Spectral Lines.
In the early part of the nineteenth century Wollaston, in England, and later Fraunhofer in Germany, discovered dark lines in the solar spectrum, a discovery which meant that certain colours were missing. The most noticeable of these so-called “Fraunhofer Lines” were named with the letters A, B, C, D, E, F, G, H, from red to violet. It was later discovered that some of the lines were double, that the D-line, for instance, can be resolved into D₁ and D₂; other letters, such as b and h, were introduced to denote new lines. With improvements in the methods of experiment and research the number of lines has increased to hundreds and even thousands. The light from a glowing solid or liquid element forms, on the other hand, a continuous spectrum, i.e. a spectrum which has no dark lines. An illustration of the solar spectrum with the strongest Fraunhofer lines is given at the end of the book.
In contrast to the solar spectrum with dark lines on a bright background are the so-called line spectra, which consist of bright lines on a dark background. The first known line spectrum was the one given by light from the spirit flame coloured with common salt, mentioned in connection with monochromatic light. As has been said, this spectrum had just one yellow line which was later found to consist of two lines close to each other. It is sodium chloride which colours the flame yellow. The colour is due, not to the chlorine, but to the sodium, for the same double yellow line can be produced by using other sodium salts not compounded with chlorine. The yellow light is therefore called sodium light. [No. 7 in the table of spectra at the end of the book] shows the spectrum produced by sodium vapour in a flame. (On account of the small scale in the figure it is not shown that the yellow line is double.)
Another interesting discovery was soon made, namely, that the sodium line has exactly the same wave-length as the light lacking in the solar spectrum, where the double D-line is located. About 1860 Kirchhoff and Bunsen explained this remarkable coincidence as well as others of the same nature. They showed by direct experiment that if sodium vapour is at a high temperature it can not only send out the yellow light, but also absorb light of the same wave-length when rays from a still warmer glowing body pass through the vapour. This phenomenon is something like that in the case of sound waves where a resonator absorbs the pitch which it can emit itself. The existence of the dark D-line in the solar spectrum must then mean that in the outer layer of the sun there is sodium vapour present of lower temperature than the white-hot interior of the sun, and that the light corresponding to the D-line is absorbed by the vapour. Several ingenious experiments, which cannot be described here, have given further evidence in favour of this explanation.
In the other line spectra, just as in that from the common salt flame, definite lines correspond to definite elements and not to chemical compounds. The emission of these lines is then not a molecular characteristic, but an atomic one. The line spectra of metals can often be produced by vaporizing a metallic salt in a spirit flame or in a hot, colourless gas flame (from a Bunsen burner). It is even better to use an electric arc or strong electric sparks. The atoms from which gaseous molecules are formed can also be made to emit light which by means of the spectroscope is shown to consist of a line spectrum. These results are obtained by means of electric discharges of various kinds, arcs, and spark discharges through tubes where the gas is in a rarefied state.
The other Fraunhofer lines in the solar spectrum correspond to bright lines in the line spectra of certain elements which exist here on earth. These Fraunhofer lines must then be assumed to be caused by the absorption of light by the elements in question. This may be explained by the presence of these elements as gases in the solar atmosphere, through which passes the light from the inner layer. This inner surface would in itself emit a continuous spectrum.
The work of Kirchhoff and Bunsen put at the disposal of science became a new tool of incalculable scope. First and foremost, spectrum examinations were taken into the service of chemistry as spectrum analysis. It has thus become possible to analyse quantities of matter so small that the general methods of chemistry would be quite powerless to detect them. It is also possible by spectrum analysis to detect minute traces of an element; several elements were in this way first discovered by the spectroscope. Moreover, chemical analysis has been extended to the study of the sun and stars. The spectral lines have given us answers to many problems of physics—problems which formerly seemed insoluble. Last but not least spectrum analysis has given us a key to the deepest secrets of the atom, a key which Niels Bohr has taught us how to use.
In the discussion of the spectrum we have hitherto restricted ourselves to the visible spectrum limited on the one side by red and on the other by violet. But these boundaries are in reality fortuitous, determined by the human eye. The spectrum can be studied by other methods than those of direct observation. The more indirect methods include the effect of the rays on photographic plates and their heating effect on fine conducting wires for electricity, held in various parts of the spectrum. It has thus been discovered that beyond the visible violet end of the spectrum there is an ultra-violet region with strong photographic activity and an infra-red region producing marked heat effects. There are both dark and light spectral lines in these new parts of the spectrum. The fact that glass is not transparent to ultra-violet or infra-red rays has been an obstacle in the experiments, but the difficulty can be overcome by using other substances, such as quartz or rock salt, for the prisms and lenses, or by substituting concave gratings. By special means it has been possible to detect rays with wave-lengths as great as 300 μ and as small as about 0·02 μ, corresponding to frequencies between 10¹², and 15 × 10¹⁵ vibrations per second, while the wave-lengths of the luminous rays lie between 0·8 and 0·4 μ. The term “light wave” is often used to refer to the ultra-violet and infra-red rays which can be shown in the spectra produced by prisms or gratings.
Fig. 11.—Photographic effect of X-rays, which are
passed through the atom grating in a magnesia crystal.
The electrically produced electromagnetic waves, as already mentioned, have wave-lengths much greater than 300 μ. In wireless telegraphy there are generally used wave-lengths of one kilometre or more, corresponding to frequencies of 300,000 vibrations per second or less. By direct electrical methods it has, however, not been possible to obtain wave-lengths less than about one-half a centimetre, a length differing considerably from the 0·3 millimetre wave of the longest infra-red rays. Wave-lengths much less than 0·02 μ or 20 μμ exist in the so-called Röntgen rays or X-rays with wave-lengths as small as 0·01 μμ corresponding to a frequency of 30 × 10¹⁸. These rays cannot possibly be studied even with the finest artificially made gratings, but crystals, on account of the regular arrangement of the atoms, give a kind of natural grating of extraordinary fineness. With the use of crystal gratings success has been attained in decomposing the Röntgen rays into a kind of spectrum, in measuring the wave-lengths of the X-rays and in studying the interior structure of the crystals. The German Laue, the discoverer of the peculiar action of crystals on X-rays (1912), let the X-rays beams pass through the crystal, obtaining thereby photographs of the kind illustrated in [Fig. 11]. Later on essential progress was due to the Englishmen, W. H. and W. L. Bragg, who worked out a method of investigation by which beams of X-rays are reflected from crystal faces. The greatest wave-length which it has been possible to measure for X-rays is about 1·5 μμ, which is still a long way from the 20 μμ of the furthermost ultra-violet rays.
It may be said that the spectrum since Fraunhofer has been made not only longer but also finer, for the accuracy of measuring wave-lengths has been much increased. It is now possible to determine the wave-length of a line in the spectrum to about 0·001 μμ or even less, and to measure extraordinarily small changes in wave-lengths, caused by different physical influences.
In addition to the continuous spectra emitted by glowing solids or liquids, and to the line spectra emitted by gases, and to the absorption spectra with dark lines, there are spectra of still another kind. These are the absorption spectra which are produced by the passage of white light through coloured glass or coloured fluids. Here instead of fine dark lines there are broader dark absorption bands, the spectrum being limited to the individual bright parts. There are also the band spectra proper, which, like the line spectra, are purely emission spectra, given by the light from gases under particular conditions; these seem to consist of a series of bright bands which follow each other with a certain regularity ([cf. Fig. 12]). With stronger dispersion the bands are shown to consist of groups of bright lines.
Fig. 12.—Spectra produced by discharges of different character
through a glass tube containing nitrogen at a pressure of ¹/₂₀
that of the atmosphere. Above, a band spectrum;
below, a line spectrum.
Since the line spectra are most important in the atomic theory, we shall examine them here more carefully.
The line spectra of the various elements differ very much from each other with respect to their complexity. While many metals give a great number of lines (iron, for instance, gives more than five thousand), others give only a few, at least in a simple spectroscope. With a more powerful spectroscope the simplicity of structure is lost, since weaker lines appear and other lines which had seemed single are now seen to be double or triple. Moreover, the number of lines is increased by extending the investigation to the ultra-violet and infra-red regions of the spectrum. The sodium spectrum, at first, seemed to consist of one single yellow line, but later this was shown to be a double line, and still later several pairs of weaker double lines were discovered. The kind and number of lines obtained depends not only upon the efficiency of the spectroscope, but also upon the physical conditions under which the spectrum is obtained.
The eager attempts of the physicists to find laws governing the distribution of the lines have been successful in some spectra. For instance, the line spectra of lithium, sodium, potassium and other metals can be arranged into three rows, each consisting of double lines. The difference between the frequencies of the two “components” of the double lines was found to be exactly the same for most of the lines in one of these spectra, and for the spectra of different elements there was discovered a simple relationship between this difference in frequency and the atomic weight of the element in question. But this regularity was but a scrap, so to speak; scientists were still very far from a law which could exactly account for the distribution of lines in a single series, not to mention the lines in an entire spectrum or in all the spectra.
The first important step in this direction was made about 1885 by the Swiss physicist, Balmer, in his investigations with the hydrogen spectrum, the simplest of all the spectra. In the visible part there are just three lines, one red, one green-blue and one violet, corresponding to the Fraunhofer lines C, F and h. These hydrogen lines are now generally known by the letters Hα, Hᵦ and Hᵧ. In the ultra-violet region there are many lines also.
Balmer discovered that wave-lengths of the red and of the green hydrogen line are to each other exactly as two integers, namely, as 27 to 20, and that the wave-lengths of the green and violet lines are to each other as 28 to 25. Continued reflection on this correspondence led him to enunciate a rule which can be expressed by a simple formula. When frequency is substituted for wave-length Balmer’s formula is written as
| ν = K |  | 1 | - | 1 |  | , |
| 4 | n² |
where ν is the frequency of a hydrogen line, K a constant equal to 3·29 × 10¹⁵ and n an integer. If n takes on different values, ν becomes the frequency for the different hydrogen lines. If n = 1 ν is negative, for n = 2 ν is zero. These values of n therefore have no meaning with regard to ν. But if n = 3, then ν gives the frequency for the red hydrogen line Hα; n = 4 gives the frequency of the green line Hᵦ and n = 5 that of the violet line Hᵧ. Gradually more than thirty hydrogen lines have been found, agreeing accurately with the formula for different values of n. Some of these lines were not found in experiment, but were discovered in the spectrum of certain stars; the exact agreement of these lines with Balmer’s formula was strong evidence for the belief that they are due to hydrogen. The formula thus proved itself valuable in revealing the secrets of the heavens.
As n increases 1/n² approaches zero, and can be made as close to zero as desired by letting n increase indefinitely. In mathematical terminology, as n = ∞, 1/n² = 0 and ν = K/4 = 823 × 10¹², corresponding to a wave-length of 365 μμ. Physically this means that the line spectrum of hydrogen in the ultra-violet is limited by a line corresponding to that frequency. Near this limit the hydrogen lines corresponding to Balmer’s formula are tightly packed together. For n = 20 ν differs but little from K/4, and the distance between two successive lines corresponding to an increase of 1 in n becomes more and more insignificant. [Fig. 13], where the numbers indicate the wave-lengths in the Ångström unit (0·1 μμ), shows the crowding of the hydrogen lines towards a definite boundary. [The following table], where K has the accurate value of 3·290364 × 10¹⁵, shows how exactly the values calculated from the formula agree with experiment.
Fig. 13.—Lines in the hydrogen spectrum corresponding to the Balmer series.
Table of some of the Lines of the Balmer Series
| ν = K(1/4 - 1/n²) = ν (calculated). | ν (found). | λ (found). | |
|---|---|---|---|
| n = 3 | K(¼ - ¹/₉ ) = 456,995 bills | 456,996 bills | 656·460 μμ Hα |
| n = 4 | K(¼ - ¹/₁₆ ) = 616,943 “ | 616,943 “ | 486·268 “ Hᵦ |
| n = 5 | K(¼ - ¹/₂₅ ) = 690,976 “ | 690,976 “ | 434·168 “ Hᵧ |
| n = 6 | K(¼ - ¹/₃₆ ) = 731,192 “ | 731,193 “ | 410·288 “ Hδ |
| n = 7 | K(¼ - ¹/₄₉ ) = 755,440 “ | 755,441 “ | 397·119 “ Hε |
| n = 20 | K(¼ - ¹/₄₀₀) = 814,365 “ | 814,361 “ | 368·307 “ |
From arguments in connection with the work of the Swedish scientist, Rydberg, in the spectra of other elements, Ritz, a fellow countryman of Balmer’s, has made it seem probable that the hydrogen spectrum contains other lines besides those corresponding to Balmer’s formula. He assumed that the hydrogen spectrum, like other spectra, contains several series of lines and that Balmer’s formula corresponds to only one series. Ritz then enunciated a more comprehensive formula, the Balmer-Ritz formula:
| ν = K | | 1 | - | 1 | | , |
| n″ ² | n′ ² |
where K has the same value as before, and both n′ and n″ are integers which can pass through a series of different values. For n″ = 2, the Balmer series is given; to n″ = 1, and n′ = 2, 3 ... ∞ there corresponds a second series which lies entirely in the ultra-violet region, and to n″ = 3, n′ = 4, 5 ... ∞ a series lying entirely in the infra-red. Lines have actually been found belonging to these series.
Formulæ, similar to the Ritz one, have been set up for the line spectra of other elements, and represent pretty accurately the distribution of the lines. The frequencies are each represented by the difference between two terms, each of which contains an integer, which can pass through a series of values. But while the hydrogen formula, except for the n′s, depends only upon one constant quantity K and its terms have the simple form K/n², the formula is more complicated with the other elements. The term can often be written, with a high degree of exactness, as K/(n + α)², where K is, with considerable accuracy, the same constant as in the hydrogen formula. For a given element α can assume several different values; therefore the number of series is greater and the spectrum is even more complicated than that of hydrogen.
All these formulæ are, however, purely empirical, derived from the values of wave-lengths and frequencies found in spectrum measurements. They represent certain more or less simple bookkeeping rules, by which we can register both old and new lines, enter them in rows, arrange them according to a definite system. But from the beginning there could be no doubt that these rules had a deeper physical meaning which it was not yet possible to know. There was no visible correspondence between the spectral line formulæ and the other physical characteristics of the elements which emitted the spectra; not even in their form did the formulæ show any resemblance to formulæ obtained in other physical branches.