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Binding Energy and Nuclear Forces

 

 

n The total mass of a stable nucleus is always <  the sum of the masses of its constituents.

n Where has the mass gone?

        ð It has become energy, such as radiation or kinetic energy, released during the

               formation of the nucleus. 

        ð This difference between the total mass of the constituents and the mass of the

                nucleus is called the total binding energy of the nucleus.

n The higher the binding energy per nucleon, the more stable the nucleus.

n More massive nuclei require extra neutrons to overcome the Coulomb repulsion of the

       protons in order to be stable.

n The force that binds the nucleons together is called the strong nuclear force.

         It is a very strong, but short-range, force. It is essentially zero if the nucleons are more

         than about 10-15 m apart.

n The Coulomb force is long-range; this is why extra neutrons are needed for stability in

         high-Z nuclei.

n Nuclei that are unstable decay; many such decays are governed by another force

n This other force is called the weak nuclear force.

n The four fundamental forces of nature

        ð Gravity

        ð Electromagnetism

        ð Weak Nuclear

        ð Strong Nuclear

  
 

n Binding Energy

       ð Table of the Elements and Data for Electron, Neutron, Proton, and H nucleus

       ð Note that, for He, the atomic mass is 4.0026, and the nucleus contains 2 protons. It therfore contains 2 neutrons

       ð Add the mass of the constituents*

               Add the mass of the constituents of the nucleus

              2xmass of neutron + 2xmass of proton = 2(1.0086655 u) + 2(1.0007825 u) = 4.032980 u

       ð Subtract: 4.032980 u - 4.0026 u = 03038 u

       ð The difference is the binding energy

 

 

*NOTE: The atomic mass also included the mass of the electrons. In order to account for this on both sides of the equation, we multiply by the mass of the H atom (1 proton and 1 electron)