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Published byJeremy Evans Modified over 9 years ago
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Blackbody Radiation A blackbody is something that absorbs all radiation that shines on it Are all blackbodies black? - no!! - imagine a box full of lava A constant temperature blackbody (a.k.a. a very precise oven) Order your own blackbody online
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Blackbodies and Astronomy Stars are very similar to blackbodies emit a continuous spectrum of radiation Why aren’t they black?
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Blackbodies emit light at all wavelengths Cooler blackbodies emit more red than blue light.
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Planck Function I ν (T) is the specific intensity, depends on T and ν T is temp in Kelvin (Kelvin = Celsius + 273.2) h is Planck’s constant: 6.636 x 10 -34 J s k is Boltzmann’s constant 1.38 × 10 -23 m 2 kg s -2 K -1 c is the speed of light
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Rayleigh Jeans Limit At low frequencies, hν << kT so the Planck function can be approximated as
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Properties of the Planck Law Wien Displacement Law: m T = b, where m is the wavelength at which I peaks, and b (=0.0029 m K) is called the Wien displacement law constant. Alternatively, ν m / T = 5.88 x 10 10 Hz K -1, where ν m is the frequency at which I ν peaks. Note that
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Wien’s Law The peak wavelength of a blackbody spectrum is inversely proportional to temperature: Temperatures of stars and planets are measured using Wien’s law.
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Star B Star C Star D Which star is the hottest? Red Blue Wavelength
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Properties of the Planck Law Stefan-Boltzmann law: F = T 4, where F is the total radiated power per unit area (W per square m) and is called the Stefan-Boltzmann constant: 5.67 x 10 -8 W m -2 K -4
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Stefan-Boltzmann Law: Hotter blackbodies emit more total energy notice the area under the blackbody curve: 5000 K 4000 K
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A perfect blackbody produces a continuous spectrum: Dark lines in solar spectrum are from absorption by Sun’s outer atmosphere
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Emission Line Spectra Take a thin cloud of gas composed of a pure element (e.g. hydrogen) and heat it to high temperature It does not emit a continuous spectrum. It emits light at specific wavelengths: the exact same ones at which it absorbs
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The role of density If thin gases produce only emission lines, and the Sun is made of gas, why does the Sun’s spectrum look continuous (like a rainbow?) Solar spectrum
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Low-density A high-density gas cloud produces a continuous spectrum http://astro.unl.edu/animationsLinks.html
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