Planck postulate

It is possible to find in the history of science many vivid examples illustrating the relativity of the concept fundamental . For instance, the Planck postulate of energy quantization and the Bohr postulate on the quantization on angular momentum made a revolution in physics and were actually axioms at that time. At present from the formal viewpoint, they are only ordinary consequences of Schroedinger s equation [4], Another vivid example is provided by the four famous Maxwell electrodynamic equations which, as was found later, can be derived from Coulomb s law and Einstein s relativity principle [5]. 

By combining the Planck postulate of the electromagnetic radiation quantification with that of Bohr regarding the quantification of electronic transitions between the stationary levels in atom, Moseley introduced the so-called shielding factor, related to the way in which the electrons... 

We will assume that the entropy S(T) of stationary states (EQS s or SMSs) satisfy TS(T) —>0 as the temperature T— 0. This is a much weaker condition than the conventional Nemst—Planck postulate S(T) 0 for EQS s, but is consistent with all the consequences of the latter. Our version is also applicable to SMSs, for which the entropy need not vanish at absolute zero (see Ref [16], Section 64). 

It should be noted that what one measures in experiments is the difference in the entropy, and not the absolute entropy. Assuming that the entropy is zero at absolute zero in accordance with the Nemst-Planck postulate, one can determine the absolute entropy experimentally. However, it is well known that SCL is a metastable state, and there is no reason for its entropy to vanish at absolute zero [16]. Indeed, it has been demonstrated some time ago that the residual entropy at absolute zero obtained by extrapolation is a nonzero fraction of the entropy of melting [43 ], which is not known a priori. Therefore, it is impossible to argue from experimental data that the entropy indeed falls to zero, since such a demonstration will certainly require calculating absolute entropy though efforts continue to date [61, 62]. 

We can now take the limit N oo in both cases without affecting the conclusion. The possibility that the limit is different (indeed, higher) from 1 for F /Eo is ruled out because of the Nemst-Planck postulate. This proves the theorem. 

The underlying principle of RHEED is that particles of matter have a wave character. This idea was postulated by de Broglie in (1924). He argued that since photons behave as particles, then particles should exhibit wavelike behavior as well. He predicted that a particle s wavelength is Planck s constant h divided by its momentum. The postulate was confirmed by Davisson and Germer s experiments in 1928, which demonstrated the diffraction of low-energy electrons from Ni. ... 

Historical Background.—Relativistic quantum mechanics had its beginning in 1900 with Planck s formulation of the law of black body radiation. Perhaps its inception should be attributed more accurately to Einstein (1905) who ascribed to electromagnetic radiation a corpuscular character the photons. He endowed the photons with an energy and momentum hv and hv/c, respectively, if the frequency of the radiation is v. These assignments of energy and momentum for these zero rest mass particles were consistent with the postulates of relativity. It is to be noted that zero rest mass particles can only be understood within the framework of relativistic dynamics. 

Einstein in 1905 who explained the photoelectric effect (He did so by extending an idea proposed by Planck five years earlier to postulate that the energy in a light beam was concentrated in "packets" or photons.. 

Various statistical treatments of reaction kinetics provide a physical picture for the underlying molecular basis for Arrhenius temperature dependence. One of the most common approaches is Eyring transition state theory, which postulates a thermal equilibrium between reactants and the transition state. Applying statistical mechanical methods to this equilibrium and to the inherent rate of activated molecules transiting the barrier leads to the Eyring equation (Eq. 10.3), where k is the Boltzmann constant, h is the Planck s constant, and AG is the relative free energy of the transition state [note Eq. (10.3) ignores a transmission factor, which is normally 1, in the preexponential term]. 

This is an expression of Nernst s postulate which may be stated as the entropy change in a reaction at absolute zero is zero. The above relationships were established on the basis of measurements on reactions involving completely ordered crystalline substances only. Extending Nernst s result, Planck stated that the entropy, S0, of any perfectly ordered crystalline substance at absolute zero should be zero. This is the statement of the third law of thermodynamics. The third law, therefore, provides a means of calculating the absolute value of the entropy of a substance at any temperature. The statement of the third law is confined to pure crystalline solids simply because it has been observed that entropies of solutions and supercooled liquids do not approach a value of zero on being cooled. 

In order to understand these observations it is necessary to resort to quantum mechanics, based on Planck s postulate that energy is quantized in units of E = hv and the Bohr frequency condition that requires an exact match between level spacings and the frequency of emitted radiation, hv = Eupper — Ei0wer. The mathematical models are comparatively simple and in all cases appropriate energy levels can be obtained from one-dimensional wave equations. 

In Nemst s statement of the third law, no comment is made on the value of the entropy of a substance at 0 K, although it follows from his hypothesis that all pure crystalline substances must have the same entropy at OK. Planck [2] extended Nemst s assumption by adding the postulate that the value of the entropy of a pure solid or a pure liquid approaches zero at 0 K ... 

It is more problematical to define the third law of thermodynamics compared to the first and second laws. Experimental work by Richards (1902) and Nemst (1906) led Nemst to postulate that, as the temperature approached absolute zero, the entropy of the system would also approach zero. This led to a definition for the third law of thermodynamics that at a temperature of absolute zero the entropy of a condensed system would also be zero. This was further refined by Planck (1911) who suggested this be reworded as the entropy of a pure element or substance in a perfect crystalline form is zero at absolute zero. 

The dependence of the electron ion recombination rate constant on the mean free path for electron scattering has also been analyzed on the basis of the Fokker Planck equation [40] and in terms of the fractal theory [24,25,41]. In the fractal approach, it was postulated that even when the fractal dimension of particle trajectories is not equal to 2, the motion of particles is still described by difihsion but with a distance-dependent effective diffusion coefficient. However, when the fractal dimension of trajectories is not equal to 2, the motion of particles is not described by orthodox diffusion. For the... 

One expects that the Langevin equation (1.1) is equivalent to the Fokker-Planck equation (VIII.4.6). This cannot be literally true, however, because the Fokker-Planck equation fully determines the stochastic process V(t), whereas the Langevin equation does not go beyond the first two moments. The reason is that the postulates (i), (ii), (iii) in section 1 say nothing about... 

Conclusion. For internal noise one cannot just postulate a nonlinear Langevin equation or a Fokker-Planck equation and then hope to determine its coefficients from macroscopic data. ) The more fundamental approach of the next chapter is indispensable. ... 

Max Planck, utilizing his quantum theory postulates and modifications of the Boltzmann statistical procedure, established the theoretical formula for the spectral distribution curves of a black body ... 

In 1913 Niels Bohr proposed his atomic theory with the help of the line spectrum of hydrogen atoms and Planck s quantum theory. His postulates can be summarized as follows ... 

Planck, in 1912, postulated that the value of the entropy function for all pure substances in condensed states was zero at 0 K. This statement may be taken as a preliminary statement of the third law. The postulate of Planck is more extensive than, but certainly is consistent with, the postulate of Nernst. 

Fig. 4.3 The photoelectric effect. Einstein explained the effect by extending to light Planck s idea of the absorption and emission of energy in discrete amounts he postulated that light itself consisted of discrete particles...

These facts were explained by Einstein5 in 1905 in a way that now appears very simple, but in fact relies on concepts that were at the time revolutionary. Einstein went beyond Planck and postulated that not only was the process of absorption and emission of light quantized, but that light itself was quantized, consisting in effect of particles of energy... 

According to the third postulate the energy of activation may be set equal to hv (Planck s constant X frequency of light absorbed) in agreement with the quantum theory which has been so successful in many different fields. There is no support for this hypothesis, except the general success of the quantum theory (whenever applied to radiation phenomena, and chemical activation was assumed to be a radiation phenomenon. 

Measurements of heat capacities at very low temperatures provide data for the calculation from Eq. (5.11) of entropy changes down to 0 K. When these calculations are made for different crystalline forms of the same chemical species, the entropy at 0 K appears to be the same for all forms. When the form is noncrystalline, e.g., amorphous or glassy, calculations show that the entropy of the more random form is greater than that of the crystalline form. Such calculations, which are summarized elsewhere,t lead to the postulate that the absolute entropy is zero for all perfect crystalline substances at absolute zero temperature. While the essential ideas were advanced by Nemst and Planck at the beginning of the twentieth century, more recent studies at very low temperatures have increased our confidence in this postulate, which is now accepted as the third law. 

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