If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Donate Login Sign up Search for courses, skills, and videos. Science Physics library Quantum Physics Nuclei. Some masses are given in the table. Calculate the energy released in the following fission reaction.
Step one:. Atomic numbers and mass numbers are balanced. Step two:. Total mass before the reaction. Step three:. Step four:. Significance Notice that the binding energy per nucleon for is much greater than for the hydrogen isotopes Therefore, helium nuclei cannot break down hydrogen isotopes without energy being put into the system.
Check Your Understanding If the binding energy per nucleon is large, does this make it harder or easier to strip off a nucleon from a nucleus? Explain why a bound system should have less mass than its components. Why is this not observed traditionally, say, for a building made of bricks? A bound system should have less mass than its components because of energy-mass equivalence If the energy of a system is reduced, the total mass of the system is reduced.
If two bricks are placed next to one another, the attraction between them is purely gravitational, assuming the bricks are electrically neutral.
The gravitational force between the bricks is relatively small compared to the strong nuclear force , so the mass defect is much too small to be observed.
If the bricks are glued together with cement, the mass defect is likewise small because the electrical interactions between the electrons involved in the bonding are still relatively small. Why is the number of neutrons greater than the number of protons in stable nuclei that have an A greater than about 40?
Why is this effect more pronounced for the heaviest nuclei? To obtain the most precise value of the binding energy per nucleon, it is important to take into account forces between nucleons at the surface of the nucleus. Will surface effects increase or decrease estimates of BEN?
Nucleons at the surface of a nucleus interact with fewer nucleons. This reduces the binding energy per nucleon, which is based on an average over all the nucleons in the nucleus. How much energy would be released if six hydrogen atoms and six neutrons were combined to form. It makes up more than of natural iron. Note that has even numbers of protons and neutrons. Calculate the binding energy per nucleon for and compare it with the approximate value obtained from the graph in Figure.
Calculate BEN for this nucleus and compare it with the approximate value obtained from the graph in Figure. Most of uranium is. The fact that BEN peaks at roughly implies that the range of the strong nuclear force is about the diameter of this nucleus. In a nuclear reaction the change in mass is about a million times greater than the change mass of a chemical reaction.
In an endothermic reaction the mass of the reactants is less than the mass of the products. Specifically, it is the sum of the masses of the individual nucleons minus the mass of the nucleus consisting of those nucleons. For an exothermic reaction, the binding energy of the reactants is less than the binding energy of the products; that is the nucleons for the products are more tightly bound more binding energy than those for the reactants.
For example, in a nuclear fission or fusion reaction, we "moveup" the curve of binding energy, as indicated in the following curve. Sign up to join this community. The best answers are voted up and rise to the top.
Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. What is the relationship between binding energy, energy released, and mass defect?
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