wien's displacement law
1896, German physicist Wayne obtained a formula of radiation energy distribution through semi-theoretical and semi-empirical methods:
ρ is radiation energy density, ν is frequency, and t is temperature.
1899, Planck applied electromagnetic theory to the interaction between thermal radiation and harmonic oscillator, and obtained the same result through entropy operation, thus making Wien distribution law universal.
According to Wien's law of distribution, the radiation intensity will decrease exponentially with the decrease of frequency. On February 3rd, 0899, Lummer and Pringsheim said in a report that they heated the cavity to 800K- 1000K, and the energy distribution curve obtained was consistent with Wien's formula. But in the same year, they heated the cavity to165438+1October 3.
3. Rayleigh-Jenkins Law
1June, 900, Rayleigh put forward two hypotheses: ① all possible standing waves are formed by electromagnetic radiation in the cavity, and their nodes are at the cavity wall; (2) When the system is in thermal radiation balance, according to the energy equipartition theorem, the average energy of each standing wave is kT. Based on these two assumptions, he derived another formula of radiation energy distribution, but one factor 8 in the formula was wrong, which was later revised by Jenkins in 1905. The formula is:
It is called Rayleigh-Jenkins radiation law.
However, this formula is consistent with the experimental results only in the long wave region, but not in the short wave region. Because the radiation energy is proportional to the square of the frequency ν, when the wavelength is close to ultraviolet, the energy is infinite! That is, it splits at the purple end. This result was later called "ultraviolet disaster" by P.Ehrenfest.
However, the knowledge gained by Rayleigh and Jenkins is strictly deduced from the theory of classical physics. Rayleigh and Jenkins are also recognized as rigorous people in physics. The theoretical value and experimental value are opposite in the short wave region, which reveals the serious difficulties faced by classical physics and makes people have to call it "ultraviolet disaster"
Second, Planck's research.
Planck (1858- 1947)
He was born in Germany and his father taught at Munich University. After graduating from high school, he hesitated between physics, mathematics and music. 1874 was admitted to the Mathematics Department of Munich University. Because his hobby turned to physics again, his teacher P. Jolly advised him not to choose physics, but Planck chose physics and received his doctorate in 65438+. 49638.8868686866 1
Kirchhoff's successor and director of the newly established Institute of Theoretical Physics worked in this position until his retirement. He was elected as an academician of the Royal Prussian Academy of Sciences in 1894, a member of the Royal British Society in 19 18, and the president of the Emperor William Association in 1930- 1937. 56638.66666666667
2. Planck interpolation formula
Planck combines the Wien formula representing the short wave direction with the experimental results representing the long wave direction, and obtains Planck's radiation law:
When ν→0, that is, in the long wave range, Planck's law becomes Rayleigh-Jenkins formula.
When ν→∞, that is, in the short wave range, it conforms to Wayne's law.
After learning this formula, Rubens immediately compared his experimental results with the theoretical curve, and they were completely consistent. So they gave a report to the German Physical Society in June 1900+1October19, entitled "Improvement of Wien Spectral Equation".
3. Planck's energy quantum hypothesis
Planck is a theoretical physicist. He is not satisfied with finding an empirical formula. Planck wrote: "Even if this new radiation formula is proved to be absolutely accurate, if it is only a formula guessed by luck, its value can only be limited. Therefore, since this formula was put forward in June 5438 +654381October+September, I have been trying to find the real physical meaning of this formula. This question makes me directly consider the relationship between entropy and probability.
Episode: At first, Planck disagreed with Boltzmann's statistical viewpoint and had an argument with Boltzmann. However, after several months of efforts, Planck did not derive a new radiation law from the general theory of thermodynamics. Later, he had to try to use Boltzmann's thermodynamic probability theory to derive Planck's radiation formula.
Planck quantum hypothesis
The vibration of molecules and atoms in a radiation blackbody can be regarded as a linear harmonic oscillator, which can emit and absorb radiation energy. These harmonic oscillators can only be in some discrete states. In these states, the energy of the harmonic oscillator cannot take any value, but can only be an integer multiple of a certain minimum energy. , where n is an integer, called quantum number.
For a harmonic oscillator with frequency (), the minimum energy (is:, (called energy quantum).
Planck can get his blackbody radiation formula from these assumptions:
Planck calculated the constant H value according to the data of blackbody radiation: h=6.65× 10-34 Joule seconds.
H-Planck constant, like a spark from Prometheus, liberates people from the bondage of traditional ideas! Blackbody radiation, photoelectric effect, atomic spectrum and Compton effect are all the development results of Planck hypothesis, which cannot be explained by classical physics.
Planck contradiction
Planck's energy quantum hypothesis has a serious impact on the view of energy continuity. People only recognize Planck's formula and don't accept his energy quantum hypothesis. Even Planck himself could not correctly understand the physical meaning of energy quantum. His mood is ambivalent. On the one hand, his intuition tells him that this discovery is unusual, on the other hand, he always wants to return to the position of classical theory. He said, "We should be as conservative as possible when introducing the action quantum H into the theory." In other words, don't change the existing theory unless absolutely necessary. "
In 19 1 1, Planck thinks that it is only quantized during emission, and the absorption is completely continuous. By 19 14, the quantum hypothesis (ε→0) was simply cancelled. He believes that the launch process is also continuous. However, due to repeated failures, he finally gave up his retrogressive position. Because of this, he has mixed feelings: "It took me several years (up to 19 15) to make the action quantum fit the classical theory in some way, and they cost me a lot of energy ... Now I understand the fact that the basic action quantum plays a far more important role in physics than.
Planck 19 18 won the nobel prize.
Under the influence of Boltzmann, Planck clearly put forward the concept of energy quantum on the day 1900 12 14, and pointed out that the energy e of each energy quantum is proportional to the frequency ν, which is called the birth day of quantum mechanics.
Bohr: This discovery shattered the foundation of human thought-not only about classical science, but also the usual way of thinking.