Why does the nuclear binding energy curve rise and fall?

In summary: J. Epstein, a physicist at the Massachusetts Institute of Technology, proposed the semi-empirical mass formula in the early 1950s. Epstein hypothesized that the total binding energy of a nucleus increases whenever the number of nucleons increase. This theory is based on the principle of nuclear magic numbers, which are certain nuclei that have a higher mass than the sum of its parts.
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huey910
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If the total nuclear binding energy of a nucleus increases whenever the number of nucleons increase, why does the nuclear binding energy curve rise and then fall? Don't protons and neutrons 'bring in' the same amount of binding energy every time one of them is added? Please explain. In addition, if fission can release energy, does that not mean that the nucleus itself has a higher mass than the separated, smaller and stabler nuclei produced? Thank you.
 
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  • #2
The curve you are thinking of is the binding energy per nucleon, not the total binding energy.
 
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If you bring a collection of neutrons and protons together to form a stable nucleus then it will have LESS mass than the constituent particles (this is called the mass defect). If the mass defect is m then the binding energy is E=mc2.

If the binding energy of a system was negative ie the nucleus had more mass than the sum of its parts, it would spontaneously decay back into its parts.

The curve by the way is the binding energy divided by the number of nucleons.

The question of why the curve rises and then falls – and on close inspection not without many smaller 'wiggles' is because of the very complex, and not fully understood, interaction between nucleons.

The factors which come into play include the electric repulsion between the protons a number of quantum terms to do with the strong nuclear force (which is not a true central force like electric force) including spin effects and shell effects (similar to but more complex than the shells of electron orbitals in atoms).

The whole lot is summed up in the semi empirical mas formula – look it up. It is called semi empirical because it is the sum of the terms we expect to see each multiplied by a constant. Experimental (ie empirical) information is used to find the best fit for the constants.

The formula works fairly well except for a handful of nuclei (look up nuclear magic numbers)

Hope this helps

Regards

Sam
 

1. What is a nuclear binding energy curve?

A nuclear binding energy curve, also known as a binding energy per nucleon curve, is a graph that shows the relationship between the number of nucleons (protons and neutrons) in a nucleus and the amount of energy required to break apart that nucleus into its individual nucleons. It is a representation of the stability of different nuclides.

2. How is the nuclear binding energy curve calculated?

The nuclear binding energy curve is calculated by using the mass defect of a nucleus. The mass defect is the difference between the mass of a nucleus and the combined masses of its individual nucleons. This difference in mass is converted into energy using Einstein's famous equation, E=mc².

3. What does the shape of the nuclear binding energy curve indicate?

The shape of the nuclear binding energy curve indicates the stability of different nuclides. The curve typically has a peak at the element iron, which is the most stable element, indicating that it requires the least amount of energy to break apart. Elements with a higher or lower number of nucleons have less stability and therefore require more energy to break apart.

4. What can we learn from the nuclear binding energy curve?

The nuclear binding energy curve can tell us about the stability and energy release of different elements. It also helps us understand why certain elements are more abundant in nature than others, as elements with higher stability are more likely to be found in nature. Additionally, the curve is important in nuclear physics and for understanding nuclear reactions and processes.

5. How does the nuclear binding energy curve relate to nuclear fission and fusion?

The nuclear binding energy curve is essential in understanding nuclear fission and fusion reactions. Nuclear fission is the process of splitting an atom into two or more smaller atoms, releasing energy in the process. This reaction is only possible for elements with a higher number of nucleons than iron, as seen on the binding energy curve. In contrast, nuclear fusion is the process of combining two or more smaller atoms into a larger one, also releasing energy. This reaction is only possible for elements with a lower number of nucleons than iron. The binding energy curve helps us understand the energy release and stability of these reactions.

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