Blackbody radiation.pdf
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BLACKBODY RADIATION
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THERMAL RADIATION
Thermal radiationEmitted by a body as a result of its temperature
Examples
How color of emitted radiation changes with temperature
1000 K 2500 K 5000 K 6500 K 9000 K
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ELECTROMAGNETIC SPECTRUM
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ELECTROMAGNETIC SPECTRUM
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SPECTRAL RADIANCY
DefinitionEnergy emitted by a unit area in unit time as radiation of
given frequency (power emitted by a unit area)
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BLACKBODY
BlackbodyAbsorbs all incoming radiation, does not reflectAll emitted radiation is produced by the blackbody
A cavity hole is a nice blackbody.
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WHY BLACKBODY?
Universal characterEvery blackbody has the same spectral radiancyThe radiancy depends only on wavelength and temperature
Kirchhoffs law of thermal radiationAt thermal equilibrium good absorbers are good emitters
Rreal
T()
() =RT
(
)
absorption coefficient(absorbed fraction of incident power)
spectral radiancyof a real body
(emitted power)
spectral radiancy of blackbody
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OUR SUN IS ALMOST A BLACKBODY
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HUMAN EYE EVOLUTION
Adapted to the sunAlmost the greatest part of its radiation lies within visible rangeMost sensitive to wavelengths radiated most intensively
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COSMIC MICROWAVE BACKGROUND RADIATION
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NIGHT VISION & INFRARED THERMOMETERS
HumansThermal radiation mainly in infrared
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HISTORY OF SCIENCE
Nobel prizes related to blackbody radiation
Wilhelm Wien (1911)for his discoveries regarding the laws governing the radiation of heat
Max Planck (1918)
in recognition of the services he rendered to the advancement ofPhysics by his discovery of energy quanta
John Mather & George Smoot (2006)for their discovery of the blackbody form and anisotropy ofthe cosmic microwave background radiation
Arno Penzias & Robert Wilson (1978)for their discovery of cosmic microwave background radiation
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PROPERTIES OF BLACKBODY RADIATION
Stefan-Boltzmann lawPower radiated per unit surface area is proportional to T4
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PROPERTIES OF BLACKBODY RADIATION
Stefan-Boltzmann lawArea under the spectral radiancy curve
Z1
0
RT()d = T4
= 5.67 108W
m2K4
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PROPERTIES OF BLACKBODY RADIATION
Wiens displacement lawPeak wavelength is inversely proportional to T
maxT = 2.898 103m K
peak wavelength of spectral radiancy
temperature
Wiens displacement constant
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THEORIST POINT OF VIEW: ENERGY DENSITY
Spectral radiancyDirectly experimentally accessible, emitted power
Spectral energy density
Energy in a unit volume inside the cavity
T() RT() T() =4
c
RT()
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ULTRAVIOLET CATASTROPHE
The catastropheClassically, energy density diverges for higher frequencies
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PLANCK THEORY
AimCalculate the energy density assuming quantization of energy
Steps as in the Rayleigh-Jeans theory
The average total energy of each standing wave is now different
T()d=82
c3h
exp(h/kT) 1d
T()d =8hc5
1exp(hc/kT) 1
d
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PERFECT AGREEMENT OF PLANCK THEORY WITH EXPERIMENT
Stefan-Boltzmann lawIntegrate over all frequencies
Wiens displacement lawCalculate derivate and set it to zero
Classical limitRayleigh-Jeans result for long wavelengths
Matches the shape of spectral radiancy
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PLANCK CONSTANT
Tiny in macroscopic units
h = 6.626 1034J s
Planck constant
Eq = h
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SUMMARY
Allowed energies are multiples of the energy quantum
Total energy of harmonic motion is quantized
Eq = h
h = 6.626
10
34
J s