Mass-energy equivalence deals with the release of large amounts of energy from nuclear reactions. An example of a nuclear reactor would be U-238. In the name of relativity, energy and mass is significantly the same thing, hence, making the mass of a U-238 nucleus equivalent to the sum of masses of the 238 nucleons that makes the nucleus up. With mass-energy equivalence, work is no longer equal to the product of force and distance. An example of mass-energy equivalence would be going into the U-238 nucleus and removing each nucleon one by one, using a greater force than the attractive nuclear force, and keeping the removed 238 nucleons separate from each other. An excessive amount of work went into removing every single nucleon which results in having a greater mass with the separated nucleons than the mass of the former nucleus. The extra mass is known as mass-energy. When the extra mass is multiplied by the square root of the speed of light ( E= mcІ), it equals the energy input.
To determine the mass change could be simply stated that a nucleon inside a nucleus has less mass than its mass when it rests outside of the nucleus. The nucleus is the one that determines how much less. “Binding energy” of the nucleus is similar to the mass difference. An example would be of uranium. The mass of uranium differs about 0.7% in a thousand. That 0.7% is reduced nucleon mass which determines the binding energy which states how much work it would take to dismantle the atom.
In figure 40.11, a mass spectrum is represented. A mass spectrum measures the masses of ions of isotopes of different kinds of elements. Mass spectrums work by deflects ions with a magnetic field into circular arms. The ions then travel at the same speed to go into the spectrum. If an ion has a great inertia, or mass, it tends to resist the deflection and enters the greater radius of its curved path. The magnetic field force heavy ions to go into large arcs and smaller ions to go into small arcs. Once all of the ions are in the spectrum, the nuclear masses are compared.
In figure 40.12, a graph depicts how nuclear mass increases with the atomic number. The elements used in the graph are hydrogen through uranium. A more detailed graph would show results from the plat of nuclear mass per nucleon, which is shown in figure 40.13. To get the nuclear mass per nucleon, one must divide the nuclear mass by the number of nucleons in the nucleus. The graph then concludes the average effective masses of nucleons within the atomic nuclei. In further details of the graph, the highest point on the graph involve protons in the nucleus of hydrogen have the heaviest mass, but beyond hydrogen, masses of nucleons in more massive nucleuses are similar. The lowest point on the graph would be the pulling apart of iron which involves more work of separating nucleon than in any other element.
In figure 40.14, the graph shows that energy is released when a uranium nucleus is divided into nuclei lower than the atomic number. This is because the masses of the uranium turn into fission fragments remain between hydrogen and uranium. The graph also shows how the mass per nucleon in fission is less massive when the nucleons are joined with the uranium nucleus. When the decreased mass is divided by the square root of the speed of light, it equals the amount of energy that each uranium nucleus underwent during the fission.
As stated earlier, iron is the lowest point on the graph and hydrogen is the highest. Iron is the lowest because it has the greatest binding energy per nucleon. Whenever a nuclear transformation occurs and moves toward iron, it is guaranteed that energy will be released. However, more massive nuclei that move toward iron undergo nuclear fission. Nuclear fission set the fragments and energy back because they become radioactive. A more reliable source of energy could be found when nuclei that are lighter than iron more toward iron and combine. Either way, the mass of a nucleus is never equal to the sum of the masses of its parts even when elements undergo nuclear fission, which always results in mass-energy equivalence.
Hewitt, Paul G.. Conceptual Physics the High School Physics Program.