08Early - Pre-quantum mechanics Modern Physics Historical...

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P460 - Early Modern 1 Pre-quantum mechanics Modern Physics • Historical “problems” were resolved by modern treatments which lead to the development of quantum mechanics • need special relativity • EM radiation is transmitted by massless photons which have energy and momentum. Mathematically use wave functions (wavelength, frequency, amplitude, phases) to describe • “particles” with non-zero mass have E and P and use wave functions to describe SAME
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P460 - Early Modern 2 Blackbody Radiation • Late 19th Century: try to derive Wien and Stefan- Boltzman Laws and shape of observed light spectra • used Statistical Mechanics (we’ll do later in 461) to determine relative probability for any wavelength λ • need::number of states (“nodes”) for any λ energy of any state - probability versus energy • the number of states = number of standing waves = N( λ )d λ = 8 π V/ λ 4 d λ with V = volume • Classical (that is wrong) assigned each node the same energy E = kt and same relative probability this gives energy density u( λ ) = 8 π/λ 4 *kT wavelength u b infinity as wavelength b 0 u
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P460 - Early Modern 3 Blackbody Radiation II • Modern, Planck, correct: E = h ν = hc/ λ Energy and frequency are the same. Didn’t quite realize photons were a particle • From stat. Mech -- higher energy nodes/states should have smaller probability try 1: Prob = exp(-h ν /kt) - wrong try 2: Prob(E) = 1/(exp(h ν /kt) - 1) did work • will do this later. Planck’s reasoning was obscure but did get correct answer…. .Bose had more complete understanding of statistics • Gives u (λ) = 8 π / λ 4 * hc/ λ * 1/(exp(hc/ λ kt) - 1) wavelength u Agrees with experimental observations Higher Temp
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P460 - Early Modern 4 Photoelectric effect • Photon absorbed by electron in a solid (usually metal or semiconductor as “easier” to free the electron) . Momentum conserved by lattice • if E γ > φ electron emitted with E
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08Early - Pre-quantum mechanics Modern Physics Historical...

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