The A B C of atoms

by Bertrand Russell

The application of the spectroscope that concerns us is different. We are concerned with the explanation of the lines emitted by different elements. Why does an element have a spectrum consisting of certain sharp lines? What connection is there between the different lines in a single spectrum? Why are the lines sharp instead of being diffuse bands of colours? Until recent years, no answer whatever was known to these questions; now the answer is known with a considerable approach to completeness. In the two cases of hydrogen and positively electrified helium, the answer is exhaustive; everything has been explained, down to the tiniest peculiarities. It is quite clear that the same principles that have been successful in those two cases are applicable throughout, and in part the principles have been shown to yield observed results; but the mathematics involved in the case of atoms that have many electrons is too difficult to enable us to deduce their spectra completely from theory, as we can in the simplest cases. In the cases that can be worked out, the calculations are not difficult. Those who are not afraid of a little mathematics can find an outline in Norman Campbell’s “Series Spectra” (Cambridge, 1921), and a fuller account in Sommerfeld’s “Atomic Structures and Spectral Lines,” of which an English translation is published by E. P. Dutton & Co., New York, and Methuen in London.

As every one knows, light consists of waves. Light-waves are distinguished from sound-waves by being what is called “transverse,” whereas sound-waves are what is called “longitudinal.” It is easy to explain the difference by an illustration. Suppose a procession marching up Piccadilly. From time to time the police will make them halt in Piccadilly Circus; whenever this happens, the people behind will press up until they too have to halt, and a wave of stoppage will travel all down the procession. When the people in front begin to move on, they will thin out, and the process of thinning out will travel down the whole procession just as the previous process of condensation did. This is what a sound-wave is like; it is called a “longitudinal” wave, because the people move all the time in the same direction in which the wave moves. But now suppose a mounted policeman, whose duty it is to keep half the road clear, rides along the right-hand edge of the procession. As he approaches, the people on the right will move to the left, and this movement to the left will travel along the procession as the policeman rides on. This is a “transverse” wave, because, while the wave travels straight on, the people move from right to left, at right angles to the direction in which the wave is travelling. This is the way a light-wave is constructed; the vibration which makes the wave is at right angles to the direction in which the wave is travelling.

This is, of course, not the only difference between light-waves and sound-waves. Sound waves only travel about a mile in five seconds, whereas light-waves travel about 180,000 miles a second. Sound-waves consist of vibrations of the air, or of whatever material medium is transmitting them, and cannot be propagated in a vacuum; whereas light-waves require no material medium. People have invented a medium, the æther, for the express purpose of transmitting light-waves. Put all we really know is that the waves are transmitted; the æther is purely hypothetical, and does not really add anything to our knowledge. We know the mathematical properties of light-waves, and the sensations they produce when they reach the human eye, but we do not know what it is that undulates. We only suppose that something must undulate because we find it difficult to imagine waves otherwise.

Different colours of the rainbow have different wave-lengths, that is to say, different distances between the crest of one wave and the crest of the next. Of the visible colours, red has the greatest wave-length and violet the smallest. But there are longer and shorter waves, just like those that make light, except that our eyes are not adapted for seeing them. The longest waves of this sort that we know of are those used in wireless-telegraphy, which sometimes have a wave-length of several miles. X-rays are rays of the same sort as those that make visible light, but very much shorter; y-rays, which occur in radio-activity, are still shorter, and are the shortest we know. Many waves that are too long or too short to be seen can nevertheless be photographed. In speaking of the spectrum of an element, we do not confine ourselves to visible colours, but include all experimentally discoverable waves of the same sort as those that make visible colours. The X-ray spectra, which are in some ways peculiarly instructive, require quite special methods, and are a recent discovery, beginning in 1912. Between the wave-lengths of wireless-telegraphy and those of visible light there is a vast gap; the wave-lengths of ordinary light (including ultra-violet) are between a ten-thousandth and about a hundred-thousandth of a centimetre. There is another long gap between visible light and X-rays, which are on the average composed of waves about ten thousand times shorter than those that make visible light. The gap between X-rays and

-rays is not large.

In studying the connection between the different lines in the spectrum of an element, it is convenient to characterize a wave, not by its wave-length, but by its “wave-number,” which means the number of waves in a centimetre. Thus if the wave-length is one ten-thousandth of a centimetre, the wave-number is 10,000; if the wave-length is one hundred-thousandth of a centimetre, the wave-number is 100,000, and so on. The shorter the wave-length, the greater is the wave-number. The laws of the spectrum are simpler when they are stated in terms of wave-numbers than when they are stated in terms of wave-lengths. The wave-number is also sometimes called the “frequency,” but this term is more properly employed to express the number of waves that pass a given place in a second. This is obtained by multiplying the wave-number by the number of centimetres that light travels in a second, i.e. thirty thousand million. These three terms, wave-length, wave-number, and frequency must be borne in mind in reading spectroscopic work.

In stating the law’s which determine the spectrum of an element, we shall for the present confine ourselves to hydrogen, because for all other elements the laws are less simple.

For many years no progress was made towards finding any connection between the different lines in the spectrum of hydrogen. It was supposed that there must be one fundamental line, and that the others must be like harmonies in music. The atom was supposed to be in a state of complicated vibration, which sent out light-waves having the same frequencies that it had itself. Along these lines, however, the relations between the different lines remained quite undiscoverable.

At last, in 1908, a curious discovery was made by W. Ritz, which he called the Principle of Combination. He found that all the lines were connected with a certain number of inferred wave-numbers which are called “terms,” in such a way that every line has a wave-number which is the difference of two terms, and the difference between any two terms (apart from certain easily explicable exceptions) gives a line. The point of this law will become clearer by the help of an imaginary analogy. Suppose a shop belonging to an eccentric shopkeeper had gone bankrupt, and it was your business to look through the accounts. Suppose you found that the only sums ever spent by customers in the shop were the following: 19s:11d, 19s, 15s, 10s, 9s:11d, 9s, 5s, 4s:11d, 4s, 11d. At first these sums might seem to have no connection with each other, but if it were worth your while you might presently notice that they were the sums that would be spent by customers who gave 20s, 10s, 5s, or 1s, and got 10s, 5s, 1s, or 1d. in change. You would certainly think this very odd, but the oddity would be explained if you found that the shopkeeper’s eccentricity took the form of insisting upon giving one coin or note in change, no more and no less. The sums spent in the shop correspond to the lines in the spectrum, while the sums of 20s, 10s, 5s, 1s, and 1d. correspond to the terms. You will observe that there are more lines than terms (10 lines and 5 terms, in our illustration). As the number of both increases, the disproportion grows greater; 6 terms would give 15 lines, 7 terms would give 21, 8 would give 28, 100 would give 4950. This shows that, the more lines and terms there are, the more surprising it becomes that the Principle of Combination should be true, and the less possible it becomes to attribute its truth to chance. The number of lines in the spectrum of hydrogen is very large.