The binding energy of an atomic nucleus: formula, meaning and definition

Each of the atomic nuclei of absolutely any chemical substance consists of a certain set of protons and neutrons. They are held together due to the fact that inside the particle there is a binding energy of the atomic nucleus.

A characteristic feature of nuclear forces of attraction is their very high power at relatively small distances (from about 10 -13 cm). With increasing distance between particles, the attractive forces inside the atom also weaken.

atomic nucleus binding energy

Reasoning about the binding energy inside the nucleus

If you imagine that there is a way to separate protons and neutrons from the atomic nucleus in turn and arrange them at such a distance that the binding energy of the atomic nucleus ceases to act, then this should be very hard work. In order to extract its components from the nucleus of an atom, one must try to overcome intra-atomic forces. These efforts will be aimed at dividing the atom into the nucleons contained in it. Therefore, we can judge that the energy of the atomic nucleus is less than the energy of those particles of which it consists.

the binding energy of an atomic nucleus is

Is the mass of intra-atomic particles equal to the mass of an atom?

Already in 1919, researchers learned how to measure the mass of an atomic nucleus. Most often it is "weighed" using special technical devices, which are called mass spectrometers. The principle of operation of such devices is that the characteristics of the motion of particles with different masses are compared. Moreover, such particles have the same electric charges. Calculations show that those particles that have different mass indices move along different trajectories.

Modern scientists have found with great accuracy the masses of all nuclei, as well as their protons and neutrons. If we compare the mass of a certain nucleus with the sum of the masses of the particles contained in it, then it turns out that in each case the mass of the nucleus will be greater than the mass of individual protons and neutrons. This difference will be approximately 1% for any chemical. Therefore, we can conclude that the binding energy of the atomic nucleus is 1% of its rest energy.

binding energy of atomic nuclei formula

Properties of intranuclear forces

The neutrons that are inside the nucleus are repelled from each other by Coulomb forces. But at the same time, the atom does not fall apart. This is facilitated by the presence of an attractive force between the particles in the atom. Such forces, which have a nature other than electric, are called nuclear. And the interaction of neutrons and protons is called strong interaction.

Briefly, the properties of nuclear forces are as follows:

  • it is charge independence;
  • action only at short distances;
  • and also saturation, which is understood to mean keeping only a certain number of nucleons near each other.

According to the law of conservation of energy, at the moment when the nuclear particles are connected, energy is released in the form of radiation.

helium core binding energy

Binding energy of atomic nuclei: formula

For the above calculations, the generally accepted formula is used:

E sv = (Z Β· m p + (AZ) Β· m n -M i ) Β· cΒ²

Here, by E sv is understood the binding energy of the nucleus; c is the speed of light; Z is the number of protons; (AZ ) is the number of neutrons; m p is the mass of the proton; and m n is the neutron mass. M i denotes the mass of the nucleus of an atom.

The internal energy of the nuclei of various substances

To determine the binding energy of the nucleus, the same formula is used. The binding energy calculated by the formula, as previously mentioned, is not more than 1% of the total atomic energy or the rest energy. However, upon a detailed examination, it turns out that this number fluctuates quite strongly during the transition from substance to substance. If you try to determine its exact values, then they will especially differ in the so-called light nuclei.

For example, the binding energy inside the hydrogen atom is zero, because there is only one proton in it. The binding energy of the helium core will be equal to 0.74%. For cores of a substance called tritium, this number will be 0.27%. Oxygen has 0.85%. In nuclei, where about sixty nucleons are located, the energy of the intra-atomic bond will be about 0.92%. For atomic nuclei with a larger mass, this number will gradually decrease to 0.78%.

To determine the binding energy of the nucleus of helium, tritium, oxygen, or any other substance, the same formula is used.

determine the binding energy of the helium core

Types of protons and neutrons

The main reasons for these differences can be explained. Scientists have found that all nucleons that are contained inside the nucleus are divided into two categories: surface and internal. Internal nucleons are those that are surrounded by other protons and neutrons on all sides. The surface ones are surrounded by them only from the inside.

The binding energy of an atomic nucleus is a force that is expressed more in internal nucleons. Something similar, by the way, also occurs with the surface tension of various liquids.

How many nucleons fit in the nucleus

It was found that the number of internal nucleons is especially small in the so-called light nuclei. And for those that belong to the category of the lightest, almost all nucleons are regarded as superficial. It is believed that the binding energy of an atomic nucleus is a quantity that should increase with the number of protons and neutrons. But even such growth cannot continue indefinitely. With a certain number of nucleons - and this is from 50 to 60 - another force comes into action - their electrical repulsion. It occurs even regardless of the presence of binding energy inside the nucleus.

The binding energy of the atomic nucleus in various substances is used by scientists in order to release nuclear energy.

Many scientists have always been interested in the question: where does the energy come from when lighter nuclei merge into heavy ones? In fact, this situation is similar to atomic fission. In the process of fusion of light nuclei, in the same way as occurs during the splitting of heavy nuclei, nuclei of a stronger type are always formed. In order to "get" all the nucleons in them from light nuclei, it is necessary to spend less amount of energy than what is released when they are combined. The converse is also true. In fact, the synthesis energy, which falls on a certain unit of mass, may be greater than the specific fission energy.

determine the binding energy of the nucleus

Scientists researching nuclear fission processes

The process of nuclear fission was discovered by scientists Hahn and Strasman in 1938. Within the walls of the Berlin University of Chemistry, researchers discovered that during the bombardment of uranium by other neutrons, it turns into lighter elements in the middle of the periodic table.

A significant contribution to the development of this field of knowledge was also made by Lisa Meitner, whom Gan had proposed at the time to study radioactivity together. Gan allowed Meitner to work only on the condition that she would conduct her research in the basement and would never rise to the upper floors, which was a fact of discrimination. However, this did not prevent her from achieving significant success in researching the atomic nucleus.


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