*Wien's Law* was an early attempt to describe the
blackbody radiation spectrum, proposed by the
German scientist Wilhelm Wien in 1896. The Wien Law
closely approximated the true shape of the blackbody
spectrum at short wavelengths, but ultimately failed because
it relied solely on classical physics. It was superseded by
Planck's radiation law which correctly describes the
blackbody spectrum at all wavelengths. However, Wien's
Law is still used as a convenient approximation to the
blackbody spectrum at short wavelengths.

###
The mystery of the blackbody

The nature of blackbody radiation was believed to be
one of the last great
unsolved problems in physics at the close of the nineteenth
century. Although much work had been done on both
thermodynamics and electromagnetic radiation, no one
had yet combined both to
explain the spectrum of light emitted by hot objects,
first described by
Kirchhoff in 1859.

Kirchhoff showed that blackbody radiation should be some
function of the wavelength and temperature, as in

E_{λ} = constant
× f(&lambda,T)

a relation based upon proven thermodynamic principles.
The problem was that no one knew the exact form of that
function, *f*.

###
Wien's Law

In 1893, Wilhelm Wien first derived his
Displacement Law, performing a
gedankenexperiment with a hypothetical blackbody --
a cavity, filled with radiation, that could be
expanded and contracted at will. His work
showed that the wavelength at which most radiation
is emitted by a blackbody is inversely proportional to
its temperature. This was an important step, as it
suggested how the blackbody spectrum was related to the
temperature, but it still didn't fully uncover the form
of Kirchhoff's function.

In his 1896 paper (Ann. Physik, v.58, 622), Wien combined
his Displacement Law with the Stefan-Boltzmann Law,
and suggested that the blackbody spectrum could be fit
to a function of the form

E_{λ} =
(c_{1} / λ^{5}) /
exp(c_{2}/λT)

where *c*_{1} and *c*_{2}
are empirically defined constants. This relation
is known as *Wien's Law* of blackbody radiation.

Wien's assumptions on exactly why the blackbody spectrum
should have this form aren't entirely correct, but they
matched observations very well. For a while, Wien's Law
was believed to be reasonably correct. However, experiments
to measure the blackbody spectrum in the far infrared
(out to 60 microns) showed that Wien's Law
diverged badly from reality. Thus, the Wien Law was
incorrect, and the mystery of the blackbody continued.

###
Planck gets it right

In 1900 Max Planck derived his relation for a blackbody,
which was found to be in perfect agreement with measurements
at all wavelengths and all temperatures -- the problem of
the blackbody was solved. Planck's Law appears
nearly identical to Wien's
except for the constants and a slight difference in the exponential term:

E_{λ} =
(2hc^{2}/
λ^{5}) /
(exp(hc/
λk
T) - 1)

However, that "slight" difference masks a radical change
in physical assumptions, particularly in Planck's treatment
of light as individual "quanta", and the use of
statistical mechanics to describe the emitting blackbody
as a collection of quantum oscillators. Planck's relation
is also radically different in that the constants are
derived from physical principles, not from experimental
fitting. The correct blackbody relation is generally
considered one of the most important nails in the
coffin of classical physics, and the birth of
quantum mechanics.

Although Wien's law was proven incorrect, it was an
important step in Planck's eventual derivation of
the correct blackbody relation. Wien received the
1911 Nobel Prize in Physics mainly for his
derivation of the
Displacement Law and
for his work on using cavities as experimental
blackbodies, but his attempt at a law of blackbody
radiation certainly contributed to his award.

Like many quantum
mechanical and relativistic relations, Planck's
Law reduces to the classical laws of both Wien
and Rayleigh and Jeans
in the short- and long-wavelength approximations.
For the Wien Law, this happens when *hc/λ*
is much larger than *kT*, making the
exponential term much larger than -1.

Sources:

Rybicki, G. and Lightman, A.,
*Radiative Processes In Astrophysics*,
J. Wiley and Sons, 1976

Richtmeyer, F.K.,
*Introduction to Modern Physics*,
McGraw-Hill, 1934

blackbody radiation

Rayleigh-Jeans Law -- Planck's radiation law -- Wien's Law