To illustrate further this kind of deduction, let us consider the spectrum shown in [Fig. 9] and see what may be learnt from it. With a little trouble we can disentangle a beautifully regular series of bright lines. The marks above will assist you to pick out the first few lines of the series from the numerous other spectra mixed up with it. Noticing the diminishing spacing from right to left, you will be able to see that the series continues to the left for at least fifteen lines beyond the last one marked, the lines ultimately drawing close together and forming a ‘head’ to the series. This is the famous Balmer Series of hydrogen, and having recognized it we identify hydrogen as one of the elements present in the source of the light. But that is only the first step, and we can proceed to further inferences.
Professor Bohr’s theory of the hydrogen atom teaches us that each line of the series is emitted by an atom in a different state. These ‘states of excitation’ can be numbered consecutively, starting from the normal state of the hydrogen atom as No. 1. The light emitted in the first few states comes into the part of the spectrum not reproduced here, and the first line in our picture corresponds to state No. 8. Counting to the left from this you will recognize the successive lines without much difficulty up to state No. 30. Now the successive states correspond to more and more swollen atoms, that is to say, the planet electron[17] makes a wider and wider circuit. The radius (or more strictly the semi-axis) of its orbit is proportional to the square of the number of the state, so that the orbit for state No. 30 is 900 times larger than the orbit for the normal atom No. 1. The diameter of the orbit in No. 30 is approximately a ten-thousandth of a millimetre. One inference can be drawn immediately—the spectrum shown in [Fig. 9] was not produced in any terrestrial laboratory. In the highest vacuum that can be used in terrestrial spectroscopy the atoms are still too crowded to leave room for an orbit so large as this. The source must be matter so tenuous that there is vacant space for the electron to make this wide circuit without colliding with or suffering interference from other atoms. Without entering into further detail we can conclude that [Fig. 9] is a spectrum of matter more rarefied than the highest vacuum known on the earth.[18]
It is interesting to notice that, whereas throughout most of the picture the lines are shown on a dark background, at the extreme left the background is bright; the change occurs just at the point where the Balmer Series comes to an end. This background of light is also due to hydrogen and it is caused in the following way. The swollen atoms in state No. 30 or thereabouts are perilously near the bursting-point, so it is natural that along with them there should be atoms which have overstepped the limit and burst. They have lost their planet electrons and are occupied in catching new ones. Just as energy is required in order to wrench away an electron from an atom, so there will be superfluous energy to be got rid of when the atom tames a wild electron. This superfluous energy is radiated and forms the bright background referred to. Without entering into technicalities of the theory, we can see that it is appropriate that this light from the burst atoms should appear in the spectrum immediately beyond the lines from the most swollen atoms, since bursting is a sequel to overswelling.
Whilst you have this photograph of the Balmer Series before you I may take the opportunity of recounting the history of another famous series. In some of the hottest stars a related series of lines known as the Pickering Series was discovered in 1896. This is spaced on precisely the same regular plan, but the lines fall half way between the lines of the Balmer Series—not exactly half way because of the gradually diminishing intervals from right to left, but just where one would naturally interpolate lines in order to double their number whilst keeping the spacing regular. Unlike the Balmer Series, the Pickering Series had never been produced in any laboratory. What element was causing it? The answer seemed obvious; surely these two related series, one fitting half way between the other, must belong to different modes of vibration of the same atom, hydrogen. That seemed to be the only possible answer at the time; but we have learned more about atoms since then. We may fairly argue that the ideal simplicity of these two series indicates that they are produced by an atomic system of the simplest possible type, viz. an atom with one planet electron; but it must be remembered that this condition only tells us how the atom is clothed, not what the atom is. The helium atom (or, for that matter, the uranium atom) can on occasion masquerade in the scanty attire of the hydrogen atom. Normal helium has two planet electrons; but if one of these is lost, it becomes hydrogen-like and copies the simple hydrogen system on a different scale. It is significant that the Pickering Series appears only in the very hottest stars—in conditions likely to cause loss of an electron. The difference between hydrogen and hydrogen-like helium is firstly the difference of atomic weight; the helium nucleus is four times as massive. But this scarcely affects the spectrum because both nuclei are so massive that they remain almost unshaken by the dancing electron. Secondly, the helium nucleus has a double electric charge; this is equivalent to substituting in the vibrating system a controlling spring of twice the strength. What can be more natural than that the doubled force of the spring should double the number of lines in the series without otherwise altering its plan? In this way Professor Bohr discovered the real origin of the Pickering Series; it is due to ionized helium, not to hydrogen.[19]
The heavy nucleus, whether of hydrogen or helium, remains almost unshaken by the atomic vibration—almost, but not quite. At a later date Professor A. Fowler succeeded in reproducing the Pickering Series in the laboratory and was able to measure the lines with much greater accuracy than could be achieved in stellar spectroscopy; he was then able to show from his measures that the nucleus is not quite irresponsive. It was a delicate double-star problem transferred to the interior of the atom; or perhaps a closer analogy would be the mutual influence of the sun and Jupiter, because Jupiter, having a thousandth of the mass of the sun, disturbs it to about the same extent that the light electron disturbs the hydrogen nucleus. Ionized helium is a faithful copy of the hydrogen atom (on the altered scale) in everything except the ‘shake’; the shake is less than in hydrogen because the helium nucleus is still more massive and rock-like. The difference of shake throws the Pickering Series of helium and the Balmer Series of hydrogen slightly out of step with respect to one another; and by measuring this misfit Professor Fowler was able to make a very accurate determination of the shake and therefore of the mass of the electron. In this way the mass of the electron is found to be ¹⁄₁₈₄₄th of the mass of the hydrogen nucleus; this agrees well with the mass found by other methods, and the determination is probably not inferior in accuracy to any of them.
And so the clue first picked up in stars 300 light years away, followed in turn by the theoretical and the experimental physicist, leads in the end to the smallest of all things known.
[The Cloud in Space]
Having already considered the densest matter in the universe, we now turn to consider the rarest.
In spite of great improvements in the art of exhausting vessels we are still a long way from producing a real vacuum. The atoms in a vacuum tube before it is exhausted muster a formidable number containing about twenty digits. High exhaustion means knocking off five or six noughts at the end of that number; and the most strenuous efforts to knock off one more nought seem ludicrously ineffective—a mere nibbling at the huge number that must remain.
Some of the stars are extremely rarefied. Betelgeuse, for example, has a density about a thousandth that of air. We should call it a vacuum were it not contrasted with the much greater vacuosity of surrounding space. Nowadays physicists have no difficulty in producing a better vacuum than Betelgeuse; but in earlier times this star would have been regarded as a very creditable attempt at a vacuum.