Sunday, August 18, 2019

Unizor - Physics4Teens - Energy - Energy of Nucleus - Fusion

Notes to a video lecture on

Nucleus Fusion

Fusion is a nuclear reaction, when light nuclei are brought together and combined into a heavier ones.

The reason for this reaction to release the energy is the difference
between amount of energy needed to overcome the repulsion between nuclei
because they have the same positive electric charge (this energy is
consumed by fusion) and the potential energy released by strong forces, when the formation of a combined nucleus occurs (this energy is released by fusion).

The former is less than the latter.

When the light nuclei are fused into a heavier one, the excess of potential energy of strong forces, released in the process of fusion,
over the energy needed to squeeze together protons against their
repulsion is converted into thermal and electromagnetic field energy.

Analogy to this process can be two magnets separated by a spring.

The magnets represent two separate protons, the magnetic force of attraction between them represents the strong force
that is supposed to hold the nucleus together, when these particles are
close to each other, the spring represents the electrical repulsive
force between them, acting on a larger distance, as both are positively

It's known that magnetic force is inversely proportional to a square of a
distance between objects, while the resistance of a spring against
contraction obeys the Hooke's Law and is proportional to the length of

On the picture magnets are separated. To bring them together, we have to
spend certain amount of energy to move against a spring that resists
contraction. But the magnetic attraction grows faster then the
resistance of the spring, so, at some moment this attraction will be
greater than the resistance of a spring. At this moment nothing would
prevent magnets to fuse.

As is in the above analogy, if we want to fuse two protons, we have to bring them together sufficiently close for strong forces to overtake the repulsion of their positive charges.

Consider the following nuclear reaction of fusion.

One nucleus of hydrogen isotope deuterium 1H2 with atomic mass 2 contains one proton and one neutron.

One nucleus of hydrogen isotope tritium 1H3 with atomic mass 3 contains one proton and two neutrons.

If we force these two nuclei to fuse, they will form a nucleus of helium 2He4 and releasing certain amount of energy:

1H2 + 1H3 = 2He4 + 0n1

It's not easy to overcome the repulsion of protons. High temperature and
pressure, like in the core of our Sun, are conditions where it happens.
On Earth these conditions are created in the nuclear bomb, using the
atomic bomd to achieve proper amount of heat and pressure, thus creating
an uncontrlled fusion.

Controlled nuclear reaction of fusion is what scientists are working on right now. So far, it's still in the experimental stage.

Monday, August 12, 2019

Unizor - Physics4Teens - Energy - Energy of a Nucleus - Fission

Notes to a video lecture on

Nucleus Fission

Fission, first of all, is a nuclear reaction, when heavier nuclei are split into lighter ones.
The reason for this reaction to release the energy is the difference between amount of energy needed to break strong forces that hold the nucleus together (this energy is consumed by fission) and amount of potential energy in positively charged and repelling protons inside nucleus (this energy is released by fission).
The former is less than the latter.

When the heavy nucleus is broken into parts, the excess of potential energy of squeezed together protons against their repelling force over the energy of strong forces that keep nucleus together is converted into thermal and electromagnetic field energy.

Analogy of this is a spring squeezed tightly and held in this position by a thread. A thread plays the role of strong forces, while a potential energy of a squeezed spring plays the role of protons kept close to each other by a this force. When you cut a thread, the spring will release the potential energy, similarly to protons repelling from each other.

Electrically positively charged protons repel each other and, at the same time, are bonded together by strong forces inside a nucleus. At the same time neutrons are also bonded by strong forces among themselves and with protons without any repulsion.
So, the more neutrons the nucleus has - the stronger it is. Neutrons only add "bonding material" to a nucleus without adding any repelling forces that work against the nucleus' stability.

Uranium-238 with 92 protons and 146 neutrons (92U238) naturally occurs on Earth and is relatively stable.
Uranium-235 with the same 92 protons and 143 neutrons (92U235) has less "bonding material" (less neutrons) and is more susceptible to fission.

All it takes to break the nucleus of 92U235 is a little "push" from outside, which can be accomplished by bombarding it with neutrons. In the process of fission, caused by hitting a nucleus of 92U235 with a neutron, it can transforms into Barium-141 with 56 protons and 85 neutrons 56Ba141, Krypton-92 with 36 protons and 56 neutrons 36Kr92 and 3 free neutrons.
As we see, the numbers of protons is balanced (input: 92, output: 56 and 36), as well as a number of neutrons (input: 1 free hitting neutron and 143 in a nucleus of 92U235 total 144, output: 85 in a nucleus 56Ba141, 56 in a nucleus of 36Kr92 and 3 new free neutrons total 144).

Let's express this reaction in a formula (letter n denotes a neutron):
0n1 + 92U235 =
56Ba141 + 36Kr92 + 3·0n1

What's interesting in this reaction is that it not only produces energy because we break a heavy nucleus into lighter ones, but also that it produces 2 new neutrons that can bombard other atoms, causing a chain reaction and, potentially, an explosion (atomic bomb). However, if we absorb extra neutrons, it will allow to slowly release of nuclear energy (nuclear power stations).

Monday, August 5, 2019

Unizor - Physics4Teens - Energy - Energy of a Nucleus

Notes to a video lecture on

Energy of Nucleus

In this lecture we will analyze the energy aspect of nucleus - the central part of an atom.

By now we have built a pyramid of energy types, related to the depth of our view inside the matter.

First, we analyzed the mechanical energy - the energy of moving macro-objects.

Our next view deep into the world of macro-objects uncovered the molecules - the smallest parts of macro-objects that retain their characteristics. The movement of these molecules was the source of thermal energy, which we often call the heat.

Next step inside the molecules uncovered atoms, as the molecules'
components. There are about 100 types of atoms and their composition
inside the molecules creates all the thousands of different molecules. Chemical reactions
change the composition of atoms in molecules, thereby creating new
molecules from the atoms of old molecules. This process broke some
inter-atomic bonds and created the new ones and is the source of chemical energy.

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.

There is another form of nuclear reaction related to
transformation of elementary particles. Under certain circumstance a
neutron inside a nucleus can transform into proton and, to keep the
total electrical charge in balance, it emits an electron. This reaction
is called beta-decay and it also produces energy in the form of electromagnetic waves of very high frequency (gamma-rays).

Nuclear reactions are a very powerful source of nuclear energy, which is
so much more powerful than other types of energy, that, if misused, it
might represent a danger for life on our planet.

There is a clear analogy between nuclear and chemical reactions.

What happens with atoms in the chemical reaction, happens with protons
and neutrons in nuclear reaction. Some atomic bonds break in a chemical
reaction, some are created. Some nuclear bonds between protons and
neutrons break in a nuclear reaction, some are created.

Sometimes the chemical reaction happens by itself, as long as
participating substances are close together, but sometimes we have to
initiate it, like lighting methane gas with a spark or a flame of a
match to initiate continuous burning.

Similar approach is valid for nuclear reaction. Sometimes it happens by
itself, but sometimes it should be started, like bombarding the nucleus
with neutrons, after which it continues by itself.

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).