Comparison of X-rays and Light; a Summary.---This covers the best known cases of excitation of line spectra by electron impact, and the form of the Bohr theory, that is required by them.Comparison of Emission and Absorption.---The above phenomena are compared with corresponding absorption phenomena, with especial reference to the accumulation of energy for photoelectrons by absorption.Deductions.---Theories of the type of Bohr's appears inconsistent with these facts. The phenomena suggest that the law of the conservation of energy, as applied to atomic oscillators, holds only statistically. A set of postulates to replace it for individual oscillators is outlined.
Comparison of X-rays and Light; a Summary.---This covers the best known cases of excitation of line spectra by electron impact, and the form of the Bohr theory, that is required by them.Comparison of Emission and Absorption.---The above phenomena are compared with corresponding absorption phenomena, with especial reference to the accumulation of energy for photoelectrons by absorption.Deductions.---Theories of the type of Bohr's appears inconsistent with these facts. The phenomena suggest that the law of the conservation of energy, as applied to atomic oscillators, holds only statistically. A set of postulates to replace it for individual oscillators is outlined.
An attempt is made to present a consistent detailed theory of optical phenomena, based on the suggestion recently made by the author in collaboration with Bohr and Kramers. This suggestion is that atoms are radiating or absorbing continuously, during their stationary states, and that transitions influence radiation only in terminating the radiation characteristic of the old state, and substituting that of the new. The atoms, on the other hand, are supposed not to change their energy while radiating, but to change it discontinuously on transition. This necessitates giving up the detailed application of the conservation of energy in interaction between atoms and radiation. In the present paper, an additional suggestion is made, namely that resonance radiation is to be identified with the radiation carried out by the spherical wavelets which, by their interference with the external field, also produce absorption. This is practically a return to the classical picture of resonance radiation. Statement of the theory consists formally of two parts: the description of the behavior of atoms, and of radiation, when the two interact. The first involves the statement of the probabilities of transition of atoms, and is taken without change from Einstein. The probability of interruption of coherent vibrations is also discussed. The second requires the specification of the fields emitted by atoms in any steady state under the influence of any external field. These consist of spherical wavelets of the frequencies of the various quantum lines which the atom can emit or absorb in the stationary state in which it is. For emission frequencies, wavelets are emitted even in the absence of an external field; for absorption frequencies, external fields induce wavelets, similar to the wavelets of linearly bound electrons in electron theory, which on the one hand interfere with the external field to produce the phenomena of dispersion, etc., and on the other carry out the resonance radiation in all directions. Detailed descriptions of these fields are given. In a discussion of the theory, it is first shown that the assumptions which have been made about the field satisfy the correspondence principle, in that for large quantum numbers the field aproaches that which would be emitted classically on account of the interaction of an external field and a multiply periodic atom. On the other hand, it is shown that the field has a character essentially like that of classical electron theory, which is known to be in general agreement with experiments. Next, the energy and momentum relations at interaction of atoms and light are investigated, and it is shown that, although these quantities are not precisely conserved, still the assumptions as to atomic and radiation processes have been so made that they are conserved on an average over a great number of atomic processes. Finally the spectral resolution of emitted and absorbed radiation is considered; the theory gives a minimum breadth for the lines, depending on the finite length of wave trains resulting from the finite life in stationary states, and it is shown that Kirchhoff's law is obeyed, the emission and absorption lines being of the same breadth. By way of illustration, specific application of the theory is made to the simple examples of emission of light by bombardment of electrons at the resonance potential, resonance radiation, its quenching by presence of foreign gases, absorption, scattering, and disperison.
Introduction The preceding chapters have focused on atomic transitions induced by applied radiation. That is, there is an optical field illuminating the atoms, and their response is calculated. It is implicitly assumed that an excited atom left alone will spontaneously return to the ground state, and conserve energy by emitting light that satisfies E 2 − E 1 = ħ ω 21 in accordance with the Planck and Bohr pictures. But this spontaneous emission process is not addressed quantitatively in these earlier chapters. Spontaneous emission is one of the most pervasive phenomena of atomic physics, and yet its origins remain among the least well-understood. The number of misconceptions is enormous, and they are to be found in textbooks, journal articles, and lecture notes. Because the natural decay of an excited atom adds energy to what is usually an empty mode of the electromagnetic field, the process is fundamentally quantum mechanical. Classical or even semi-classical descriptions cannot be assured to give correct answers. This is not to say that such discussion is to be avoided, but only that caution is needed in interpreting the results. Toward the end of the nineteenth century, many experimental results made it clear that classical mechanics needed to be supplemented by new theories. The first venture into the new physics was Planck's hypothesis that the energy of classical radiating oscillators like those discussed in Chap. 1 would have to be quantized into integer multiples of ħ ω. This notion led to his famous formula for the spectrum of thermal radiation from a non-reflective object (black body), and this formula describes a radiation field in thermodynamic equilibrium with its environment. The result of Planck's hypothesis in the context of thermal equilibrium plays a vital role in the discussion of spontaneous emission. Einstein A - and B -coefficients Soon after Bohr proposed a model of atomic structure consisting of discrete energy levels, connected by radiation whose energy satisfied Δ E = ħω when atoms made transition between them, Einstein published the first serious attempt to connect the absorption and emission processes. Absorption, he reasoned, could occur only in the presence of applied radiation, whereas spontaneous decay occurred without the application of any field.
1. The origin of the quantum theory Planck's radiation formula 2. The nuclear theory of the atom Bohr's theory of the hydrogen spectrum 3. The correspondence principle the photo-electric effect Einstein's deduction of Planck's formula 4. The adiabatic principle of Ehrenfest the stationary states of a periodic system 5. General dynamical theory 6. Contact transformations the Hamilton-Jacobi differential equation 7. The use of angle variables multiply periodic systems 8. The relativity theory of the fine structure of the hydrogen lines electron in a central field 9. The Stark effect 10. The Zeeman effect 11. The series spectra of the elements 12. The multiple structure of series lines theory of the Ritz formula 13. Arc and spark spectra excitation of lines by electrons or radiation 14. X-ray spectra 15. Absorption spectra and absorption edges Bohr's table of the atomic structures of the elements 17. Band spectra in the infra-red 18. Band spectra in the optical region molecular rotation and specific heat 19. The Keplerian orbit the Delaunay elements 20. The astronomical theory of perturbations and atom mechanics 21. General perturbation theory 22. The effect of electric and magnetic fields on the spectra of elements of higher atomic number. Recent developments of the quantum theory: the doublet theories of Sommerfield and Lande the dispersion theory of Kramers the quantum-kinematics of Heisenberg Index of authors.
This chapter provides a basis for an insight into the nature of quantum effects. The Newtonian approach cannot explain diffraction phenomena. The wave theory of the nature of light proposed by Huygens was able to account for these phenomena as well as for geometric optics. Planck was not only able to overcome the difficulties encountered by his predecessors, but included their findings as special cases of his analysis. Planck considered that the radiating surface was composed of electric dipole oscillators, and that a relationship should exist between the energy of the radiation and the frequency of the oscillators. According to classical theory a continuous spectrum is expected when matter is excited by an arc, or spark, as in spectroscopy. It is found experimentally that only “lines”, or discrete radiations, occur when the light is diffracted. Bohr’s revolutinary ideas provided a significant portion of the bases for the modern understanding of spectra and, consequently, of atomic structure.
In many practical cases a stationary system is perturbed in some way, inducing it to undergo transitions between the otherwise stationary states. Perhaps the best example concerns the radiative transitions of atomic electrons in which the disturbance of an external electromagnetic field causes the electrons to jump between energy levels, emitting or absorbing photons. Equation is a statement of the classical law of conservation of energy. The stimulated emission and absorption of radiation both have close classical analogues. If a simple harmonic oscillator is driven by a sinusoidal electromagnetic field it can gain or lose energy depending on phase angles. The existence of spontaneous emission implies that all excited states of electrical systems are unstable and will eventually decay to the ground state by photon emission. Quantum systems thus comply with the fundamental principle that physical systems tend to seek out their state of lowest energy and maximum entropy.
The phenomena which are principally responsible for the interaction of radiation with matter in everyday life are absorption and spontaneous emis sion. Light falling on matter is absorbed, leaving atoms in excited states which spontaneously emit radiation with a spread of frequency inversely proportional to the decay time. The situation is modified when the atomic decay times are sufficiently long and the radiation sufficiently intense, for then radiation may fall on excited atoms, resulting in stimulated emission rather than absorption. We saw in Chap. 2 that this third process was required to obtain the Planck blackbody radiation law in Einstein’s derivation. It is stimulated emission which enables an atomic medium to amplify incident radiation, and therefore is an essential ingredient in light amplifiers and oscillators. In fact, the word LASER is an acronym for Light Amplification by Stimulated Emission of Radiation.