![]() Then one must average over all angles, which gives another factor of 1/2 for the angular dependence which is the square of the cosine. The density above is for thermal equilibrium, so setting inward=outward gives a factor of 1/2 for the radiated power outward. To find the radiated power per unit area from a surface at this temperature, multiply the energy density by c/4. The above expressions are obtained by multiplying the density of states in terms of frequency or wavelength times the photon energy times the Bose-Einstein distribution function with normalization constant A=1. The Planck radiation formula is an example of the distribution of energy according to Bose-Einstein statistics. Gives the energy density, the Planck radiation formula. This average energy times the density of such states, expressed in terms of either frequency or wavelength ![]() The average energy per "mode" or "quantum" is the energy of the quantum times the probability that it will be occupied (the Einstein-Bose distribution function): Careful analysis by Rayleigh and Jeans showed that the number of modes was proportional to the frequency squared.įrom the assumption that the electromagnetic modes in a cavity were quantized in energy with the quantum energy equal to Planck's constant times the frequency, Planck derived a radiation formula. If the mode is of shorter wavelength, there are more ways you can fit it into the cavity to meet that condition. Nature knew better.Ĭavity Modes A mode for an electromagnetic wave in a cavity must satisfy the condition of zero electric field at the wall. The best of classical physics suggested that all modes had an equal chance of being produced, and that the number of modes went up proportional to the square of the frequency.īut the predicted continual increase in radiated energy with frequency (dubbed the " ultraviolet catastrophe") did not happen. The amount of radiation emitted in a given frequency range should be proportional to the number of modes in that range. The radiated energy can be considered to be produced by standing wave or resonant modes of the cavity which is radiating. ![]() ![]() Blackbody Radiation Blackbody Radiation "Blackbody radiation" or "cavity radiation" refers to an object or system which absorbs all radiation incident upon it and re-radiates energy which is characteristic of this radiating system only, not dependent upon the type of radiation which is incident upon it. ![]()
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