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14 Nuclear Binding Energies The sum of masses of the individual components of a nucleus that contains Z protons and (A − Z) neutrons is larger than the mass of the nucleus. 14 Nuclear Binding Energies 17 Fig. 3. Binding energy per nucleon in MeV/nucleon against atomic mass number A difference in masses is called the mass defect (deficit) ∆m and its energy equivalent ∆mc2 is called the total binding energy EB of the nucleus. • The total binding energy EB of a nucleus can thus be defined as: 1. The positive work required to disassemble a nucleus into its individual components: Z protons and (A − Z) neutrons.
The main attributes of wave functions Ψ (z, t) are: • Wave functions are generally but not necessarily complex and contain the imaginary number i. • Wave functions cannot be measured with any physical instrument. • Wave functions serve in the context of Schr¨odinger’s wave theory but contain physical information about the particle they describe. • Wave functions must be single-valued and continuous functions of z and t to avoid ambiguities in predictions of the theory. The information on a particle can be extracted from a complex wave function Ψ (z, t) through a postulate proposed by Max Born in 1926 relating the probability density dP (z, t)/dz in one dimension with the wave function Ψ (z, t) as follows: dP (z, t)/dz = Ψ ∗ (z, t) · Ψ (z, t) .
The total nuclear binding energy EB is then written as follows: EB = C1 A − C2 A2/3 − C3 Z(Z − 1) (A − 2Z)2 . 16) is referred to as the Weizs¨ acker’s semi-empirical binding energy formula in which the various components are deduced theoretically but their relative magnitudes are determined empirically to match the calculated results with experimental data. 7 MeV, and C4 ≈ 24 MeV. 2 Shell Structure Nuclear Model Experiments have shown that the number of nucleons the nucleus contains affects the stability of nuclei.