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BLACKBODY RADIATION: PLANCK

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COLOR and SPECTRAL CLASS – PowerPoint PPT presentation

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Title: BLACKBODY RADIATION: PLANCK


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(No Transcript)
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BLACKBODY RADIATION PLANCKS 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.

4
When a beam of white light is passed through a
prism, it is broken up into a rainbow-like
spectrum.
5
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.

6
  • 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
8
Plancks Law Intensity 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).

9
Plancks Law Intensity of Radiation vs. Wavelength
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Plancks Law Radiation Intensity vs. Wavelength
at 3000oK (Note Peak in Infrared)
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Plancks Law Radiation Intensity vs. Wavelength
at 6000oK (Note Peak in Visible)
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Plancks Law Radiation Intensity vs. Wavelength
at 10000oK (Note Peak in Ultraviolet)
13
Plancks Law Actual Radiation Intensity vs.
Wavelength at 3000, 6000, and 10000oK
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Plancks Law Intensity of Radiation vs.
Wavelength Normalized Intensity vs. Wavelength
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Plancks Law Normalized Intensity vs.
Wavelength at 3000, 6000, and 10000 oK
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Plancks Law Normalized Radiation Intensity vs.
Wavelength at Various Temperatures
17
Plancks Law Normalized Radiation Intensity vs.
Wavelength at Various Temperatures
18
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
19
  • Wilhelm
  • Carl
  • Werner
  • Otto
  • Fritz
  • Franz
  • Wien
  • 1864 - 1928

20
  • 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
21
  • 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.

22
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.

23
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.

27
  • 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
30
  • 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.

31
T H E E N D
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