Bohr frequency principle

This is not surprising, for the principles used are not really consistent on the one hand the classical differential relation is replaced by a difference relation, in the shape of the Bohr frequency condition,... 

Therefore, the rule is that as much the quantum levels are higher as the quantum and classical frequencies approaches each other, establishing the so called Bohr correspondence principle between the quantum and classical worlds . 

According to the well-known principles of quantum mechanics, the rotational energies of a rotating molecule, considered approximately as a rigid framework of atoms, are hmited to certain discrete, quantized values ,. Upon irradiation of a gaseous molecular sample by microwave radiation, an absorption of radiation is possible only if the frequency V of the radiation satisfies the Bohr frequency relation... 

The experimental set-up on the 2S—nS/D transitions has also been used in Paris to deduce the Lamb shift of the IS1 level via a comparison of the frequencies of the IS1 — 3S and 2S — 6S/D transitions [57]. The principle of this experiment is similar to the ones made at Garching and at Yale, where the IS1 — 2S frequency was compared to the 2S — 4S, 2S — 4P or 2S — 4D frequencies [23,58], In the Bohr model, these frequencies lie exactly in a ratio 4 1, and the deviation from this factor is mainly due to the Lamb shifts which vary as 1/n3. 

Bohr theory (4.2) build-up principle (4.4) degenerate (4.4) discrete energy levels (4.2) electromagnetic spectrum (4.1) electronic configuration (4.5) energy level diagram (4.7) excited state (4.3) frequency (4.1) ground state (4.3)... 

Here we conclude our account of Bohr s theory. Although it has led to an enormous advance in our knowledge of the atom, and in particular of the laws of line spectra, it involves many difficulties of principle. At the very outset, the fundamental assumption of the validity of Bohr s frequency condition amounts to a. direct and unexplained contradiction of the laws of the classical theory. Again, the purely formal quantisation rule, which stands at the head of the theory, is a foreign element which in the first instance is absolutely unintelligible from the physical point of view. We shall see later how both of these difficulties are removed in a perfectly natural way in wave mechanics. 

Bohr points out in a later paper [16] that for any system containing one electron rotating in a closed orbit, the replacement of W by the average kinetic energy (which is equal to W)> secures an identity between the frequency of radiation calculated by equation 3.9 and that to be expected from ordinary electrodynamics in the limit when the difference between the frequencies of rotation of the electron in successive stationary states is much less than the absolute value of the frequency. The requirement that these two frequencies be identical is a partial statement of the Correspondence Principle. 

Bohr has succeeded in overcoming these difficulties by rejecting the classical principles in favour of the quantum principles discussed in 1 and 2. He postulates the existence of discrete stationary states, fixed by quantum conditions, the exchange of energy between these states and the radiation field being governed by his frequency condition (1), 2. The existence of a stationary state of minimum energy, which the atom cannot spontaneously abandon, provides for the absolute stability of atoms which is required by experience. Further,... 

As mentioned in the introduction, the interaction of the atomic systems with the radiation is governed by a further independent quantum principle, Bohr s frequency condition,... 

This relation between classical and quantum frequencies forms the substance of Bohr s correspondence principle. 

The two quantum principles hitherto given do not, however, provide a complete description of the radiation processes. A light wave is characterised not only by a frequency, but also by intensity, phase, and state of polarisation. The quantum theory is at present unable to give exact information with regard to these features. Bohr has, however, shown that it is possible, by extending the correspondence principle from frequencies to amplitudes, to make at any rate approximate estimates regarding the intensity and polarisation. 

To this is added, as the second quantum principle, Bohr s frequency condition hv=WW—W<2>. 

In 1926, the Austrian physicist Erwin Schrodinger used the hypothesis that electrons have a dual wave-particle nature to develop an equation that treated electrons in atoms as waves. Unlike Bohr s theory, which assumed quantization as a fact, quantization of electron energies was a natural outcome of Schrodinger s equation. Only waves of specific energies, and therefore frequencies, provided solutions to the equation. Along with the uncertainty principle, the Schrodinger wave equation laid the foundation for modem quantum theory. Quantum theory describes mathematically the wave properties of electrons and other very small particles. 

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