Absorption.
In the experiments previously described it was the electron collisions which furnished the energy required to excite the atoms, i.e., to carry them from the normal state over into a stationary state with greater energy. This “excitation energy” may, however, also be furnished to the atoms in the form of radiation energy; we shall now examine this case more closely.
Let us assume that to transfer an atom from the normal state to another stationary state, or, in other words, to transfer one of the electrons to an outer stationary orbit, a certain quantity of energy E is demanded; then the radiation emitted by the atom when it returns to the normal state will have a frequency ν depending upon the relation E=hν or ν=E/h, where h, as usual, is the Planck constant. But just as the atom in the transition from the stationary state to the normal state can emit radiation only with the definite frequency ν, then the opposite transition can only be performed by absorption of radiation with the same frequency; when this happens the absorbed radiation energy has exactly the value E=hν.
This reciprocity, which may be considered as a direct consequence of the Bohr postulates, agrees with what has been said ([cf. p. 50]) about the correspondence between the lines in the line spectrum of an element and the dark absorption lines of that element—e.g., the Fraunhofer lines in the solar spectrum. Let us examine, as an example, the yellow sodium line, the D-line. Light with the corresponding frequency, 526 × 10¹² vibrations per second, is emitted by a sodium atom, when the loosest bound electron goes over from a stationary orbit with quantum numbers 3₂ to the orbit 3₁, which belongs to the normal state of the sodium atom. The transition in the opposite direction, 3₁ to 3₂, can take place under absorption of radiation only when in the light from some other source of light, which passes the sodium atoms, there are found rays with the frequency 526 × 10¹². Even if there is present radiation energy with some other frequency, the sodium atoms take no notice of this energy; they absorb only rays with the frequency stated, and every time an atom absorbs energy from a ray the energy taken is always an energy quantum of the magnitude hν, i.e. about 6·54 × 10⁻²⁷ × 526 × 10¹² = 3·44 × 10⁻¹² ergs (1 erg is the unit of energy used in the determination of h). When there are present a large number of sodium atoms (as, for instance, in the previously mentioned common salt flame), the transition 3₁ to 3₂ can take place in some atoms, the transition 3₂ to 3₁ in others; therefore, at the same time there can be absorption and radiation of the light in question. Whether absorption or radiation at any given time has the upper hand depends upon various conditions (temperature, etc.).
For the sake of simplicity we have here tacitly understood that there can be but one definite transition (from the normal state) corresponding to the assumption that the sodium spectrum had no other lines than the D-line. In reality this is not the case, and there can equally occur absorption of rays with larger frequencies belonging to other spectral lines in the sodium atom and corresponding to other possible transitions between stationary states in the sodium atom. If the temperature of the sodium vapour is sufficiently low, in which case almost all the atoms are in the normal state, it is evident that in the absorption only those lines will appear which correspond to transitions from the normal state, and which therefore form only a part of all the lines of the sodium spectrum. We thus obtain an explanation of the previously enigmatical circumstance that not all spectral lines which can appear in emission will be found in absorption. At the same time we get, in absorption experiments, valuable information about the structure of the atom beyond what the observations in the emission spectra are able to give.
Interesting phenomena may arise owing to the fact that the jumps between the stationary states of the atom sometimes, as we know, take place in single jumps, sometimes in double or multiple jumps, so that the intermediate stationary states are jumped over. There is then evidently a possibility that absorption can take place, for instance, with a double jump of an electron, which may later return to the original stationary orbit in two single jumps. The absorbed radiation energy will then appear in emission with two frequencies which are entirely different from the frequency of the absorbed rays (this latter in this case will be the sum of the other two). When an element is illuminated with a certain kind of rays, it can, in other words, emit in return rays of a different nature. Such changes of frequencies have also been observed in experiment; they contain, in principle, an explanation of the characteristic phenomenon called fluorescence.
We shall not go further into this problem, but dwell for a time on the characteristic phenomenon of absorption which is known as the photoelectric effect. In this phenomenon ([cf. p. 116]) a metal plate, by illumination with ultra-violet light, is made to send out electrons with velocities the maximum value of which is independent of the strength of the illumination, but depends only on the frequency of the rays. What happens is that some of the electrons in the metal which otherwise have, as their function, the conduction of the electric current, by absorbing radiation energy, free themselves from the metal and leave it with a certain velocity. The reason why the rays for most metals must be ultra-violet (i.e. have a high frequency and consequently correspond to a proportionately large energy quantum) depends upon the fact that the energy quantum absorbed by the electrons must be large enough to carry out the work of freeing the electrons. But as long as the frequency of the rays (and therefore their energy quantum) is no less than what is needed for the freeing process, it does not need to have certain fixed values. If the energy quantum hν which the rays can give off is greater than is required to free the electrons, the surplus becomes kinetic energy in the electrons, which thus acquire a velocity which is the greater the greater the frequency ν, and which coincides with the maximum velocity observed in the experiments. What happens here is evidently something which can be considered as the reverse of the process which leads to the production of the continuous hydrogen spectrum ([described on p. 163]). In the latter case, electrons with different velocities are bound by the hydrogen atoms, which thus emit rays with frequencies increasing with increasing velocity, while, vice versa, in the photoelectric effect rays with different frequencies free the electrons and give them velocities increasing with increasing frequencies.
It must be acknowledged that there is something very curious in this effect. If the electromagnetic waves, as has been assumed, are distributed evenly over the field of radiation, it is not easy to understand why they give energy to some atoms and not to others, and why the selected ones always—with a given frequency—acquire a definite energy quantum, independent of the intensity of the radiation. For small intensities of the incident radiation, the atom, in order to acquire the proper quantum, must absorb energy from a greater part of the field of radiation (or for a longer time) than for large intensities. When the atoms acquire energy in electron collisions, the situation is apparently easier to understand, since in this case the colliding electrons give their kinetic energy to definite atoms, namely, those which they strike.
Einstein, in 1905, when there was not yet any talk of the nuclear atom or the Bohr theory, enunciated his theory of light quanta, according to which the energy of radiation is not only emitted and absorbed by the atoms in certain quanta, with magnitudes determined by the frequency ν, but is also present in the field of radiation in such quanta. When an atom emits an energy quantum hν, this energy will not spread out in waves on all sides, but will travel in a definite direction—like a little lump of energy, we might say. These light quanta, as they are called, can, like the electrons, hit certain atoms.
But even if in this theory the difficulties mentioned are, apparently, overcome, far greater difficulties are introduced; indeed it may be said that the whole wave theory becomes shrouded in darkness. The very number ν which characterizes the different kinds of rays loses its significance as a frequency and the phenomena of interference—reflection, dispersion, diffraction, and so on—which are so fundamental in the wave theory of the propagation of light, and on which, for instance, the mechanism of the human eye is based, receive no explanation in the theory of light quanta.
For instance, in order to understand that grating spectra can be produced at all, we must think of a co-operation of the light from all the rulings ([cf. Fig. 10, p. 47]), and this co-operation cannot arise if all the slits at a given moment do not receive light emitted from the same atom. In a bundle of rays which comes in at right angles to a grating, we must, in order to explain the interference, assume that the state of oscillation at a given moment is the same in all slits, that, for instance, there are wave crests in all at the same time, if we borrow a picture from the representation of water waves. Only in this case there can behind the grating at certain fixed places—for which the difference in the wave-length of the distances from successive slits is a whole number of wave-lengths—steadily come wave crests from all the slits at one moment and wave troughs from all at another moment (the classical explanation of the “mechanism” of a grating). If we imagine, however, that some slits are hit by light quanta from one atom and others from a second atom, it is pure chance if there are wave crests simultaneously in all slits, because the different atoms in a source of light emit light at different times, depending purely on chance. An understanding of the observed effect of a grating on light seems then out of question.
The theory of light quanta may thus be compared with medicine which will cause the disease to vanish but kill the patient. When Einstein, who has made so many essential contributions in the field of the quantum theory, advocated these remarkable representations about the propagation of radiation energy he was naturally not blind to the great difficulties just indicated. His apprehension of the mysterious light in which the phenomena of interference appear on his theory is shown in the fact that in his considerations he introduces something which he calls a “ghost” field of radiation to help to account for the observed facts. But he has evidently wished to follow the paradoxical in the phenomena of radiation out to the end in the hope of making some advance in our knowledge.
This matter is introduced here because the Einstein light quanta have played an important part in discussions about the quantum theory, and some readers may have heard about them without being clear as to the real standing of the theory of light quanta. The fact must be emphasized that this theory in no way has sprung from the Bohr theory, to say nothing of its being a necessary consequence of it.
In the Bohr theory, absorption and radiation must be said to be completely reciprocal processes, i.e. processes of essentially the same nature, but proceeding in opposite directions. In itself it cannot be said to be more incomprehensible that an atom absorbs energy from a field of radiation in agreement with the Bohr postulates than that it emits energy into the field; but in both cases we naturally encounter the great difficulties mentioned in [Chap. V].
We have hitherto restricted ourselves to the purely atomic processes. But just as in the emission of radiation we meet spectra which owe their characteristics to molecular processes (band spectra, [cf. p. 162]), we have also absorption spectra with characteristics depending essentially upon motions of the atomic nuclei in the molecules. A particularly interesting and instructive example of this nature is met with in the infra-red region of the spectrum in certain broad absorption lines or absorption bands, which are due to gases having molecules containing several atoms. In hydrogen chloride, for instance, there is found, in the region of the spectrum which corresponds to a wave-length of about 3·5 μ, such an absorption band, which by more accurate investigation has been shown to consist of a great number of absorption lines.
The explanation of this collection of lines must be sought in the motions which the hydrogen nucleus and the chlorine nucleus perform, as they in part vibrate with respect to each other and in part rotate about their common centre of gravity. Just as in the case of the motions of the electrons in the atom, there are also certain stationary states for the nuclear motions. When the molecule absorbs radiation energy it will go from one of these states to another, where the energy content is greater. This absorption of energy proceeds according to the quantum rule, i.e., the product of the Planck constant h and the frequency ν for the absorbed radiation must be equal to the difference in energy between the two stationary states; only those rays which have frequencies fulfilling this condition are absorbed.
Fig. 32.—Schematic representation of possible motions in a molecule of hydrogen chloride. O is the centre of gravity of the molecule. The black circles give the states of equilibrium of the nuclei, the circles s their outer positions in oscillating, and the circles r positions during the rotation of the nuclei.
In hydrogen chloride, at standard temperature, the molecules will be in different stationary states of rotation ([cf. the remarks on p. 27]), corresponding to different definite values of the rotation frequency, while the nuclei, on the other hand, must be assumed to be at rest with reference to each other, i.e., they preserve their mutual distance. In [Fig. 32], H and Cl indicate the circles which the two nuclei will describe about the centre of gravity; here, however, it must be remarked that the hydrogen circle is drawn too small in comparison with that of chlorine. If heat rays with all possible wave-lengths around 3·5 μ are sent through the hydrogen chloride, that radiation energy will be absorbed which can in part set the nuclei in oscillation and in part change the state of rotation. Let us for a moment assume that only the former change could happen. Then a ray with wave-length 3·46 μ would be absorbed, this frequency corresponding to the energy in the stationary state of oscillation into which the molecule goes; this frequency is very nearly equal to the frequency with which the nuclei vibrate relatively to each other. In reality, at the same time that the nucleus is set in oscillation, there will always be a change in the state of rotation—consisting either in an increase or in a decrease in the velocity of rotation. The energy absorbed, and therefore the frequency for the radiation absorbed, is thereby changed a little, so that in the spectrum of the rays sent through we do not obtain an absorption line corresponding to 3·46 μ, but a line somewhat removed from that. Since there are, however, many stationary states of rotation to start from, and since in some molecules there is one transition, in others another, we get many absorption lines on each side of 3·46 μ.
Even before Bohr propounded his theory, at a time when the quantum theory did not yet have a clarified form, the Danish chemist, Niels Bjerrum, had predicted that the infra-red absorption lines ought to have such a structure. This structure must be interpreted in the above way which differs somewhat from Bjerrum’s ideas, but his prediction was essentially strengthened by investigations, and it was one of the most significant features in the development of the quantum theory prior to 1913. The first to detect the structure of the infra-red absorption bands was the Swedish physicist, Eva von Bahr. Her experiments were later extended in a most significant way by the work of Imes and other American investigators. They enable us to calculate exactly the distance between the two nuclei in the molecule.
It may be asked what becomes of the energy which the hydrogen chloride molecule thus absorbs, and whether it necessarily after a longer or shorter time must be re-emitted as radiation. The latter is not the case. In a collision between molecules or atoms, the energy which one molecule (or atom) has absorbed by radiation can undoubtedly be transferred to another molecule, the velocity of which is thereby increased. The theoretical necessity of the occurrence of such collisions was clearly shown for the first time in a very significant investigation by two of Bohr’s students, Klein and Rosseland. Without collisions of this nature the radiation energy absorbed could never be transformed into heat energy. Here we come to a very great and important field, which has a very close connection with the theory of the chemical processes and to a better explanation of which the more recent experiments of Franck and his co-workers have made important contributions.