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Chapter 10

Chapter 10 The Derivation ofthe planck FormulaTopicsThe planck formula for black-body radiation. Revision of waves in a box. Radiationin thermal equilibrium. The equipartition theorem and the ultraviolet photoelectric effect. The wave-particle duality. Quantisation of radiation andthe derivation of the planck spectrum. The Stefan-Boltzmann IntroductionIn the first lecture, we stated that the energy den-sity of radiation per unit frequency intervalu( )for black-body radiation is described by thePlanckformula(Figure ),u( ) d =8 h 3c31(eh /kT 1)d ( )wherePlanck s constant,h= 10 34J this lecture, we demonstrate why quantum con-cepts are necessary to account for this formula. Theprogramme to derive this formula is as follows.

The Derivation of the Planck Formula 3 is sin!t, where! = 2…” is the angular frequency of the wave. Therefore, the expression for the wave is A(r;t) = A0 sin(kr ¡!t); and the speed of the wave is c =!=k. 10.3 Electromagnetic Modes in a Box

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