Planck's principal assumption was that the energies of the electronicoscillators can have only the values &n=nhv and that Aε = hv.(a) Further assume that the number of oscillators with the energyEn, Nn, is proportional to e-En/kT at the temperature T, namelyNn xe-En/kT, where N is the total number of oscillators. ShowNthat the average energy per oscillator is ɛ̃ =formula, Edv =formula as v → 0.ΣNnEnNc3 ehv/kT-1'=(b) As v→ 0, then Aɛ → 0 and & is essentially continuous. Hence,we should expect the non-classical Planck distribution to goover to the classical Rayleigh-Jeans distribution at lowfrequencies, where Ac→ 0. Show that the Planck radiation8πhy3 dvreduces to the Rayleigh-Jeanshvehv/kT-1

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that the average energy per oscillator is ΣNnEn N = hv ehv/kT-1 (b) As v→ 0, then Aɛ → 0 and & is essentially continuous. Hence, we should expect the non-classical Planck distribution to go over to the classical Rayleigh-Jeans distribution at low frequencies, where Aɛ→ 0. Show that the Planck radiation 8nhv³ dv c3 ehv/kT-1' formula, Eydv = reduces to the Rayleigh-Jeans formula as v→ 0.

that the average energy per oscillator is ΣNnEn N = hv ehv/kT-1 (b) As v→ 0, then Aɛ → 0 and & is essentially continuous. Hence, we should expect the non-classical Planck distribution to go over to the classical Rayleigh-Jeans distribution at low frequencies, where Aɛ→ 0. Show that the Planck radiation 8nhv³ dv c3 ehv/kT-1' formula, Eydv = reduces to the Rayleigh-Jeans formula as v→ 0.