Unizor - Physics4Teens - Energy - Energy of a Nucleus
Channel: Zor Shekhtman on UNIZOR Education
Date: 2019-08-06

Unizor - Physics through a Looking Glass of Mathematician


Energy of Nucleus

Now we look deep inside the atoms and find there 3 major elementary particles - electrically positively charged protons and electrically neutral neutrons inside a small but heavy nucleus and electrically negatively charged electrons, circulating around nucleus on different orbits. For electrically neutral atoms the numbers of protons and electrons are equal. Nuclear energy is hidden inside the nucleus and is the subject of this lecture.

The first question we would like to answer is "What holds nucleus, its protons and neutrons, together, considering protons, as electrically positively charged particles must repel each other?"

The answer is simple. There are other forces in the Universe, not only electrostatic ones, that act in this case. These intra-nucleus forces that hold the nucleus together are called strong forces. They are strong because they are the source of attraction between the protons that is stronger than electrostatic repelling. However, these strong forces act only on a very small distance, comparable to the size of a nucleus inside an atom. For example, at a distance 10−15m the strong force is more than 100 times stronger than electrostatic one.

If, by regrouping protons and neutrons, we will be able to create different atoms (inasmuch as regrouping atoms in chemical reaction we create new molecules), a new source of energy, based on strong forces, the nuclear energy, can be uncovered in the course of nuclear reaction.

Here is an interesting fact.
Physicists have measured the masses of protons, neutrons and many different nuclei that contain these protons and neutrons and have discovered that the sum of masses of individual protons and neutrons is greater than the mass of a nucleus that contain these exact particles.
For example,
mass of proton is 1.0072766 atomic mass units or 1.6726·10-27kg,
mass of neutron is 1.0086654 atomic mass units or 1.6749·10-27kg.
At the same time, mass of deuterium nucleus, that contains 1 proton and 1 neutron is 2.0135532 atomic mass units, which is smaller than the sum of masses of proton and neutron (1.0072766 + 1.0086654 = 2.015942).
This so-called "mass defect" is directly related to nuclear energy - the energy of strong forces that hold the nucleus together.

A simplified explanation of this effect is based on the law of energy conservation. Consider the force of gravity between a planet and an object above its surface. The object has certain potential energy and, if dropped to the ground, this potential energy transforms into other forms, like kinetic, thermal etc.

Similarly, if we consider two independent neutrons (or neutron and proton, or two protons) on a very small distance from each other, but not forming a nucleus, there is a potential energy of the strong forces acting between them. If we let these two particles to form a nucleus, analogously to an object falling towards the surface of a planet, this potential energy should be transformed into other forms, like thermal.

Now the Theory of Relativity comes to play, that has established the equivalence of mass and energy by a famous formula E=m·c². According to this equivalence, if some energy is released during the formation of a nucleus from individual protons and neutrons, there must be certain amount of mass released associated with this energy. That is the explanation of "mass defect".

It should be noted that to form a nucleus of deuterium from 1 proton and 1 neutron is easier than to form a nucleus that contains more than one proton, because electrostatic repulsion between positively charged protons prevents their bonding. So, to bring protons sufficiently close to each other for strong forces to overcome the electrostatic repulsion, we have to spend some energy. The net energy released by forming a nucleus from protons and neutrons is the difference between the energy released from strong forces taking hold of these particles inside a nucleus and the energy consumed to overcome repulsion of protons.

Actually, as we attempt to form bigger nuclei, the energy we have to spend to overcome electrostatic repulsion forces become greater than amount of energy released by forming a nucleus. This border line is approximately around the nucleus of iron Fe. Forming iron and heavier elements from protons and electrons is a process that consumes more energy than releases. These heavier nuclei will produce energy, if we reverse the procedure, breaking them into individual protons and neutrons.

The mechanisms described above are used in nuclear reactors and atomic bomb, where heavier elements are broken into lighter ones (fission), releasing energy, and in hydrogen bomb, where lighter elements are bonded together to release the energy (fusion).