Nuclear Energy (English)

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3-1: The Origin of the Nuclear Energy

[Exothermic Chemical Reactions]

Heat is evolved

in the chemical reaction

in which hydrogen and oxygen

are combined to be water;

i.e. the combustion

of hydrogen.

Such chemical reaction

in which heat is evolved

is called exothermic

reaction.

The chemical equation

of this reaction

for one mol of hydrogen

is written

Namely, when one mol of hydrogen

burns, 286 kJ of heat is evolved.

Another example is

where one mol of carbon

is oxidated to be

carbon dioxide

with producing

394 kJ of heat.

The above chemical equations,

(1) and (2), are for

one mol of hydrogen and carbon,

respectively.

In order to compare these chemical

reactions with nuclear reactions,

it is convenient to rewrite these

equations "for one molecule".

For this, let us divide

the heat production

by the Avogadro constant

Then they are rewritten as

Equation (3) means that

the process in which

two hydrogen and one oxygen

molecules combine to be

one water molecule

generates 3.0 eV energy emission.

And Eq. (4) says that,

when a carbon atom combines with

an oxygen molecule to be

a carbon dioxiside molecule,

4.1 eV energy is released.

As learned before,

eV is a unit of energy

extensively used

in the atomic and nuclear world.

It is the work done on an electron

that is accelerated through

a potential difference

of one volt.

Its value is

Moreover, the units of energy,

keV and MeV,

are often used in the nuclear world;

the former is 1,000 times eV

and the latter 1,000,000 times eV.

We can understand that

"the energy evolved from one process of an exothermic chemical reaction is about 3 or 4 eV".

[Exothermic Nuclear Reactions]

Nuclei show

various types of reaction:

For example, one nuclide

splits

into two or more fragments.

This type of reaction is called

nuclear fission.

Contrarily, two nuclides sometimes

combine with each other

to be a new nuclide.

This type of reaction is called

nuclear fusion.

There are many other types of

reaction processes;

they are generally called

nuclear reaction.

Among these various types

of nuclear reactions,

there are some types of

exothermic reactions

which are sometimes called

"exoergic" reaction

in nuclear physics.

The nucleus of deuterium

atom is called deuteron

which consists of

a proton and a neutron.

It is represented by

a symbol "d".

The nuclear reaction

in which two deuterons

bind with each other is

an example of nuclear fusion.

This exoergic reaction is written as

If a neutron is

absorbed in

the uranium-235 nucleus

(

it would split

into two fragments

of almost equal masses

and evolves some number

of neutrons and

energy Q.

One of the equations

for the processes is written

This is an example of

nuclear fission.

Here it is quite interesting

how much the amount of the

energy emission Q

is.

It must be about 200 MeV.

Let us explain below why it is so.

The details of the mechanism

of nuclear fission and fusion

will be given

on the following pages.

[The Origin of the Nuclear Energy]

Let us take up

the d-d fusion reaction

shown by the above Eq. (5)

as an example.

Since the experimental value of

the binding energy

of deuteron is 2.2246 MeV,

the sum of the binding energies

of the two deuterons

before the reaction

(on the left-hand side of Eq.(5))

is 4.449 MeV.

On the other hand,

the experimental value of

the binding energy of

is 7.719 MeV.

Therefore the total

binding energy after the reaction

(on the right-hand side of Eq. (5)) is

3.27 MeV (= 7.719 - 4.449)

larger than the binding energy

before the reaction

(on the left-hand side of Eq. (5)).

Thereby the total mass

decreases after the reaction

and the mass defect corresponding

to the above increase of the binding energy

occurs.

This mass defect is

released as the heat (or energy)

production in

this exothermic (or exoergic)

process.

Next, we shall discuss

the change of the binding energy

before and after the fission of uranium-235

(

)

shown by Eq. (6).

As seen in the figure on

Page 2-4, [Comparison between Mass formula and Experiment] ,

the binding energy per nucleon

in nuclei around

A = 240

is about 7.5 MeV.

On the other hand,

that

in nuclei around

A = 120

is about 8.5 MeV.

Accordingly, if a uranium nucleus

splits into two fragments

with almost equal masses,

the binding energy per nucleon

would increase

by about 1 MeV

and the total mass of

the fission fragments

would decrease

by the corresponding amount.

This loss of mass

(or mass defect)

is converted into

the heat (or energy) product

Since an energy of about 1 MeV

per nucleon is released,

the total energy

would be more than

200 MeV.

According to the above discussions,

it becomes clear that

"the origin of nuclear energy is the change of nuclear masses",

and it is based on

the principle of

Einstein's Mass-Energy Equivalence.

If the total binding energy after the reaction is larger than before, the total sum of the masses of the reaction products becomes smaller than that before the reaction. This decrease in mass is converted into an energy, so that the process would be an exothermic (exoergic) reaction.

[The Origin of the Heat in Exothermic Chemical Reaction, Law of Energy Conservation]

We have learned that,

if hydrogen and carbon burn

in oxygen gas, heat or energy

is evolved.

What is the origin of this

heat or energy?

The principle of the heat production in chemical reaction is just the same as that in the nuclear reaction.

The hydrogen molecule

is a bound system of two hydrogen atoms.

The mass of a hydrogen molecule

is slightly smaller than

the sum of the masses of two hydrogen atoms.

Converting this

difference (= mass defect)

into an energy with

Einstein's Mass-Energy Equivalence,

we have the binding energy of the hydrogen molecule.

In the process of

combustion of hydrogen

represented by Eq. (3),

the total mass

after the reaction

is slightly smaller

than before,

and this decrease in mass

is transformed into the heat emission

in the exothermic reaction.

Strictly speaking,

conservation of mass does not hold

even in a chemical reaction.

Both in chemical and

nuclear reactions,

the energy of the total system with converting mass into energy conserves before and after the reaction.

[Huge Amount of Nuclear Energy]

Comparing Eq. (3) with (5),

and Eq. (4) with (6),

we can easily understand

that the nuclear reactions

yield a huge amount of energy

in comparison with

ordinary combustion processes.

As explained above,

"the energy evolved from an exothermic chemical reaction like combustion of hydrogen or carbon is about 3 or 4 eV".

In contrast,

d-d fusion reaction

shown by Eq. (5) releases

3.27 MeV of energy.

It is about several million times

as large as the ordinary combustion.

In the fission of

uranium-235 shown by Eq. (6),

the more energy than 200 MeV

is emitted.

It is about several 100 million times

as large as an ordinary

chemical reaction.

Thus, the nuclear energy released in nuclear fission and fusion is several million or 100 million times as large as an ordinary chemical reaction like a combustion

process.

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