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.
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Transcribed Image Text:Planck's principal assumption was that the energies of the electronic
oscillators can have only the values &n=nhv and that Aε = hv.
(a) Further assume that the number of oscillators with the energy
En, Nn, is proportional to e-En/kT at the temperature T, namely
Nn xe-En/kT, where N is the total number of oscillators. Show
N
that the average energy per oscillator is ɛ̃ =
formula, Edv =
formula as v → 0.
ΣNnEn
N
c3 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 Ac→ 0. Show that the Planck radiation
8πhy3 dv
reduces to the Rayleigh-Jeans
hv
ehv/kT-1
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