Planck Radiation Calculator
Calculate the spectral radiance of a blackbody at a given wavelength and temperature using Planck's law.
Spectral Radiance
26,408,428,444,454.965000 W/m2/sr/m
Formula
## Planck's Law of Blackbody Radiation Planck's law gives the spectral radiance of a blackbody as a function of wavelength and temperature. ### Formula **B(lambda, T) = (2hc^2 / lambda^5) / (exp(hc / (lambda k_B T)) - 1)** - *h* = 6.626 x 10^-34 J s - *c* = 2.998 x 10^8 m/s - *k_B* = 1.381 x 10^-23 J/K This resolved the ultraviolet catastrophe and launched quantum mechanics.
Exemplo Resolvido
Sun (5778 K) at 500 nm (green light).
- 01Numerator: 2hc^2 / lambda^5
- 022 * 6.626e-34 * (2.998e8)^2 = 1.191e-16
- 03(5e-7)^5 = 3.125e-32
- 04Numerator = 1.191e-16 / 3.125e-32 = 3.811e15
- 05Exponent: hc/(lambda k T) = 6.626e-34 * 2.998e8 / (5e-7 * 1.381e-23 * 5778) = 4.97
- 06exp(4.97) - 1 = 143.6
- 07B = 3.811e15 / 143.6 = 2.654e13 W/m2/sr/m
Perguntas Frequentes
What was the ultraviolet catastrophe?
Classical physics predicted infinite energy at short wavelengths for a blackbody. Planck resolved this by proposing that energy is emitted in quantised packets (quanta).
How does this relate to the Stefan-Boltzmann law?
Integrating Planck's law over all wavelengths and angles gives the Stefan-Boltzmann law: total power = sigma * T^4 per unit area.
Is anything a perfect blackbody?
No real object is a perfect blackbody, but many approximate it well: stars, cosmic microwave background, and lab cavity radiators.
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