Applied Physics I: Chapter 7: Quantum Mechanics
Basic Laws for explaining the energy distribution
1. Stefan‒Boltzmann's law 2. Wien's Displacement law 3. Rayleigh‒Jean's law - Different laws were proposed for explaining the energy distribution with respect to the wavelength.
BASIC
LAWS FOR EXPLAINING THE ENERGY DISTRIBUTION
Different
laws were proposed for explaining the energy distribution with respect to the
wavelength. They are as follows:
1. Stefan‒Boltzmann's law
According
to this law the radiant energy (E) of a body is directly proportional to the
fourth power of the temperature (T) of the body.
(i.e)
E ∝ T4
(or)
E = σ T4
where
σ → Stefan constant, given by σ = 2π5KB4 / 15h3c2
2. Wien's Displacement law
This
law states that the product of the wavelength (λm) corresponding to
maximum energy and the absolute temperature (T) is a constant.
(i.e.,)
λmT= constant
This
law shows that, as the temperature increases, the wavelength corresponding to
maximum energy decreases.
Wien
also showed that the maximum energy (Emax) is directly proportional
to the fifth power of the absolute
temperature.
(i.e)
Emax ∝
T5
(or)
Emax = constant T5
By
deducing this law, he obtained a law called Wien's law of distribution of energy (Eλ), given by
Eλ = C1 λ‒5 e‒C2/λT
where
C1 and C2 are constants given by С1 = 8πhс and С2 = hc / KB
This law holds good
only for shorter wavelengths and not for longer wavelengths.
3. Rayleigh‒Jean's law
According
to this law, the energy distribution is directly proportional to the absolute
temperature and is inversely proportional to the fourth power of the
wavelength.
It
is governed by the equation
Eλ= 8πKBT / λ4
where
KB is the Boltzmann constant.
This law holds good
only for longer wavelength regions and not for shorter wavelengths.
It
is found that, both Wien's and Rayleigh‒Jeans law do not agree with the
experimental results. Therefore we can conclude that the classical theory was
not able to explain the emission of black body radiation. Thus, Max Planck used
Quantum theory to explain the black body radiation.
Applied Physics I: Chapter 7: Quantum Mechanics : Tag: Applied Physics : - Basic Laws for explaining the energy distribution
Applied Physics I: Chapter 7: Quantum Mechanics
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