The Weizsaecker formula is an empirically refined form of the liquid drop model for the binding energy of nuclei. It describes forces in atomic nuclei as if a tiny liquid drop formed the atomic nucleus. But in this nuclear scale, the fluid is made of nucleons (protons and neutrons). The Weizsaecker formula has the following terms:
- Volume term
- Surface term
- Asymmetry term
- Pairing term
Using the Weizsaecker formula, the binding energies and also masses of atomic nuclei can be derived. Therefore, we can also derive the energy released per fission.
One of the first models that could describe the behavior of the nuclear binding energies and therefore of nuclear masses was the mass formula of von Weizsaecker (also called the semi-empirical mass formula – SEMF) published in 1935 by German physicist Carl Friedrich von Weizsäcker. This theory is based on the liquid drop model proposed by George Gamow. The physical meaning of this equation can be discussed term by term.
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.
The coefficients aV, aS, aC, aA, and aP must be known to calculate the binding energy. 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 the 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 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 a reaction will be approximately 235 x (8.5 – 7.6) ≈ 200 MeV.
See also: Liquid Drop Model