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3RF Sciences, LLC

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Blackbody defined… A blackbody is an object that absorbs all light that hits it Also emits light provided that its temperature is above absolute zero com/HP/WCL/IMG/bbo dy.gif

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A Blackbody… Perfect “black body” – something which absorbs all the radiation that falls on it Good absorber of radiant heat is also a good emitter Main scientist , G. Kirchhoff Foundation of blackbody radiation lies in the idea that radiation is released from blackbodies in the form of "quanta" or discrete packets of light called photons Main scientist – 1900, Max Planck

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More about a Blackbody… Is the best possible emitter of radiant energy Must both radiate and absorb energy at the same rate in order to maintain a constant temperature Total radiation from a black body depends only on temperature of the body, not on chemical or physical characteristics

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Plotting Curves A curve can be generated plotting the temperature, intensity, or brightness of the black body versus the wavelength coming from it. These curves are sometimes called Planck curves.

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Blackbody curves, 4 objects a) Cool, invisible galactic gas cloud called Rho Ophiuchi. Temperature of 60 K Emits mostly low- frequency radio radiation astron2e/AT_MEDIA/CH03/ CHAP03AT/AT03FG13.JPG

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Blackbody curves, 4 objects b) A dim, young star (shown here in red) near the center of the Orion Nebula. Temperature of star's atmosphere ~ 600 K Radiates primarily in infrared (IR) astron2e/AT_MEDIA/CH03/ CHAP03AT/AT03FG13.JPG

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c) The Sun Surface ~ 6000 K Brightest in the visible (v) region of the electromagnetic spectrum astron2e/AT_MEDIA/CH03/ CHAP03AT/AT03FG13.JPG Blackbody curves, 4 objects

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d) A cluster of very bright stars, called Omega Centauri, as observed by a telescope aboard the space shuttle Temperature ~ 60,000 K Radiate strongly in ultraviolet (UV) astron2e/AT_MEDIA/CH03/ CHAP03AT/AT03FG13.JPG

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How is a star a blackbody? Because blackbody radiation is solely dependent on temperature (simple) And to maintain a constant temperature, a blackbody must emit radiation in the same amount as it absorbs

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Wein’s Law The hotter a blackbody becomes, the shorter its wavelength of peak emission becomes The wavelength of peak emission is simply the wavelength at which a blackbody emits most of its radiation

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Wein’s Law 1893, German physicist Wilhelm Wien Quantified relationship between blackbody temperature and wavelength of spectral peak λ max = 2.9 x (microns)/T λ max (lambda max) = wavelength of Peak emission 2898 microns T = temperature of Blackbody in Kelvin (K)

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Wein’s Law in action…

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Plank Curves - 1 1900, Max Planck Electromagnetic radiation absorbed or emitted only in “chunks” of energy, quanta, E Quanta are proportional to the frequency of the radiation E = h. (Constant of proportionality “h” is Planck's constant.) Wanted to understand the shape of Wien's radiative energy distribution as a function of frequency.

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Plank Curves - 2 Postulated that radiators or oscillators can only emit electromagnetic radiation in finite amounts of energy of size. At a given temperature T, there is not enough thermal energy available to create and emit many large radiation quanta. More large energy quanta can be emitted when temperature is raised.

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Plank’s Law The amount of blackbody radiative flux emitted by a blackbody for a given wavelength is given by Planck's Law: Where T is object temperature (in degrees Kelvin); l is wavelength in microns; units are (W/m 2 ) per micron The wavelength of peak emission is:

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Stefan–Boltzmann Law Independently formulated by Josef Stefan (1879) and Ludwig Boltzmann (1884, 1889) Relationship between radiant energy and temperature for a black body radiator Relates total radiant flux (F) (in W/m 2 ), from surface of black body to its temperature (T) F= σ T 4 σ = x watt / m 2 K 4

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Stefan–Boltzmann Law 2 How much power a blackbody radiates per unit area of its surface For a blackbody of temperature T, the power radiated per unit area is: P = constant x T 4 ~imamura/122/images/st efanboltzmanlaw.jpg

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Stefan–Boltzmann Law

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Why use Stefan-Boltzmann(S-B) Law? Using the Stefan-Boltzmann law in conjunction with other known quantities, it can be used to infer properties of a star For example, if a star radiates like a blackbody, then the luminosity of the star can be written as L = (Surface Area of the Star) x (power per unit area produced by the star) = 12.6 x R 2 x constant x T 4 So, if we know certain information (obtained through independent means) about a star, we can infer other properties. For example,

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What can we learn from S-B law? If we know the luminosity and temperature, we can infer the radius of the star; If we know the luminosity and radius of a star, we can infer its temperature; If we know the radius and temperature of a star, we can infer its luminosity

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Blackbody Review Stefan-Boltzmann Law - Area under the curve increases as the temperature is increased Wien's Law – Peak of the curve in emitted energy changes wavelength Planck’s Law – Peak of the curve or the peak emission wavelength of a blackbody is related to the temperature of the object – hotter objects emit in higher wavelengths.

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