Ch01 Newtonian mechanics

12 where k is boltzmanns constant however this

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Unformatted text preview: = 2πkT λ2 (1.12) where k is Boltzmann’s constant. However, this formula yielded agreement with experiments only for long wavelengths. For short wavelengths, namely in the ultraviolet region, the formula has a singularity, i. e. I(λ → 0) → ∞. Thus, the formula cannot be physical meaningful. Planck (1900) postulated that the oscillating atoms of a black body radiate energy only in the discrete, i. e. quantized amounts E = h ω, 2 h ω, 3 h ω, L = h c 2π 2π 2π , 2hc , 3h c ,L λ λ λ (1.13) where ħ = h / (2 π) is Planck’s constant divided by 2 π, c is the velocity of light, and ω = 2 π f is the intrinsic angular frequency of the radiating oscillators. The quantum constant or Planck’s constant has a value of h = h / (2 π) = 1.05 × 10 −34 Js . (1.12) Employing this postulate in the black-body radiation problem, Planck obtained the following formula for the spectral intensity distribution of a black body at temperature T © E. F. Schubert 4 I (λ ) = 4 π h c2 ⎛ ⎛ 2πhc λ ⎜ exp ⎜ ⎜ λkT ⎜ ⎝ ⎝ 5 ⎞ ⎞ ⎟...
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