Binding energy per nucleon

Introduction

As you know, the nucleus plays a vital role in every field of science, whether it is in physics, chemistry or biology. Here we explore the theory of the nucleus and its binding energy per nucleon. It is a very important topic in physics and pretty much interesting too. Have you ever wondered when you think about the nucleus of an atom? What does it look like? What’s its role? Here, we shall look for the answers to these questions. But before getting into our topic, let’s understand the basic properties and definition of nucleus and atoms.

We know that each element has an atom, and further, each atom contains protons and neutrons. Protons repel each other as they are positively charged but having neutrally  charged neutrons attract the protons and hold them to stay together or close to each other by the nuclear force. Let me ask you a question: What are an element’s isotopes? The answer is when a molecule of the same element having the same number of protons and different number of neutrons is called isotopes of an element.

Body

At the center of an atom, there is a positive charge called a cation. When an atom accepts an electron that is an extra electron, then this is referred to as an anion. The nucleus is present at the center of the atom carrying positive charges. The nucleus carries the mass of atoms at the center. In simple words, the atom is almost empty. All the charges and mass are at the nucleus. Don’t forget that the radius of a nucleus is smaller than the radius of an atom. The reactions are classified into two categories based on nuclear reactions. Two things can happen in nuclear reactions: either liberation of energy or absorption of energy. When energy is released, it is called exothermic reactions, and when energy is absorbed, it is an endothermic reaction. Based on exothermic reactions, two reactions occur: atomic fusion and atomic fission.

Nuclear fission is when heavy atomic nuclei get separated into two or more lighter nuclei having individual protons and neutrons.

Nuclear fusion is when two or more lighter atomic nuclei are combined to form a heavy nucleus.

There is a huge requirement for energy for all these reactions to occur.

Now come to the topic that is nuclear binding energy.

What is nuclear binding energy?

Take an example to understand this energy, say carbon – 12 means carbon having six protons and six neutrons. In a carbon nucleus, the nuclear force makes the proton and neutron stick together by overcoming the repulsion of protons.

Definition: To split the nucleus of an atom into smaller or lighter nuclei or its nucleons, forming an individual mass of proton and neutron, some amount of energy is required, and that energy is called nuclear binding energy.

You should know,the total of the masses of protons and neutrons is always less than the mass of nuclei.

BINDING ENERGY PER NUCLEONS

The difference between nuclear attraction and disruptive energy is the binding energy per nucleon. To calculate the binding energy per nucleon, we have to convert mass to energy by using Einstein’s formula.

E = mc2

Where, E is the binding energy of nucleus

            c is the speed of light in vacuum

m is the mass difference between the nuclei and the sum of the individual masses of protons and neutrons

This formula is called binding energy per nucleon formula.

NOTE – Mass must be taken in kg.

Binding energy per nucleon refers to the average energy per nucleon required to separate a nucleus into its nucleons. The average binding energy per nucleon is 8 Mev.

VARIATION OF BINDING ENERGY WITH MASS NUMBER

Let’s understand the variation of binding energy with mass number.

To understand the variation of binding energy with mass number, we need to draw a graph between these two parameters. This graph shows that the binding energy is less for both light and heavy nuclei.

By this, we understand that,

1. To produce binding energy per nucleon, the force should be attractive and sufficiently strong.
2. The binding energy is less for heavy and light nuclei because their nucleus is short-range.
3. If the nucleus is at a distance more than the nuclear force from the particular nucleons, it will not influence binding energy.
4. Nucleons having a  maximum range of nuclear force, their binding energy will be proportional.

Let’s take an example to understand this concept in a better way,

Consider a very heavy nucleus. Say A = 240 has lower binding energy per nucleon when compared to the nucleus that is A = 120. In this case, when a nucleus of 240 breaks into  A = 120, their nucleons get more tightly bound together.

Note – The fused heavier nuclei have more binding energy when compared to the lighter nuclei. This means that the final nucleus is more tightly bound than the initial one.

In simple words, when mass increases, the binding energy per nucleon decreases.

STABILITY OF ELEMENTS BASED ON THE BINDING ENERGY PER NUCLEONS

Two major factors determine nuclear stability. The neutron/proton ratio is one, while the total number of nucleons in the nucleus is the other.

Those elements with greater mass, defect, and higher binding energy are considered more stable.

As a result, nuclear stability is proportional to the nuclear binding energy.

Example: Iron – 56 has more binding energy value. Thus, the nucleus of iron is most efficiently bounded and is most stable.

NUCLEAR FORCE

Now let’s discuss the nuclear force. The nuclear force is the force required by the nuclear particles like the protons or neutrons to stick together, resulting in binding the nucleus together. This force is stronger than the repulsive force of protons, which is the Coulomb’s force, as the nuclear binding force is dominant over the repulsive Coulomb force.

It is interesting to note that the nuclear force between neutron-neutron, proton-neutron and proton-proton is approximately the same. Also, nuclear force never depends on electric charges.

Exoergic reaction – In this reaction, some free amount of energy is released during a nuclear reaction. This reaction is positive because it liberates the energy. It is also called the exothermic reaction. 

Endoergic reactions occur when there is an absorption of energy during nuclear reactions. This reaction is always negative because this reaction takes up the energy. It is also called an endothermic reaction.

MASS DEFECT

Mass defect is the amount of mass of an atom by which the mass of an atomic nucleus differs from the sum of masses of its constituent particles. This mass defect is caused by nuclear binding energy. In other words, the mass of the nucleus is less than the sum of the masses of the constituents of the nuclei. Mass defect is explained by the nuclear binding energy formula –

E = mc2

Where m is the mass defect.

Conclusion 

From all of the above, we learned that binding energy is the energy that is required to split the heavier nucleus of an atom into a smaller one by forming the mass of their proton and neutron. As we studied above, the higher the number of nucleons, the higher will be the binding energy. This energy also defines the stability of atoms. The atom will be more stable if the binding energy is higher. The energy from fusion and fission generates electric power in several industries. The Einstein formula that is E = mc2  can determine the nuclear binding energy.