8 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 1 



Values of the known packing fractions are given in Table 2 and plotted in 

 Fig. 2. The smooth curve is given by a semiempirical formula calculated by- 

 Fowler [3]. 



/ = -79.0 + 4.0^ + 242.1 £ 2 + ™* + 7.42 ^^ X 10"* 



where I = A — 2Z 



1.4. Binding Energy. The exact atomic mass of an atom is in all cases 

 less than the mass of an equivalent number of free neutrons and protons plus 

 Z electrons. This mass difference is given by 



AM = M (A ,z) - 1.008132Z - 1 .00893 U - Z) 



where 1.008132 is the mass of a proton plus one electron and 1.00893 is the 

 neutron mass. The apparent decrease in the mass of elementary particles 

 bound in a nucleus is exactly equivalent to the total binding energy of the 

 particles. From Einstein's law of equivalence of mass and energy, the bind- 

 ing energy is then E = AMc 2 . One mass unit (mass of 16 /16) energy 

 equivalent is 



1 MU = 931.05 mev = 1.49 X 10" 3 erg 



from which the binding energy of a nucleus may be calculated when its exact 

 mass is known. 



A semiempirical formula for calculating the binding energy or the mass 

 defect has been derived which is based mainly on the liquid-drop model of the 

 nucleus [1,6,7]. The total binding energy of a nucleus of atomic weight A 

 and charge Z may be expressed as the sum of a volume energy, a surface 

 energy, a symmetry (or isotopic spin) energy [7], a coulomb or electrostatic 

 energy, and a somewhat uncertain term involving the fluctuations associated 

 with the even-odd combination of nuclear particles. Evaluation of explicit 

 expressions for the terms has not yet been possible, but the factor to which 

 each term is proportional is readily found as indicated below. 



With but few exceptions (deuterium and lithium notably) the average 

 binding energy per nucleon in light and medium nuclei is approximately 8.5 

 mev. In the heaviest nuclei (Z > 82) the binding energy decreases to 

 approximately 6 mev per particle. Over the greater part of the mass range 

 of nuclei the total binding energy is roughly proportional to the number of 

 nucleons or to the nuclear volume. Each particle is influenced by the short- 

 range attractive fields of only those particles next to it and will remain 

 unaffected by more distant particles in the nucleus. To a first approxi- 

 mation then, saturation of the intrinsically nuclear forces leads to a volume 

 energy that is proportional to the number of particles, A. 



Particles lying at the surface of the nucleus would not be expected to 



