S I G N F I C A K C E O F T H E “PACKIKG FRACTION” ni- MARCEL
FRANCOX
The discovery of the radioactive propert’ies and of the electron, common constituent of all atoms, led to the assumption that the atoms of all elements were formed of protons and electrons. Thus Prout’s hypothesis, according to which all the elements would be formed of hydrogen and would have whole numbers for atomic weights, was considered again with great attention. If, indeed, the atomic weights of the elements are not whole numbers, in general, the atomic masses of the different isotopes had been found to be whole numbers, except for hydrogen. Costa,’ however, began to determine the atomic masses with a greater accuracy than dst,on’s first apparatus had enabled him to reach. Aston? then built an apparatus the resolving power of which was five times greater than that of his first apparatus, and t,hanks to which he could make measurements with an approsinlation of I,’IOOOO. The experimental results showed then that as a rule the mass numbers were not whole numbers, in the system 0 = 16. &on3 had introduced the notion of “packing” in order to describe the compression of the protons and of the electrons in the nucleus of all the atoms except those of hydrogen. He thus explained how hydrogen seemed alone to have an atomic mass which was not a whole number. I n 19’7, Aston’ introduced the term of “packing fraction” which is the divergence of the mass number of an atom froni a whole number, divided by the mass number. hston drew a curve representing t,he variations of the “packing fractions” with the mass numbers. He found that all the atoms, except the light atoms of even number, can be put on the same curve, descending rapidly from hydrogen to reach a minimum in the region of the element, bromine (mass number 8 0 ) ; then the curve goes up again and crosses the line of zero packing for mercury. The curve for the atoms of even mass number starts below the first curve, with helium and goes to t,he minimum much less steeply than the first curve does. rlston points out that the packing fraction is not a periodic property; this shows that the nucleus has a structure very different from the arrangement of the electrons outside the nucleus. Thus the packing fraction would give us information on the structure of the nuclei and, therefore, on the relative stability of the atoms. Cabrera4 has remarked that the atoms could be put into two classes according to their position a t the right or at the left of the minimum of Xston‘s curye. On one side are the light elemcnts for which the packing fraction is decreasing rapidly, passing from a high positive value for hydrogen to a negative value. On the other side, are the heavy elements
3 i
Costa: Compt. rend.. 180, 1661; Ann. I’hys.. 4, 425 .iston: Proc. Roy. Sac., 115.1, 1 6 7 I 1927). Aston: “Isotropes” !I923 1 (’abrera: Compt. rend., 186, 228. jOI 1 1 9 2 8 ) .
1192jl
SIGSIFIC.4SCE OF THE PACKIXG FRACTIOS
297
for which the packing fraction is changing slowly; between the two classes there is a flat space of the curve where it is difficult to determine exactly the minimum. I n 1913,Langevin,' adopting the relativity formula, ni = E/v? showing the relation between the variation of mass, the variation of energy and the light velocity, wrote that the divergences from the whole number rule might be due to the variation of internal energy by emission or absorption of radiation according to the case during the formation of the elements from the elementary constituents. Costa2 took up this theory3 again applying it to mass numbers and not to atomic weights as Langevin had done. Costa saw that the value of the "packing fraction" could give us information as to the energy emitted or absorbed during the formation of the elements. If the dissociation of a radio element into helium and a derivative element is exothermic, it means that the sum of the atomic weights of helium and of the derivative element is inferior to the atomic weight of the parent, element. If the dissociabion had been endothermic, the reverse would be true. Thus a diminution of mass would correspond t o a diminution of energy; the greater the loss of mass would be, the more stable the element would be. If we consider again the two classes of elements of which we spoke above, in one class are the elements which would tend to produce elements with a smaller packing fraction and a greater mass number; in the other class, there would be elements which would tend to produce elements with a smaller packing fraction and a smaller mass number; the elements of each class would tend to produce elements which are placed on the minimum of Xston's curve, since a t this minimum the elements have the smallest packing fraction and the greatest stability. These considerations seem to be in accord with the radioactive transformations of the heavy elements on one hand and on the other hand with the building up of heavier atoms with the help of light elements, as the formation of oii with an atom of nitrogen, an alpha particle and a loss of a proton.' Recently 1Iillikan and Cameron5 have shown that the powerful cosmic rays were formed of bands of definite frequency. The cosmic rays would coniprehend four chief radiations which would correspond to the energy liberated during the formation, with the help of protons: ( I ) of helium atoms; ( 2 ) of oxygen and nitrogen; 13) of silicium and magnesium; (4) of iron. Thus the loss of mass corresponding to the formation of helium from hydrogen Langevin: J. Phys., 1913,js3. Compt. rend., 180, 1661;.Inn. Phys., 4,42j (19zji. J. Perrin (Trans. Faraday Soc., 17, 546 (1921-1922)) calculated that the !oss of mass corresponding t o the transformation of hydrogen into helium was about 3 X ioig ergs, and thought it possible for iodine and caesium to exhibit a loss of mass. He (.Inn. Phys., 10, 90 (19191;Scientia. 30, 335 ,1921). Pj. also Czeslaw Bealobrzeske: Bull. intern. acad. Polonaise, 1927-1,349-362,explains the radiation from the stars, by the energy evolved during the formation of heavier elements from hydrogen, and can account for the continuous radiation from the sun during the geological times. Cf."Ejection of Protons from Sitrogen Sucxlei. photographed by the Kilson Method." 1'. >I S. Blackett: Proc. Roy. Soc., 107.1, 3 9 (1925)."Disintegration of Light Elements by dipha Particles." E. Rutherford and J. (!hadwick: Phil. Mag., ( 6 ) ,44, 4 1 7 (1922). Llillikan and Cameron: Science (28, 67,401 (1928i;Phys. Rev. ( z ) ,31. 921 11928).
+
(or -4.002 4 X 1.00778) would be equivalent to the energy corresponding to the ether wave with the most characteristic frequency among the cosmic rays. Cabrera has tried to calculate the packing fraction wibh the help of the heat evolved during the transformation of radium into radium C and C'. Thus it seems that the packing fracbion can be calculated in the case of the radioactive decompositions as well as in the case of t,he building up of atoms. I t seems that the elements tend towards the formation of the elements for which the packing fraction is as small as possible and which correspond to as large a loss of mass as possible or to a maximum loss of energy, the light elements continually forming heavier elements, the heavy elements transforming t'hemeelves into light'er ones. The region of greatest stability would correspond to the elements of mass 60 or about, or of atomic number 26 (iron group). Thus would be explained the rarity of the heavy elements and the relatively great amount of iron in the composition of the earth as well as the great proportion of iron and nickel in meteorites.' Above iron, the elements are comparatively rare in the earth. Clark? points out that in several groups, the greater the atomic iyeight the rarer the element, it is the case for K, Rb, Cs; 3,Se, T e ; C1, Br, I ; As, Sb, Bi. This fact could be explained by the position of K a t the left of the minimum, rubidium and caesium at the right, rubidium (85.45) being nearer to the minimum than caesium (132.81); in the same way, sulphur at the left, selenium (79.2) and tellurium (127.5) a t t'he right; chlorine at the left, bromine and iodine at the right, while Asj Sb, Bi are all a t the right, but As (74.95) being nearer to the minimum than both [both] Sb and Bi. For, indeed, if it were admitted that all matter is made up of protons and electrons, it could be conceived that a t the beginning the most abundant elements were the simplest and the lightest; then the light elements would evolve towards the elements with the smallest packing fraction, while the heavy elements, which might have been formed in an unknown and t,ransitive way in small quantities, would tend to disintegrate into lighter elements, so that, in fine, t,he element,s on the descending curve and near the minimum packing fraction would be the most abundant of all; and, for the elements of mass number superior to 60, the most abundant would be near the minimum also. Thus, iron might be the ultimate term of t'he evolution of the elements. I t seems that matter3 obeys t,he two principles of thermodynamics: the principle of the conservation of masq being another way of stating the prinF. IT-. Clarke: ',The Data of Geochemistry'' :15241. F. Yi Clarke: "The Relative Abundance of tlie Chemical Elements." Phil. Soc. Washington (1889'). 3According t o 0 . Stern (Trans. Faraday Hoc., 21, q j (1925-192611, mho adopts t h r stellai theory of Eddinrrton, a star would l&e a considerable portion of its mass during its evolution hy radiation; matter would he transformed into radiation and radiation \voultl be transformed into matter. 0 . Stern tries to calculate the equilibrium betc$-een these two processes P. Jordon, (Z. Physik. 41, 7 1 1 - 7 ( 1 5 2 j ) studied the probability laws for the traniformation of matter into radiation.
S I G S I F I C . i N C E OF THE P.4CKISG F R A C T I O S
299
ciple of the conservation of energy' while the evolution of the elements would obey the second principle of thermodynamics, according to which a t constant energy the entropy tends towards a maximum value or, a t constant entropy, the internal energy tends toward a minimum value. The chemical reactions are assumed to be due t'o the outside electrons, Fhile the radioactive changes would depend on the protons and electrons of the nucleus; but it seems that the chemical reactions and the radioactive changes might both be submitted to the general principles of energetics. If, under certain conditions of temperature, pressure and volume, chemical reactions mag take place in a reversible manner and can be affected by varying the conditions, the enornious variations of energy which accompany a radioact,ive change might make it impossible for us, so far and with our means, to act upon such changes; but it is not illogical t,o suppose that the radioactive changes might have taken place in a reversible %-yay,under conditions very different from what they are today. The radioactive phenomena obey statistical laws and can very well obey the laws of thermodynamics since this science is nothing after all but statistical mechanics. Aniong the elements at the left of the niasimum, potassium* only is .supposed to be radioactive, while all the other radioactive elements are a t the right of the maximum. By emission of a beta particle, potassium would produce an isotope of calcium, the evolution being towards the production of Pleinents with greater atomic nurnber, for the light elements, and the reverre for the heavy elements which disintegrate by ejection of alpha particles and beta particles, ultimately to form lead. The precise determination of the packing fraction is of the utmost importance, since the packing fraction gives us information on the forces which hold the protons and the electrons together in the nucleus and on the relative stability of t'he different nuclei. The determination of packing fraction is, in general, made with the help of the mass spect,rograph; but, for the simple elements, the ordinary physical and chemical methods used for the determination of at'omic weights could give the packing fraction tTith as great a precision as the determinations made with the mass ~pectrograph.~ Theodore W. Richards and Marcel Franqonl have furnished a confirmation of the atomic weight of caseium determined by Richards and hrchiba!d.j If it is assumed that capsiuni is simple, as =Iston6claims, the packing The doctrine of electrons forces us to admit the variability of mass with veloeity and even the elrctro-magnetic natdre of mass. E Henriot: Radium, 7 , 10.48;S . R . Campbell and A. Wood: Proc. Cambridge Phil. Soc., 14, r j r190~-1908~; 31. Levin and It. Ruer: Physik. Z., 10, j i 6 (1909); Martin Biltz and Hans Ziegert: Physik. Z . 29. 197-200 (1928). Thus Baster found for the atomic weight of helium 4.002 which corresponds t o the atomic mass found by Aston. ' T. K.Richards and Marcel Francon: J. .Im. Chem. Sac., 50, 2162 ;1928). T. K. Riehards and E. H. Archibald: Proc. . h i . Acad. Arts Sei., 38, 443 (1903;. ii .\ston: Phil. >lag. (61. 4 2 , 436 (1921 I .
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MARCEL FRANCOX
fraction of caesium would be about three times as great as Aston's curve mould indicate; the last deteiminations of the atomic weight of titanium' would indicate a packing fraction greater than would be expected, but, for titanium, it is quite possible that an isotope may exist. It would be very important to verify the non-existence of an isotope of caesium, for the anomaly of caesium might be of great significance. I n fine, the packing fraction contributes with the atomic number and the mass number to our knowledge of the nucleus: its charge, its mass, the number of electrons in the nucleus and the possible arrangement of protons and electrons in the nucleus. Besides, the packing fraction may be indicative of the evolution of the elements, it helps us to understand the rarity of certain elements and gives us a clue for the radiation emitted by the stars. 1
G. P. Baxter and A. Q. Butler: J. Am. Chem. SOC, 50, 408 (1928).
