Nuclear binding energy curve.
With the aid of the Weizsaecker formula the binding energy can be calculated very well for nearly all isotopes. This formula provides a good fit for heavier nuclei. For light nuclei, especially for 4He, it provides a poor fit. The main reason is the formula does not consider the internal shell structure of the nucleus.
In order to calculate the binding energy, the coefficients aV, aS, aC, aA and aP must be known. The coefficients have units of megaelectronvolts (MeV) and are calculated by fitting to experimentally measured masses of nuclei. They usually vary depending on the fitting methodology. According to ROHLF, J. W., Modern Physics from α to Z0 , Wiley, 1994., the coefficients in the equation are following:Using the Weizsaecker formula, also the mass of an atomic nucleus can be derived and is given by:
m = Z.mp +N.mn -Eb/c2
where mp and mn are the rest mass of a proton and a neutron, respectively, and Eb is the nuclear binding energy of the nucleus.From the nuclear binding energy curve and from the table it can be seen that, in the case of splitting a 235U nucleus into two parts, the binding energy of the fragments (A ≈ 120) together is larger than that of the original 235U nucleus.
According to the Weizsaecker formula, the total energy released for such reaction will be approximately 235 x (8.5 – 7.6) ≈ 200 MeV.
Table of binding energies fo some nuclides. Calculated according to the semi-empirical mass formula.
The minimum excitation energy required for fission to occur is known as the critical energy (Ecrit) or threshold energy.
This table shows critical energies compared to binding energies of the last neutron of a number of nuclei.