Lecture06-04.1-Planck_Distribution

# Lecture06-04.1-Planck_Distribution - Last Time Helmholtz...

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Last Time Helmholtz Free Energy Differential of Free Energy Maxwell Relations Free Energy and the Partition Function Quantum Concentration For one atom in one box Ideal Gas Law Equipartition of Energy Today Planck Blackbody Radiation Stefan-Boltzmann Law Planck Radiation Law Stars Big Bang Chapter 4 (part 1) Thermal radiation and Planck Distribution

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Radiation Everything glows according to its temperature Hot things glow brighter, and at higher frequencies. Cooler things glow dimmer, at lower frequencies. Intensity Frequency Hot things radiate photons. Sspectrum of photons is determined by temperature Deviations from Wienn’s distribution Wienn’s distribution, assumed Maxwell-Boltzman distribution of velocities: works for high frequencies (short wavelengths) Lord Rayleigh (1900): using equipartition theorem, works for low frequencies (ultraviolet catastrophe) Frequency Energy density, U Rayleigh Planck Wienn
Planck 2 2 2 U const U = σ Planck derivation, 1900 : U const U = 2 2 σ ) ( 2 2 b U U const U + = σ Lucky guess!!! 3 2 8 ) ( c kT U πν ν = - = T e U βν ν αν 3 Wienn Rayleigh •assume that energy consists of quanta Star Spectra 1) Hot Things Glow 2) Atoms Have Specific Energy Levels Intensity Frequency

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The Sun “Black Body” Radiation EM radiation in thermal equilibrium… Energy of a photon is quantized : “s” tells you how many photons are in the mode, and corresponds to the amplitude of the EM wave. photons in a box E one photon two photons one photon two photons
How It Equilibrates: Atoms and Light Absorb a Photon Absorb a Photon Adding a photon increases the energy Unexcited atom Excited atom Really excited atom Atoms and Light

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