Catastrophe, ultraviolet

For nineteenth-century scientists, the obvious way to account for the laws of black-body radiation was to use classical physics to derive its characteristics. However, much to their dismay, they found that the characteristics they deduced did not match their observations. Worst of all was the ultraviolet catastrophe classical physics predicted that any hot body should emit intense ultraviolet radiation and even x-rays and y-rays According to classical physics, a hot object would devastate the countryside with high-frequency radiation. Even a human body at 37°C would glow in the dark. There would, in fact, be no darkness. 

Ernest Rutherfords proposed atomic structure added to the problems posed to nineteenth century physics by the ultraviolet catastrophe and the photoelectric effect. Rutherfords atom had a negatively charged electron circling a positively charged nucleus. The physics of the day predicted that the atom would emit radiation, causing the electron to lose energy and spiral down into the nucleus. Theory predicted that Rutherfords atom could not exist. Clearly, science needed new ideas to explain these three anomalies. 

Planck presented his solution to the ultraviolet catastrophe at the December 1900 meeting of the Berlin Physical Society. No one grasped the implications of the breakthrough, probably not even Planck himself His equation was considered to be a nice mathematical trick, but one with no particular physical significance. 

By the end of the nineteenth century it was realized that the wave theory of electromagnetic radiation could not by itself explain the form of the black-body radiation shown in Fig. 1.9. In particular, it was predicted that the energy distribution should rise indefinitely as the wavelength became shorter, rather than falling to zero as found. This alarming prediction, known as the ultraviolet catastrophe, gave the first serious clue that the theory was in need of modification,... 

Rayleigh found the v2 dependence, Jeans later supplied the rest). Their distribution function g(v) increases as v2, with no provision for a fall-off to zero as the frequency and the energy go to infinity ("ultraviolet catastrophe"). 

These calculated results, shown for 5000 and 7000 K by the dashed curves in Figure 4.6, agree well with experiment at lower frequency. But the theory does not predict a maximum in the intensity distribution, and even worse, it disagrees badly with the experimental results at high frequencies. This feature of the result was called the ultraviolet catastrophe because it predicts an infinite intensity at very... 

The peak observed in the frequency distribution of blackbody radiation is completely inconsistent with the predictions of classical electromagnetic theory. This failure of classical physics is called the ultraviolet catastrophe. 

Resolved the ultraviolet catastrophe of classical physics, which predicted intense ultraviolet radiation for all heated objects (7 > 0)... 

Q.7.10 What was the ultraviolet catastrophe and how did Planck s proposal resolve it ... 

Quantum mechanics represents one of the cornerstones of modem physics. Though there were a variety of different clues (such as the ultraviolet catastrophe associated with blackbody radiation, the low-temperature specific heats of solids, the photoelectric effect and the existence of discrete spectral lines) which each pointed towards quantum mechanics in its own way, we will focus on one of these threads, the so-called wave-particle duality, since this duality can at least point us in the direction of the Schrodinger equation. 

This is Wien s displacement law. Classical principles had failed to explain the shape of the curve in Fig. 19.4 and f ailed to predict the displacement law. The application of the classical law of equipartition of energy between the various degrees of freedom by Rayleigh and Jeans was satisfactory at long wavelengths but failed at short wavelengths, in the ultraviolet ( ultraviolet catastrophe ). 

Describe the ultraviolet catastrophe and its empirical resolution by the Planck radiation law. 

It can be seen that the Rayleigh-Jeans law reproduces the experimental data at low frequencies fairly well. However, at high frequencies, the Rayleigh-Jeans law diverges as v. Since the frequency increases in the ultraviolet region of the spectrum, this divergence was called the ultraviolet catastrophe, a phenomenon that classical physics was unable to explain theoretically. This was the first such phenomenon to be observed in physics and did in fact mark a major milestone in the annals of physics. 

---