BetheWeizsäckerFormel

The Bethe-Weizsäcker formula, also known as the semi-empirical mass formula, is an approximation for the binding energy of atomic nuclei. It was developed by Carl Friedrich von Weizsäcker in 1935 and later refined by Hans Bethe. The formula attempts to explain the observed masses of nuclei by considering various terms that contribute to the binding energy.

The formula expresses the binding energy of a nucleus with atomic number Z and mass number A as a sum of several terms: a volume term, a surface term, a Coulomb term, an asymmetry term, and a pairing term. The volume term, proportional to A, represents the attractive strong nuclear force acting equally on all nucleons within the nucleus. The surface term, proportional to A^(2/3), accounts for the fact that nucleons on the surface experience fewer attractive forces. The Coulomb term, proportional to Z(Z-1)/A^(1/3), describes the repulsive electrostatic force between protons. The asymmetry term, dependent on the difference between the number of neutrons and protons, reflects the tendency for nuclei to have a roughly equal number of these particles for stability. Finally, the pairing term accounts for the additional binding energy observed in nuclei with even numbers of protons or neutrons.

While an approximation, the Bethe-Weizsäcker formula has been remarkably successful in reproducing the general trend of nuclear binding energies across the periodic table. It provides valuable insights into nuclear stability and the processes of nuclear fission and fusion. It serves as a fundamental concept in nuclear physics, helping to understand why certain isotopes are more stable than others and predicting the energy released or absorbed in nuclear reactions.