiation is emitted at that wavelength, approaching infinity.
Among other issues, this implies objects would cool to zero in zero
time. This anomaly between theory and observation was termed the
**ultraviolet catastrophe**. The Planck function matched observation
and quantum mechanics developed from the physical rules this
implied. Toward longer wavelengths, the Planck function approaches
the Raleigh-Jeans law's formula, and the formula is in some
situations referred to as the **Rayleigh-Jeans limit**.

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