648 Table 851 



PACKING FRACTIONS (ASTON) 



(See Table 596.) 



A reason for the failure of the additive law within the nucleus in atom building is 

 because the protons and electrons become so closely packed that their electromagnetic fields 

 interfere and a certain fraction of the mass is destroyed and appears as an electromagnetic 

 radiation. The greater this loss, the more stable is the resulting nucleus. A convenient and 

 informative expression for this loss is the " packing fraction," the mean gain or loss of 

 mass per proton when the nuclear packing is changed from that of oxygen to the atom 

 under consideration. These are given in Table 506 as parts per 10,000, and their run is 

 indicated in the following plot (ordinates). It is a measure of the forces binding together 

 the protons and electrons of the nucleus. The abscissae are mass numbers. It is to be noted 

 that the more stable (even atomic numbers) lie on the lower of the two lines drawn. (See 

 Millikan, Phys. Rev., 32, 535, 1928, for the following use of this curve.) 



Aston's curve indicates that only very heavy elements can evolve energy by disintegration 

 and there are no abundant elements above at. wt. 80 (less than 1% of all matter). 



The condition necessary that even a heavy atom may liberate energy through the emission 

 of an a particle may be seen at once from Aston's curve. Such liberation can happen only 

 where the curve is rising so rapidly with increasing atomic weight that 



nAy > 4 X (0.00054 — .V» ) • 



n is the at. wt. of the active atom, Ay, the difference in ordinate between (n — 4) and n, y n , 

 the ordinate for the at. wt. n, and 0.00054 the value of y for He., i.e., it is the mass of the 

 H nucleus within the a particle. 



Therefore, not only very heavy atoms alone can disintegrate with the ejection of a rays 

 and the evolution of energy, but we can compute the max. hardness, or penetrating power, 

 of any radiations producible by radioactive disintegration. 



When thorium, e.g., throws off an a particle (^ = 232, y n = 0.00031), the increase in 

 the mass of the a particle per gram-atom, because it has escaped from the nucleus, is 

 4(0.00054-0.00030=0.00092. The loss in mass of the residue of the Th atom nAy 

 = 0.000034 X 228 = 0.007752. Therefore the total loss in mass through the emission of 

 the a ray is 0.00775 — 0.00092 = 0.00683 grams per gram-atom. By Einstein's equation 

 the energy available for emission from this loss of mass is 0.00683c 2 ergs/g-atom. The 

 total energy from each ejection of an a particle is this divided by the Avogadro number or 

 1.004 X io" 5 ergs. The highest speed a ray known to be given off from Ra has an energy 

 of 8,800,000 volts (1.2 X io" 5 ergs). ThC ejects in one instance an a ray with 14% more 

 energy than this. Similarly the "upper limit" for the speed of a /3 ray ejected by any 

 of the disintegration products of Th or Ra is 7,540,000 volts or again ? 1.2 X io" 5 ergs. 

 Einstein's equation predicts quite within the limits of reliabilty of Aston's measurements 

 of mass, the maximum energy available in the radioactive process. 



Smithsonian Tables 



