BLACKBODY RADIATION: PLANCK

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BLACKBODYRADIATIONPLANCKS LAW
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COLOR and SPECTRAL CLASS

• The light emitted by stars consists of a mixture
  of all colors, but our eyes (and brain) perceive
  such light as being white or tinged with pastel
  color.
• In fact, different stars have varying amounts of
  each color in their light this causes stars to
  have different colors.
• Most people, however, have never noticed that
  stars come in a variety of colors.
• When light from the Sun (or any other star) is
  passed through a prism, it is separated into its
  component colors -- a continuous spectrum.

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When a beam of white light is passed through a
prism, it is broken up into a rainbow-like
spectrum.
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COLOR and SPECTRAL CLASS

• If the spectra of different stars are analyzed,
  it is found that the intensity of the various
  colors differs from star to star.
• Relatively cool stars have their peak intensity
  in the red or orange part of the spectrum.
• The hottest stars emit blue light most strongly.
• In other words, the color (or wavelength, ?) of
  the maximum intensity depends upon the
  temperature of the star.
• The star is not necessarily the color of the
  max-imum intensity in fact, there are no green
  stars.

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• Max
• Karl
• Ernst
• Ludwig
• Planck
• 1858 - 1947

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• In the late 1890s, Wien and Rayleigh had
  unsuccessfully attempted to formulate an
  equation expressing the intensity of
  electromagnetic radiation as a function of
  wavelength and the temperature of the source.
• In 1900, Planck derived the equation empirically.
• By December of 1900, Planck had derived the
  equation from fundamental principles.

Max Planck 1858 - 1947
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Plancks LawIntensity of Radiation vs. Wavelength

• The intensity (I) of electromagnetic radiation at
  a given wavelength (?) is a complicated function
  of the wavelength and the temperature (T).

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Plancks LawIntensity of Radiation vs. Wavelength
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Plancks LawRadiation Intensity vs. Wavelength
at 3000oK(Note Peak in Infrared)
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Plancks LawRadiation Intensity vs. Wavelength
at 6000oK(Note Peak in Visible)
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Plancks LawRadiation Intensity vs. Wavelength
at 10000oK(Note Peak in Ultraviolet)
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Plancks LawActual Radiation Intensity vs.
Wavelength at 3000, 6000, and 10000oK
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Plancks LawIntensity of Radiation vs.
WavelengthNormalized Intensity vs. Wavelength
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Plancks LawNormalized Intensity vs.
Wavelengthat 3000, 6000, and 10000 oK
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Plancks LawNormalized Radiation Intensity vs.
Wavelength at Various Temperatures
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Plancks LawNormalized Radiation Intensity vs.
Wavelength at Various Temperatures
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Stefan-Boltzmann Law
ET ? T4 where ET total energy radiated per
unit area over all wavelengths, and ? 5.67051
? 10-12 J / cm2 s ?K4
ET
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• Wilhelm
• Carl
• Werner
• Otto
• Fritz
• Franz
• Wien
• 1864 - 1928

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• In 1896, Wilhelm Wien unsuccessfully attempted to
  derive what is now known as Plancks Law.
• However, he did notice a relationship between the
  temperature of a glowing object and the
  wavelength of its maximum intensity of emission.
• The result of his investigation is now known as
  Wiens Displacement Law.

Wilhelm Wien 1864 - 1928
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• Wiens
• Displacement
• Law
• The peak of the emission spectrum of a glowing
  object is a function of its temperature. The
  hotter the object, the shorter the peak
  wavelength.

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Wiens Displacement Law

• Gives lmax as f(T), which allows us to calculate
  the temperature of a star if we know the
  wavelength of its maximum emission, which is easy
  to measure from its spectrum.
• From Plancks Law, take dI/dl, set 0.
• Then, lmax?T 2.8979 ? 106 nm??K.
• Example lmax for the Sun 502 nm.
• Therefore, T 5770?K 5500?C.

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The three types of Spectra Continuous, Emission
Line, and Absorption Line
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• Sodium Absorption Lines
• The sodium vapor subtracts out the yellow lines
  from the continuous spectrum emitted by the
  source.

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• As an excited hydrogen atom returns to its ground
  state, it emits the extra energy in the form of a
  photon with a certain wavelength.

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• Each energy transition within an atom gives rise
  to a photon of a particular wavelength.

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• Solar Spectrum
• (Original Drawings by Fraunhofer)

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• Absorption lines in a stars spectrum reveal the
  presence of elements and compounds.

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Continuous Spectrum
Absorption Spectrum of the Sun
Bright-line Spectrum of Sodium
Bright-line Spectrum of Hydrogen
Bright-line Spectrum of Calcium
Bright-line Spectrum of Mercury
Bright-line Spectrum of Neon
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• The Inverse Square Law When light from a
  point source travels twice as far, it covers four
  times the area, and is therefore only one fourth
  as bright.

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T H E E N D
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