The constant is now known as [Planck’s constant](https://learn2.open.ac.uk/mod/oucontent/view.php?id=1817388&section=_glossary#idm2605 "The constant [eqn] introduced by Max Planck to explain the radiation emitted by blackbodies. It also...") and has the value Max Born, writing in 1926, said that Planck’s quantum hypothesis ‘marked the beginning of an entirely new conception of nature’. Its immediate impact on the problem of blackbody radiation was to provide the following new expression for the average energy of a standing wave in quantum theory, ![[../Assets/Screenshot 2023-11-02 at 13.55.45.png|300]] which differs radically from its classical counterpart, In contrast with the constant value the equation exhibits just the sort of rapid decrease as the wavelength _shortens_ which is required to tame the ultraviolet catastrophe. This result can be understood intuitively as follows: The quantum argument assumes that the energy of a standing wave cannot increase continuously under thermal agitation, but must climb a kind of ladder on which the distance apart of the rungs depends on the wavelength. At long wavelengths, the rungs are close together, many quanta will be excited and as we have seen, the classical case of continuous energy is approached. At the other extreme, when the wavelength is very short, the rungs on the ladder are far apart and the probability of even one quantum being excited is very low. In this situation, the thermodynamic average energy of a standing wave is close to zero. Note that the factor: ![[../Assets/Screenshot 2023-11-02 at 13.57.11.png|150]] represents the average number of thermally excited quanta in a standing electromagnetic wave, of wavelength in a cavity at absolute temperature (That is, it is the thermodynamic average energy of the wave mode divided by the energy quantum appropriate to that wavelength.) [[Docent/S284 Astronomy]] [[../Chapters/Part 1 The spectral continuum]]