4 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 1 



(pp) and (nn) exist, they must be nearly equal in magnitude. Assuming 

 that (nn) were greater than (pp), the maximum binding energy and, hence, 

 greatest stability would occur for nuclei with a greater proportion of neutrons. 

 Actually a variation in Z = A/2 of approximately 10 per cent does occur 

 among the isotopes of light elements, but this appears to be insufficient to 

 conclude that a significant difference exists between (nn) and (pp). 



The most stable configurations with respect to the purely nuclear forces, 

 therefore, are equal numbers of protons and neutrons. In apparent variance 

 with this, however, is the increase in the proportion of neutrons with increas- 

 ing atomic weight where, in the heaviest stable isotopes, the ratio of the 

 neutrons to protons reaches a value of 1.6. In these nuclei, however, the 

 repulsive, long-range electrostatic field of the proton becomes a significant 

 factor. The nuclear forces (np), (nn), and (pp) exhibit the property of 

 saturation due to their short range and the finite size of the nucleons. A 

 single particle, therefore, is unaffected by the intrinsically nuclear forces of 

 more distant members of the nucleus, and the total binding energy is then 

 proportional to the number of particles, A. The electrostatic field, on the 

 other hand, does not show the property of saturation, and consequently each 

 proton is affected by the presence of all other protons in the nucleus. Taken 

 together the protons contribute a total electrostatic energy proportional to 

 Z(Z - \)/R or Z(Z — l)A~tt which tends to diminish the effective total 

 binding energy of the nucleus. In the lightest nuclei the electrostatic energy 

 is less than 0.3 mev per particle, whereas the nuclear forces amount to 

 approximately 8.5 mev per particle. For greater atomic weights the electro- 

 static energy increases rapidly, and the most stable configuration for a given 

 number of particles is one with a greater proportion of neutrons. A balance 

 between the numbers of neutrons and protons for a given atomic weight is 

 achieved which provides the maximum total binding energy. 



2. (E, E) nuclei are the most stable. This fact is apparent from both the 

 number and the relative abundance of such nuclei. Of the 278 known stable 

 isotopes, this type includes 164, and where several isotopes of an element of 

 even A exist the most abundant are (E, E). This is reasonable on the basis of 

 Pauli's exclusion principle. Two particles can occupy the same state, i.e., 

 with identical spatial coordinates, if their spins are different. Pairs of 

 particles in nearly the same quantum state, it can be assumed, form closed 

 shells in which they are strongly bound. If an odd particle is added to the 

 nucleus, it forms an unclosed shell and is weakly bound by interaction with 

 the closed shells. 



3. (E, O) and (O, E) nuclei are about equally stable but less so than (E, E). 

 Stable nuclei of these types are found to occur in about equal numbers; 58 are 

 (E, 0) and 51 are (O, E). A single proton or neutron added to an (E, E) 

 nucleus is less strongly bound through interaction with completed shells at 



