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Lecture 29 — The Planck Distribution Chapter 8, Wednesday March 26 th

Lecture 29 — The Planck Distribution Chapter 8, Wednesday March 26 th. The Planck distribution The Free energy of a photon gas Radiation pressure Quiz (if time). Reading: All of chapter 8 (pages 160 - 185) Homework 8 due Mon. Mar. 31st Assigned problems, Ch. 8 : 2, 6, 8, 10, 12.

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Lecture 29 — The Planck Distribution Chapter 8, Wednesday March 26 th

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  1. Lecture 29 — The Planck Distribution Chapter 8, Wednesday March 26th • The Planck distribution • The Free energy of a photon gas • Radiation pressure • Quiz (if time) Reading: All of chapter 8 (pages 160 - 185) Homework 8 due Mon. Mar. 31st Assigned problems, Ch. 8: 2, 6, 8, 10, 12

  2. Exam 2 statistics

  3. Planck's law (quantization of light energy) N distinguishable oscillators in the walls of the cavity M indistinguishable energy elements (quanta) e =hn, so that UN = Me

  4. Maxwell-Boltzmann statistics Planck postulated that the energies of harmonic oscillators could only take on discrete values equal to multiples of a fundamental energy e = hn, where n is the frequency of the harmonic oscillator, i.e. 0, e, 2e, 3e, etc.... Then, Un = ne = nhn = 0, 1, 2... Where n is the number of modes excited with frequency n. Although Planck knew of no physical reason for doing this, he is credited with the birth of quantum mechanics. Define energy distribution function: Then, This is simply the result that Rayleigh and others used, i.e. the average energy of a classical harmonic oscillator is kBT, regardless of its frequency.

  5. The new quantum statistics Solving these equations together, one obtains: Multiplying by D(l), to give.... This is Planck's law Replace the continuous integrals with a discrete sums:

  6. Vibrational energy levels for diatomic molecules n = 0, 1, 2... (quantum number) w w = natural frequency of vibration Energy

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