This enables the most sweeping simplifications to be made in our ideas of mass. The original hypothesis of Prout, put forward in 1815, that all atoms were themselves built of atoms of protyle, a hypothetical element which he tried to identify with hydrogen, is now reëstablished, with the modification that the primordial atoms are of two kinds: Protons and electrons, the atoms of positive and negative electricity. The Rutherford atom, whether we take Bohr's or Langmuir's development of it, consists essentially of a positively charged central nucleus around which are set planetary electrons at distances great compared with the dimensions of the nucleus itself. As has been stated, the chemical properties of an element depend solely on its atomic number, which is the charge on its nucleus expressed in terms of the unit charge, e. A neutral atom of an element of atomic number N has a nucleus consisting of K+N protons and K electrons, and around this nucleus are set N electrons. The weight of an electron on the scale we are using is 0.0005, so that it may be neglected. The weight of this atom will therefore be K+N, so that if no restrictions are placed on the value of K any number of isotopes are possible. A statistical study of the results given above shows that the natural restrictions can be stated in the form of rules as follows: In the nucleus of an atom there is never less than one electron to every two protons.-There is no known exception to this law. It is the expression of the fact that if an element has an atomic number N the atomic weight of its lightest isotope can not be less than 2N. Worded as above, the ambiguity in the case of hydrogen is avoided. True atomic weights corresponding exactly to 2N are known in the majority of the lighter elements up to 4.36 Among the heavier elements the difference between the weight of the lightest isotope and the value 2N tends to increase with the atomic weight; in the cases of mercury it amounts to 37 units. The corresponding divergence of the mean atomic weights from the value 2N has, of course, been noticed from the beginning of the idea of atomic number. The number of isotopes of an element and their range of atomic weight appear to have definite limits.-Since the atomic number only depends on the net positive charge in the nucleus there is no arithmetical reason why an element should not have any number of isotopes. So far the largest number determined with certainty is 6 in the case of krypton. It is possible that xenon has even more, but the majority of complex elements have only two each. The maximum difference between the lightest and heaviest isotope of the same element so far determined is 8 units in the cases of krypton and xenon. The greatest proportional difference, calculated on the lighter weight, is recorded in the case of lithium, where it amounts to one-sixth. It is about one-tenth in the case of boron, neon, argon, and krypton. The number of electrons in the nucleus tends to be even.—This rule expresses the fact that in the majority of cases even atomic number is associated with even atomic weight and odd with odd. If we consider the three groups of elements, the halogens, the inert gases, and the alkali metals, this tendency is very strongly marked. Of the halogens-odd atomic numbers-all 6 (+1?) atomic weights are odd. Of the inert gases-even atomic numbers 13 (+2?) are even and 3 odd. Of the alkali metals-odd atomic numbers-7 are odd and 1 In the few known cases of elements of other groups the preponderance, though not so large, is still very marked and nitrogen is the only element yet discovered to consist entirely of atoms whose nuclei contain an odd number of electrons. even. If we take the natural numbers 1 to 40, we find that those not represented by known atomic weights are 2, 3, 5, 8, 13 (17), (18), 21 (33), 34 (38). It is rather remarkable that these gaps, with the exception of the four in parentheses, are represented by a simple mathematical series of which any term is the sum of the two previous terms. In consequence of the whole number rule there is now no logical difficulty in regarding protons and electrons as the bricks out of which atoms have been constructed. An atom of atomic weight m is turned into one of atomic weight m+1 by the addition of a proton plus an electron. If both enter the nucleus, the new element will be an isotope of the old one, for the nuclear charge has not been altered. On the other hand, if the proton alone enters the nucleus and the electron remains outside, an element of next higher atomic number will be formed. If both these new configurations are possible, they will represent elements of the same atomic weight but with different chemical properties. Such elements are called "isobares" and are actually known. The case of the element hydrogen is unique; its atom appears to consist of a single proton as nucleus with one planetary electron. It is the only atom in which the nucleus is not composed of a number of protons packed exceedingly closely together. Theory indicates that when such close packing takes place the effective mass will be reduced, so that when four protons are packed together with two electrons to form the helium nucleus this will have a weight rather less than four times that of the hydrogen nucleus, which is actually the case. It has long been known that the chemical atomic weight of hydrogen was greater than one-quarter of that of helium, but so long as fractional weights were general there was no particular need to explain this fact, nor could any definite conclusions be drawn from it. The results obtained by means of the mass-spectrograph remove all doubt on this point, and no matter whether the explanation is to be ascribed to packing or not, we may consider it absolutely certain that if hydrogen is transformed into helium a certain quantity of mass must be annihilated in the process. The cosmical importance of this conclusion is profound and the possibilities it opens for the future very remarkable, greater in fact than any suggested before by science in the whole history of the human race. We know from Einstein's Theory of Relativity that mass and energy are interchangeable,28 and that in C. G. S. units a mass m at rest may be expressed as a quantity of energy mc2, where c is the velocity of light. Even in the case of the smallest mass this energy is enormous. The loss of mass when a single helium nucleus is formed from free protons and electrons amounts in energy to that acquired by a charge e falling through a potential of nearly thirty million volts. If instead of considering single atoms we deal with quantities of matter in ordinary experience the figures for the energy become prodigious. Take the case of one gram atom of hydrogen; that is to say, the quantity of hydrogen in 9 c. c. of water. If this is entirely transformed into helium the energy liberated will be .0077 X 9 X 1020 6.93 X 1018 ergs. Expressed in terms of heat this is 1.66 X 1011 calories or in terms of work 200,000 kilowatt hours. We have here at last a source of energy sufficient to account for the heat of the sun.29 In this connection Eddington remarks that if only 10 per cent of the total hydrogen on the sun were transformed into helium enough energy would be liberated to maintain its present radiation for a thousand million years. Should the research worker of the future discover some means of releasing this energy in a form which could be employed, the human race will have at its command powers beyond the dreams of scientific fiction; but the remote possibility must always be considered that the energy once liberated will be completely uncontrollable and by its intense violence detonate all neighboring substances. In this event the whole of the hydrogen on the earth might be transformed at once and the success of the experiment published at large to the universe as a new star. In considering the spectra of isotopes there is every reason to suppose that the light emitted by an atom will depend upon the movements of its planetary electrons, and therefore upon the force controlling these that is, the nuclear charge. We therefore expect that the difference between the spectra of two isotopes will be extremely small, since the nuclear charges are identical. This expecta *Eddington: "Time, Space and Gravitation," p. 146, Cambridge, 1920. "Eddington: Brit. Assoc. address, 1920; Perrin: Scientia, Nov., 1921. tion is borne out in practice and the difference in wave length has only been detected in the case of the isotopes of lead. Aronberg,30 in 1917, discovered a shift of 0.0044 A between ordinary lead and a radio lead of atomic weight 206.3. This result has been confirmed by the subsequent work of Merton,31 who has recently measured a shift of 0.011 A in one of the lines of an extremely pure Carnotite lead as compared with the same line in ordinary lead. These shifts, though extremely minute, are, however, hundreds of times larger than the ones predicted by the simple application of the Bohr theory. The artificial separation of the isotopes of nonradioactive elements is an exceedingly difficult operation; indeed, had it been otherwise they must have been discovered long ago. In the case of neon, already described, which is a particularly favorable one, the extreme difference between the lightest and heaviest fractions amounted to 0.13 of a unit of atomic weight. Harkins,32 using a somewhat similar diffusion method, has successfully separated the isotopic hydrochloric acids and obtained a shift of 0.055 of a unit. A beautiful method applicable to certain liquids has been developed by Bronsted and Hevesy. This consists in allowing the liquid to evaporate at so low a temperature and pressure that none of the molecules escaping from its surface can ever return to it again; a concentration of the heavier constituent in the residue must then result. They first applied it to mercury, and the latest separation achieved with the isotopes of that element is indicated by the figure 0.99974 and 1.00023 for the densities of the lightest and heaviest fraction, respectively, the normal density being taken as unity. In atomic weight this separation corresponds to a shift of 0.1 of a unit. They have also applied the same method to a solution of hydrochloric acid in water and obtained a change of atomic weight of about 0.02 of a unit. Several other methods of partial separation have been suggested, but the only ones which have been successful in practice are those mentioned above. Complete separation can be achieved by means of positive ray analysis, but the quantities to be obtained in this way are too minute to be of the slightest practical importance. The fact that many of the most familiar elements prove to be mixtures of isotopes is of fundamental theoretical importance, but when we consider the extreme difficulties of their separation it seems very unlikely, unless some entirely new method is discovered, that the numerical constants of chemistry are likely to be affected seriously for some time to come. 30 Aronberg: Proc. Nat. Acad. Sci., 3,710, 1917, and Astrophys. Jour., 47, 96, 1918. 31 Merton: Proc. Roy. Soc., 99A, 87, 1921. 82 Harkins and Hayes: J. Amer. Chem. Soc., 43, 1803, 1921. 3 Bronsted and Hevesy: Phil. Mag., 43, 31, 1922. MODIFYING OUR IDEAS OF NATURE: THE EINSTEIN THEORY OF RELATIVITY.1 By HENRY NORRIS RUSSELL, Professor of Astronomy in Princeton University. I. It is probably a long time since there has been any occasion on which a matter so definitely belonging to pure science as the "theory of Einstein " has excited so much popular interest. Although the statements in the newspapers concerning "the overthrow of Newton's laws" and similar "scare heads" have gone beyond the more sober statements of scientific authorities, it is nevertheless true that the theory of relativity, of which the recent work of Einstein forms an extension, has modified our conceptions of nature in a very remarkable fashion. Einstein's reported statement that there were not more than 12 men in the world who could read and fully understand his book was probably quite within the facts. But the elementary ideas on which the theory of relativity is based do not involve any difficult mathematics, and the only obstacle to grasping or holding them is their remarkable novelty. We can understand them easily enough, or at least understand what they are about, if only we begin at the beginning. It probably has not occurred to all of you that while I was speaking the last sentence we traveled several hundred miles. Yet, of course, we did. If we had not, the earth would have left us behind it somewhere in empty space. In fact, we are undergoing a very complicated series of motions, carried around with the rotating earth and swinging along much more rapidly and in a much vaster curve with its orbital motion. But of this fact we are blissfully unconscious. Why? Because the motion is perfectly smooth, without jar or shock, and in particular because not merely we ourselves, but all the objects that constitute our environment, are moving together. Reprinted by permission from Princeton Lectures, No. 2, Princeton, N. J., May 1, 101257--22 -14 197 |