We gave a brief note on binding energy calculation in the previous post. This post will learn about the binding energy curve and its characteristics.
A plot can represent binding energy possessed by any particle system. The binding energy curve illustrates the various physical signs of the binding energy, such as the stability of the nucleus against disintegration. In the below section, the graph of the binding energy curve, its nature, and its importance are well explained.
Nuclear binding energy curve
The nuclear binding energy curve is the plot of binding energy per nucleon Vs. the number of nucleons presents inside the nucleus. This plot helps to describe which nucleus has the highest binding energy and its stability.
The binding energy of one element is different from the other and thus their behavior, so the nuclear binding energy explains how they are different from one another. In the periodic table, we can observe an increase in binding energy per nucleon from hydrogen to sodium because the atomic mass of those elements increases linearly. This increase is due to all the forces acting on the nucleus, and additionally, each nucleon is attracted to the other nucleons and hence forms a tight bound inside the nucleus. So that exertion of binding energy increases rapidly.
The binding energy of hydrogen is zero because hydrogen consists of only one proton in the nucleus; thus, there will be no electrostatic repulsion offered for the proton.
The shape of the nuclear binding energy curve predicts two major consequences, such as
- Stability of the atomic nuclei –the peak of the curve indicates that the nucleus has a maximum value of binding energy.
- Possibility of converting a significant amount of mass into energy.
What is binding energy curve?
Suppose you plot a graph of the binding energy of different particle systems against an atomic mass of the respective particle system. In that case, you will obtain a curve called a binding energy curve.
A binding energy curve is another way to indicate how much amount of energy is released during the reaction, as some of the electrons or nucleons have to be disassembled from the system when the reaction occurs.
The binding energy curve usually represents the stability of the nucleus. It also helps to describe the occurrence of fission and fusion processes.
Importance of binding energy curve
Since we know that binding energy explains the fission and fusion process, the graphical representation of the binding energy can also illustrate the fission and fusion process. Along with these, the binding energy curve also explains certain advanced concepts mentioned below.
- Fission reaction –the binding energy gives an account for the stability of heavier nuclei which are a little less stable. This concept leads to the splitting up of a heavier nucleus into its constituents, so that energy can be released; this process is named as fission reaction. This technique is used in nuclear power generators.
- Fusion reaction –from the binding energy curve, we can find that some lighter elements, such as hydrogen and helium, are also a little less stable. So we can achieve the required amount of energy release by combining the lighter nuclei. This process of merging lighter nuclei by releasing a certain amount of energy is called a fusion reaction.
- The concept of fission and fusion reaction driven by the binding energy curve establishes the assumption regarding stellar energy production.
- Stars are made up of lighter elements, so it is evident that stars can’t induce a fission reaction. The only thing possible is fusion, so scientists concluded that stars are formed due to fusion reactions. Thermonuclear fusion is the reaction that is the main source of stellar energy.
- The binding energy curve also illustrates the abundance of iron and nickel in the core of the earth since iron and nickel are the most stable element and are most tightly bonded to their nucleus, which gives the basic idea for the abundance of iron and nickel inside the core.
- The Gamma decay –binding energy curve helps to illustrate the gamma decay process. Gamma rays are emitted during the gamma decay; this occurs even after other decay also, such as alpha and beta decay. The gamma rays are produced when the decay occurs at the lower energy state carried by the daughter nuclei produced during alpha and beta decay.
- The binding energy has importance in the end product of supernovae and in the final stage of the silicon-burning stars. The neutron inside the stars is free to convert itself into a proton and can release more energy.
Explain binding energy curve
The binding energy curve can be well explained by plotting the graph of average binding energy per nucleon Vs. The mass number of the nucleus. Check out the graph given below.
- From the above graph, we can observe from hydrogen to sodium, and the binding energy increases sharply with the atomic mass. We can observe the slow increase of the curve after A>20.
- We can observe the recurrence of the peaks for the nuclei having a mass number multiple of four. This is because all those nuclei have an equal number of protons and neutrons.
- From A=40 to A=120, the curve almost becomes flat, and beyond 120, the curve decreases slowly with an increase in mass number.
- The binding energy per nucleon becomes almost constant and partially independent of the mass number between 30<A<170.
- Binding energy per nucleon hit its maximum peak at A=56, whose corresponding nucleus is Iron-56; it is considered the most stable element in the universe.
- In between the mass number 40<A<120, the element possess average binding energy of 8.5MeV and are considered the most stable and non-radioactive elements.
- For higher mass number A>120, the curve drops slowly, and the average binding energy per nucleon is above 7.6MeV and is considered unstable nuclei and radioactive elements.
- The binding energy curve per nucleon for both heavier and lighter nuclei enhances the fission and fusion process to form a stable reaction.
Frequently Asked Questions
Why does the binding energy curve decrease as the mass number increases in heavier nuclei?
As the mass number increases, the number of protons and neutrons inside the nucleus increases, which causes the destabilization causing a decrease in the binding energy curve.
When the number of protons increases, the repulsive force between the positive charges increases more rapidly than the strong attraction force exerted between the nucleons, the range of this repulsive force is much larger than the attractive force; thus, protons are repelled by the nucleus. Whereas when the neutron number increases, the symmetry of the nucleus is disturbed.
On which factor binding energy is dependent?
Binding energy largely depends on the strength of the nuclear force exerted on the nucleus.
The total nuclear force in the nucleus describes the amount of binding energy required for the nucleus. For example, the case of a heavy nucleus such as uranium, which consists of many particles, possesses a greater amount of binding energy to separate its nucleus into its constituent nucleons.
How does binding energy influence stability?
The binding energy causes some of the mass to disappear, which encounters an effect the stability of the nucleus.
In order to separate the nucleons from their nucleus, average energy must be required because of the difference in the nuclear force for different nuclei. High energy is essential to pull the nucleons if the binding energy per nucleon is more than obvious. Since high energy came into action to pull the nucleon significantly, stability will be high.
What are the important features of the binding energy curve?
There are three significant features that describe the entire action of the binding energy curve; they are
- The binding energy of the element of mass number up to A=30 increases due to the exertion of strong nuclear force in the nucleus.
- The binding energy between mass number 30<A<120 roughly remains constant and stable.
- Above A=120, the binding decreases.