Einstein 1938: Light Spectra

Reference: Evolution of Physics

This paper presents Chapter IV section 4 from the book THE EVOLUTION OF PHYSICS by A. EINSTEIN and L. INFELD. The contents are from the original publication of this book by Simon and Schuster, New York (1942).

The paragraphs of the original material (in black) are accompanied by brief comments (in color) based on the present understanding.  Feedback on these comments is appreciated.

The heading below is linked to the original materials.

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Light Spectra

We already know that all matter is built of only a few kinds of particles. Electrons were the first elementary particles of matter to be discovered. But electrons are also the elementary quanta of negative electricity. We learned furthermore that some phenomena force us to assume that light is composed of elementary light quanta, differing for different wave-lengths. Before proceeding we must discuss some physical phenomena in which matter as well as radiation plays an essential role.

The sun emits radiation which can be split into its components by a prism. The continuous spectrum of the sun can thus be obtained. Every wave-length between the two ends of the visible spectrum is represented. Let us take another example. It was previously mentioned that sodium when incandescent emits homogeneous light, light of one colour or one wave-length. If incandescent sodium is placed before the prism, we see only one yellow line. In general, if a radiating body is placed before the prism, then the light it emits is split up into its components, revealing the spectrum characteristic of the emitting body.

The discharge of electricity in a tube containing gas produces a source of light such as seen in the neon tubes used for luminous advertisements. Suppose such a tube is placed before a spectroscope. The spectroscope is an instrument which acts like a prism, but with much greater accuracy and sensitiveness; it splits light into its components, that is, it analyses it. Light from the sun, seen through a spectroscope, gives a continuous spectrum; all wave-lengths are represented in it. If, however, the source of light is a gas through which a current of electricity passes, the spectrum is of a different character. Instead of the continuous, multi-coloured design of the sun’s spectrum, bright, separated stripes appear on a continuous dark background. Every stripe, if it is very narrow, corresponds to a definite colour or, in the language of the wave theory, to a definite wavelength. For example, if twenty lines are visible in the spectrum, each of them will be designated by one of twenty numbers expressing the corresponding wavelength. The vapours of the various elements possess different systems of lines, and thus different combinations of numbers designating the wave-lengths composing the emitted light spectrum. No two elements have identical systems of stripes in their characteristic spectra, just as no two persons have exactly identical finger-prints. As a catalogue of these lines was worked out by physicists, the existence of laws gradually became evident, and it was possible to replace some of the columns of seemingly disconnected numbers expressing the length of the various waves by one simple mathematical formula.

All that has just been said can now be translated into the photon language. The stripes correspond to certain definite wave-lengths or, in other words, to photons with a definite energy. Luminous gases do not, therefore, emit photons with all possible energies, but only those characteristic of the substance. Reality again limits the wealth of possibilities.

Atoms of a particular element, say, hydrogen, can emit only photons with definite energies. Only the emission of definite energy quanta is permissible, all others being prohibited. Imagine, for the sake of simplicity, that some element emits only one line, that is, photons of a quite definite energy. The atom is richer in energy before the emission and poorer afterwards. From the energy principle it must follow that the energy level of an atom is higher before emission and lower afterwards, and that the difference between the two levels must be equal to the energy of the emitted photon. Thus the fact that an atom of a certain element emits radiation of one wave-length only, that is photons of a definite energy only, could be expressed differently: only two energy levels are permissible in an atom of this element and the emission of a photon corresponds to the transition of the atom from the higher to the lower energy level.

But more than one line appears in the spectra of the elements, as a rule. The photons emitted correspond to many energies and not to one only. Or, in other words, we must assume that many energy levels are allowed in an atom and that the emission of a photon corresponds to the transition of the atom from a higher energy level to a lower one. But it is essential that not every energy level should be permitted, since not every wave-length, not every photon-energy, appears in the spectra of an element. Instead of saying that some definite lines, some definite wave-lengths, belong to the spectrum of every atom, we can say that every atom has some definite energy levels, and that the emission of light quanta is associated with the transition of the atom from one energy level to another. The energy levels are, as a rule, not continuous but discontinuous. Again we see that the possibilities are restricted by reality.

It was Bohr who showed for the first time why just these and no other lines appear in the spectra. His theory, formulated twenty-five years ago, draws a picture of the atom from which, at any rate in simple cases, the spectra of the elements can be calculated and the apparently dull and unrelated numbers are suddenly made coherent in the light of the theory.

Bohr’s theory forms an intermediate step toward a deeper and more general theory, called the wave or quantum mechanics. It is our aim in these last pages to characterize the principal ideas of this theory. Before doing so, we must mention one more theoretical and experimental result of a more special character.

Our visible spectrum begins with a certain wavelength for the violet colour and ends with a certain wave-length for the red colour. Or, in other words, the energies of the photons in the visible spectrum are always enclosed within the limits formed by the photon energies of the violet and red lights. This limitation is, of course, only a property of the human eye. If the difference in energy of some of the energy levels is sufficiently great, then an ultraviolet photon will be sent out, giving a line beyond the visible spectrum. Its presence cannot be detected by the naked eye; a photographic plate must be used.

X-rays are also composed of photons of a much greater energy than those of visible light, or in other words, their wave-lengths are much smaller, thousands of times smaller in fact, than those of visible light.

But is it possible to determine such small wavelengths experimentally? It was difficult enough to do so for ordinary light. We had to have small obstacles or small apertures. Two pinholes very near to each other, showing diffraction for ordinary light, would have to be many thousands of times smaller and closer together to show diffraction for X-rays.

How then can we measure the wave-lengths of these rays? Nature herself comes to our aid.

A crystal is a conglomeration of atoms arranged at very short distances from each other on a perfectly regular plan. Our drawing shows a simple model of the structure of a crystal. Instead of minute apertures, there are extremely small obstacles formed by the atoms of the element, arranged very close to each other in absolutely regular order. The distances between the atoms, as found from the theory of the crystal structure, are so small that they might be expected to show the effect of diffraction for X-rays. Experiment proved that it is, in fact, possible to diffract the X-ray wave by means of these closely packed obstacles disposed in the regular three-dimensional arrangement occurring in a crystal.

Suppose that a beam of X-rays falls upon a crystal and, after passing through it, is recorded on a photographic plate. The plate then shows the diffraction pattern. Various methods have been used to study the X-ray spectra, to deduce data concerning the wavelength from the diffraction pattern. What has been said here in a few words would fill volumes if all theoretical and experimental details were set forth. In Plate III we give only one diffraction pattern obtained by one of the various methods. We again see the dark and light rings so characteristic of the wave theory. In the centre the non-diffracted ray is visible. If the crystal were not brought between the X-rays and the photographic plate, only the light spot in the centre would be seen. From photographs of this kind the wave-lengths of the X-ray spectra can be calculated and, on the other hand, if the wave-length is known, conclusions can be drawn about the structure of the crystal.

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FINAL COMMENTS

If a radiating body is placed before the prism, then the light it emits is split up into its components, revealing the spectrum characteristic of the emitting body. The spectrum of the light from the Sun is continuous throughout the visible range. Most elements, however, emit light that produce discrete lines as their spectra.

Each spectral line is produced by a light of a characteristic wavelength. It was possible to express these wavelengths through one simple mathematical formula. These wavelengths could be related to the energy of corresponding photons; and from there to characteristic energy levels of atoms emitting those photons. From this data, Bohr could then develop a model of the atom.

Photons of energies beyond the visible spectra also exist, such as, those of x-rays. Ingenious experiments have been devised to measure the energy of such photons.

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