Binding energy

The energy Eb that must be supplied to separate a nucleus into its constituent protons and neutrons is called the binding energy. Different elements, and different isotopes, have different amounts of binding energy. For example, if eight protons and eight neutrons make two helium-4 nuclei, then the amount of binding energy is different compared to the same particles arranged as a single oxygen-16 nucleus. The difference in binding energy between isotopes provides the energy for nuclear reactions. Read the text aloud
When free nucleons come together in a nucleus, the binding energy is released. That means the nucleus has less rest energy and therefore less mass than the separate particles it is made from. The difference in mass, called the mass deficiency, is exactly equal to the binding energy required to hold the nucleus together. Binding energy and the mass difference are related through Einstein’s mass–energy equivalence equation. Read the text aloud
As an example, consider the nucleus of helium-4, which has two protons and two neutrons. The mass of the individual protons and neutrons is 4.0319 amu. Two protons:   m 2p =2×(1.6726× 10 27  kg)=2×1.0073 amu=2.0146 amu Two neutrons:   m 2n =2×(1.6749× 10 27  kg)=2×1.0087 amu=2.0173 amu Total mass of nucleons:   m 2p + m 2n =4.0319 amu Read the text aloud
The mass of the helium-4 nucleus is 4.0015 amu. This is 0.0304 amu less than the sum of the masses of the individual protons and neutrons. The mass difference of 0.0304 amu is helium-4’s mass deficiency, equal to 28.32 MeV in energy units: E b =(0.0304 amu)×(931.5 MeV/amu)=28.32 MeV Read the text aloud Show A more advanced binding energy calculation
Binding energy per nucleonA useful quantity in nuclear physics is the binding energy per nucleon, or the binding energy Eb divided by the number of nucleons, A. For the example of helium-4, the binding energy per nucleon (Eb/A) is (28.3 MeV)/4 = 7.08 MeV. The binding energy per nucleon increases with atomic number up to element 56, which is iron (Fe). The binding energy per nucleon decreases slowly with atomic number for elements heavier than iron. The shape of the binding energy graph reflects a balance between the repulsion of the electric force (among the protons) and the attraction of the strong force. Read the text aloud
The graph of binding energy per nucleon reflects the ultimate energy source of our universe. Stars release nuclear energy by combining light elements and moving from left to right, from hydrogen toward iron. Nuclear reactors release energy by splitting up heavy atoms and moving from right to left, from uranium toward iron. Read the text aloud
Calculate the binding energy per nucleon for carbon-12. The atomic mass of carbon-12 is 12 amu. Show

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