At the end of the 19th century, physical science had achieved great
success. With Maxwell's equations, it was understood that electricity, magnetism
and light were actually different faces of electromagnetic fields and waves.
Light is the kind of electromagnetic waves that our eyes perceive. Within a
short time, varieties of electromagnetic waves were discovered, such as radio,
ultraviolet, infrared, X-ray, which all obey the same laws and propagate with
the same speed of light c. On the other hand, with the development of
thermodynamics and statistical physics, energy conservation, which includes all
forms of energy, including heat, became a central concept. While classical
physics would seem to have been completed with these great achievements, it
turned out that some very basic observations contradicted classical physics,
were not understood in any way, and led to inconsistencies. Thus science moved
from a great victory to a great crisis.
At the beginning of the 20th century, one aspect of this crisis was
overcome by Einstein's theory of relativity, and another aspect involving many
problems was overcome by quantum mechanics. According to quantum theory,
objects have both particle and wave properties. A particle is also a wave. Planck's
constant is the fundamental natural constant that determines the relationships
between particle properties, energy and momentum, and wave properties,
frequency and wavelength.
One of the dead ends of classical physics:
"Blackbody" radiation
The first major problem that classical physics fails
to understand, pointing the way to quantum mechanics, is "blackbody"
radiation. (This term "blackbody" is somewhat misleading. What is
meant here is radiation in thermodynamic equilibrium with matter. This
radiation contains different amounts of all colors, radiation energy from all
colors is exchanged between matter and radiation, and the temperature of both
matter and radiation remains constant. Such an object also has a
temperature-dependent color, which is not black, as we will see below.)
Let us consider a system in thermodynamic equilibrium.
Thermodynamic equilibrium means that every part of this system is at a constant
temperature T, the system has come to equilibrium in energy exchange with its
surroundings, it neither heats up nor cools down, and the average energy of
each atom and molecule remains constant at the level of kBT. (The
constant kB, which determines the energy equivalent of a given temperature, is
called the Boltzmann constant.)
Now, the energies of each atom and molecule in our
body in thermodynamic equilibrium change momentarily as they interact with
other atoms and molecules around them, but the average energy remains constant.
Every particle interacts with other particles, as well as with electromagnetic
waves. This interaction was understood in great detail with Maxwell's equations.
In thermodynamic equilibrium, the amount of energy
taken in and given out per second by all atoms must be equal. Therefore, in a
system at temperature T, electromagnetic waves must also have properties
specific to temperature T. In thermodynamic equilibrium, how much energy
electromagnetic waves carry at different frequencies should also be a property
determined by temperature.
colors of the stove
Light is a type that our eyes perceive the frequency
and wavelength of electromagnetic waves, and we perceive the frequency of light
as color. We all know that an object at a certain temperature, such as a hot
stove, has a certain color. As it heats up, the color first turns red. A hotter
stove will be yellow, yellow-white, white-blue (incandescent) if orange is even
hotter. At even higher temperatures, the stove appears colorless, black,
because it emits electromagnetic waves at ultraviolet frequencies that our eyes
can no longer detect. In fact, we can measure how much radiation there is at
each frequency by separating the light emitted at any temperature into colours.
If we decompose it into colors while the stove appears red, that is, if we
observe its spectrum, it becomes blue, green, yellow etc. We understand that
there is a certain amount of radiation in all colors (frequencies), and that we
see the compound color as red.
The radiation spectrum from objects in thermodynamic
equilibrium could be measured in great detail in the 19th century. The
dispersion of the radiation into the colors always followed a typical curve in
the same way at every temperature. As the temperature increases, the most
dominant frequency in the spectrum increases, that is, the color goes towards
blue, violet and ultraviolet, and the total radiation intensity (total amount
of radiation in all colors increased in proportion to T4 with the fourth power
of the temperature).
The picture shows the luminescence spectra at
different temperatures.
It is not possible to understand these measurements with classical physics.
Calculation is done like this: first count how many different waves there are
at each frequency in the system. How many different waves can be of the same
frequency but traveling in different directions? : Let's call the frequency f,
the number of waves increases proportionally to f2 with frequency.
So how much energy does each of the different waves carry?
According to classical physics, each different wave,
regardless of its frequency, carries an average of kBT of energy,
just like an atom or molecule. Now, if we multiply the number of different
waves at each frequency with the energy carried by each, the amount of energy
at each frequency, namely the spectrum, should be proportional to the formula
(kBT f2), if classical physics is correct. This leads to
a very absurd expectation beyond not fitting the observed spectrum: If we add
up the energy emitted at all frequencies, namely (kBT f2),
the contributions increase as the frequency increases, and in the end, it
doesn't matter if the temperature is low, all objects in thermodynamic
equilibrium emit an infinite amount of radiation energy. Classical physics
gives an endlessly ridiculous result.
Where is the error in classical physics?
In classical physics, the average energy of each different wave is kBT, because the instantaneous energy E of the wave can take all values from zero to infinity. As Ludwig Boltzmann showed at the end of the 19th century, the probability of each energy value is determined by the formula P(E)=C exp (-E / kBT). It doesn't matter if you don't know what this formula means, we have a well-validated formula that tells you how often to find each energy value that matters. Assuming that the energy can take all values, if we calculate the average energy value with the Boltzmann probability formula, we get kBT.
In 1900, the German theoretical physicist Max Planck
solved the problem with a very radical assumption: The energy of the wave cannot take every value. The wave consists of particles (quantums), and the energy of each of these
particles is proportional to the frequency of the E wave. Well
E= hf
Here h is the proportionality coefficient, which we
now call Planck's constant. In this case, each wave can carry not every energy
value, but only nhf energy values depending on how many quantums there are n =
0,1,2,3… etc. When we take the weighted average of these with the Boltzmann probability
formula, the average energy that each wave type will carry in thermodynamic
equilibrium is no longer kBT. The average energy is expressed by a
more complex formula that also includes the constant h, depending on both
temperature T and frequency.
Multiplying the average energy by f2, which
gives the number of waves of the same frequency, shouldn't the resulting
formula give exactly the spectrum of radiation observed in the experiment? When
the formula calculated by Planck is applied to the observed blackbody radiation
spectrum, the value of the constant is found to be h = 6.3 10-34
Joule seconds.
Thus, Planck was able to calculate the properties of
radiation in thermodynamic equilibrium exactly as it was observed, with the
assumption that no one could understand that waves were also composed of
particles. Although the reason is not understood, an explanation that fits
perfectly with the observations on a fundamental problem in which classical
physics has failed so badly must have been correct. Electromagnetic waves
consisted of particles, namely quanta, we call these quanta 'photons'.
Another example of light becoming a particle:
Photoelectric effect
The idea that waves, including light, are composed of
particles (quantums) obeying the relation E = hf, also explained an entirely
different set of experiments, the photoelectric phenomenon. When light was sent
to a metal, it was observed that electrons were ejected from the metal. If
brighter light was sent, more electrons would come out. But no matter how
bright the light was, the energy of each ejected electron did not change. It
was observed that the energy of the ejected electrons only increased with the
frequency of the light. That is, the electrons ejected from the same metal by
the blue light with higher frequency were more energetic than the electrons
ejected by the lower frequency red light. In 1905, Einstein saw that the
photoelectric effect was explained by Planck's conjecture.
Each photon of light with an energy of E = hf transfers
its energy to an electron. If this energy exceeds the binding energy (B), the
electron is removed from the metal and the electron is released. The energy of
the released electron
Eelektron=
hf-B
is happening. So the only way to increase the energies
of electrons emanating from a particular metal is to increase the frequency.
The observed relationship between the energies of the
electrons emitted in the photoelectric effect and the frequency (color) of the
incident light is exactly like this. Thus, from the photoelectric effect
experiments, the value of Planck's constant h, together with the binding
energies of electrons to that metal, is obtained in a completely different
context, completely independent of the blackbody radiation, and again the same
h value is obtained. So Planck's constant is a universal constant of nature.
Planck's constant also plays an important role in many other physics phenomena.
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