Nuclear Energy
“Why has our sun used energy for so many years and still have
sufficient left over?” we often ask ourselves. This kind of energy is the
source of many stars, so we can “see” it. This energy the synthesis of light
elements and we call this the energy of “Fissions”. For example, if you take
two protons and two neutrons, which is a  particle and very accurately
calculate its mass, the nucleus of this  particle is lighter than its
components. “Bound energy,” according to Einstein, is this deficit of mass
multiplied by the speed of light squared. Fission energy comes out during
synthesis of light elements. Bound energy, divided by the number of
nucleons in nuclei, gives away a specific value. This specific value is not
constant and, at its minimum is at the atomic number of about 70 in the
Table of Elements. Connecting light elements, and the division of a heavy
one, has an advantage energetically. This is shown in the next figure.
Fig. 15.
The first discovery of Helium was on the sun, and then we found it on earth.
Helium is certainly one stage of the fusion of protons.
Only humans can create controlled fission, nature can’t. Controlled
fusion is the same. Feynman could say: “As far if we know.” What controls
the reaction of fission and why? Everybody assumes that a very large
gravity controls this reaction. High temperature is probably another
important factor.
We must overcome the big force of repulsion between protons so the
nuclear force starts to act. The nuclear force is called a short-distance one.
These forces are 106 times bigger than the gravitation forces. So-called
Coulomb Forces are needed to overcome the boundaries of nuclei. These
forces are much bigger than those for gravitation forces, though similar laws
govern them. Coulomb’s law, as applied to electric charges, follows next.
F=K
Q1Q2
r2
If;
K – make units to be force in Newtons (N).
Q1 and Q2 – are electric charges (1.6x10-19Coul, at this case).
r – is distance between charges in (m) (boundaries of nuclei 10-15 m
at this case)
If a temperature raises more than 10 million Kelvin, we can overcome
Coulomb’s repulsion forces. It is interesting that both electric and magnetic
forces repeal (the same) and attract (different), but gravity forces only
attract and the laws appear to be the same. Feynman did say: “As far as we
know.” I am not concerned any more with synthesis. I only add that a
human can obtain energy, not in a controlled manner, in the hydrogen bomb
where ignition comes from an atomic bomb.
In laboratory conditions, Uranium was fused before World War II
(1939). E. Fermi got the Nobel Prize in 1938. However, priority belongs to
the Germans, Hahn and Strassman. In 1939,they fused Uranium and
identified one of the possible fragments of fusion, Barium with atomic
number 56 (Z=56). Before the second word war, Hitler forbade two German
researchers, O. Fresh and L. Maither, both candidates for the Nobel Prize,
to interpret this phenomenon. Einstein wrote a special letter to the President
of the United States asking to start the project of atomic fusion. The
President started a special project called Manhattan and he employed
physicists from around the world. They constructed the atomic bomb for the
American army. This project was kept top secret. The leaders of the
Manhattan Project were non-physicists. Both atomic bombs dropped on
Hiroshima and Nagasaki finished the second word war in 1945. Big money
does almost everything. This horrible weapon got into the hands of nonphysicists. The figure on the next pages shows the products of fragments of
fusion.
235
U92. Uranium starts the reaction of analysis consuming thermal
neutrons. Uranium of
235
U92 has 92 protons and we often write 235U for
simplification.
Fig. 16.
In 1951 and 1953,there were conferences where nuclear countries
exchanged all their information regarding nuclear fusion. These countries
were the USA, England, France and the Soviet Union. We learned that
three fast neutrons (instantaneous) were created and a slow neutron
(thermal) is needed to start a fusion reaction of 235U or 233U. In natural
Uranium, these isotopes of 233U and 235U are not big numbers. The
biggest probability is that nuclear fusion comes from 235U and 233U. At
least one of these instantaneous neutrons slows down. Nuclear cross–
section (collision) for the slowing down of neutrons depends on the number
of atoms of comparable mass to neutrons i.e. protons. The best moderators
we have are: D2O, H2O and paraffin. Nuclear cross-section is the probability
that the “bullet” be in “target”, measured in barn i.e. unit of metre squared.
1 barn = 102 fm2 = 10-28 m2 (σ)
200eV is the average energy per reaction. Nuclear fusion has application to
nuclear reactors. From three (average) fast neutrons, we take away two
neutrons. We don’t want to make “avalanche” neutrons. In both atomic or
Plutonium bombs, we have a chain reaction of an increasing number of
neutrons. This is shown in figure 17.
Fig. 17.
Cadmium has a big nuclear cross-section for thermal neutrons and we “take
off” approximately two neutrons from this.
The Isotope of Cadmium is involved in the nuclear reaction, with the
production of quant
-mass’’,
or better, a “critical-volume”. This volume is the space where we have a big
probability that the neutron will be caught inside a volume. The calculation
of such a probability is not an easy task. A numbers of parameters are
involved. The percentage of U233 and U235 in a mass of Uranium,
reflection of neutrons, fuel poisoning, moderators, and other parameters
should be calculated. I will not give examples of such calculations. For
U235, the critical mass is about 40kg, for the Plutonium, it is even lower.
Where did the first neutron come from? This neutron came from the “air.”
U238 also makes fusion, but this isotope does not need the
moderator, but it needs fast neutrons with energies bigger than 1MeV.The
next reaction that could be involved is:
238
U92 + 1n0 = 239U92 = 239Nu93 +

48 min ut
=
239
Nu93 +

4.7 dnia
= 239Pu94
U238, plus the fast neutron, becomes the isotope of Uranium, which decays
to a  particle with the next element, taking 48min. Nu239 becomes an
isotope of
Plutonium (Pu239) and decays to a  particle with a time of
4.7days. Both Nu239 and Pu239 are called “transuranic elements,” and
they not exist in nature. The isotope of Pu239 may be used as a fusion
material and this has similar properties to U235.The above reaction is
frequently used in reactors called “breeder reactors.”
In “scientific reactors” or “slow neutron reactors,” we take out at least
one from three neutrons during the fusion process. Nuclear reactors must
be safe and efficient. Natural Uranium has only 0.75% of the isotopes U233
and U235. We have to decide if nuclear reactors work with natural Uranium
or enriched Uranium. The constructor of a nuclear reactor has to adjust
many parameters. He calculates optimum conditions.
For a science reactor, we used U235 and, as a moderator, H2O
(normal water). For power reactors, we generally used breeder reactors.
This is a very complicated subject and requires separate lectures. I add;
modern nuclear reactors work safely and efficiently. Nuclear reactors may
be used as an “alternative” source of energy. For now, we use the source of
natural energy from the combustion of cauls and a little from water and the
combustion of gas. We need energy increasingly. Today, about 50% of
energy comes from nuclear reactors. We call them a non-classical source of
energy.
I have said alternatively, because in the future, humans will use
fission reactors to fuse water from oceans. Products of fission are nonradioactive, in comparison to products from nuclear reactors, which are
radioactive.
For a nuclear force to start to acting, we need the approach of two
protons, to overcome repelling forces. In laboratories still, repel forces are
bigger than those coming from nuclear forces. We can’t keep hot plasma
(ionised particles) for the necessary time. A fission reactor is still a fantasy.
In 1967, Hans A. Bethe received the Nobel Prize for the solution of the
energy of stars.