The Nucleus
355
Nuclear reactors are used for producing power, producing fissionable
material, and to obtain strong neutron sources. The neutron sources may be
used for conducting scientific experiments and for producing radioactive isotopes
which are of enormous use in medicine, and in industry.
9.8 THERMONUCLEAR FUSION
It may be observed (Fig. 9.1) that the binding energy per nucleon is small for
light nuclei, and increases to maximum value for A ≈ 60. It is therefore
energetically preferable for lighter nuclei to fuse into larger nuclei. Such a process
would be accompanied by a release of energy, e.g. in the fusion of deuterium
and tritium,
2
H +
2
H → p +
3
H
(9.115)
2
H +
3
H → n +
4
He
(9.116)
energies of 4.0 MeV and 17.6 MeV respectively, are released.
For a fusion reaction to take place, the lighter nuclei must overcome
Coulomb repulsion between them [see Fig. 9.6(b)], i.e. they must have an energy
E c ≈
2
1 2
0 1
2
4
(
)
Z Z e
r r
πε
+
(9.117)
which for Z 1 = Z 2 = 1 and r 1 + r 2 = 2 fm has a value of about 0.7 MeV. Thus, each
of the two nuclei must have an energy of about 0.35 MeV. A temperature of
about 2 × 10
9
K would provide an average thermal energy of about 0.3 MeV,
and hence promote the fusion reaction. However, the fusion reaction can proceed
even at lower temperatures. This is due to the fact that (i) the energies of the
nuclei at a given temperature have Maxwell-Boltzmann distribution so that
there are always some nuclei with enough energy to overcome the Coulomb
barrier, (ii) nuclei can tunnel through the potential barrier. Therefore, and
appreciable amount of fussion takes place at temperatures of about 10
7
K. Since
the reaction is induced by high temperatures, it is known as thermonuclear
fusion.
Controlled Fusion
To have controlled fusion reactions, it is necessary to maintain nuclei at a
temperature of about 10
7
– 10
8
K in a confined region, so that nuclear reactions
can take place. At such high temperature, the atoms are ionized into positively
charged ions and electrons, forming what is known as a plasma state. The two
main problems in achieving controlled fusion are the containment of the plasma
within a suitable volume, and the heating of the plasma to the required high
temperatures.
355
Nuclear reactors are used for producing power, producing fissionable
material, and to obtain strong neutron sources. The neutron sources may be
used for conducting scientific experiments and for producing radioactive isotopes
which are of enormous use in medicine, and in industry.
9.8 THERMONUCLEAR FUSION
It may be observed (Fig. 9.1) that the binding energy per nucleon is small for
light nuclei, and increases to maximum value for A ≈ 60. It is therefore
energetically preferable for lighter nuclei to fuse into larger nuclei. Such a process
would be accompanied by a release of energy, e.g. in the fusion of deuterium
and tritium,
2
H +
2
H → p +
3
H
(9.115)
2
H +
3
H → n +
4
He
(9.116)
energies of 4.0 MeV and 17.6 MeV respectively, are released.
For a fusion reaction to take place, the lighter nuclei must overcome
Coulomb repulsion between them [see Fig. 9.6(b)], i.e. they must have an energy
E c ≈
2
1 2
0 1
2
4
(
)
Z Z e
r r
πε
+
(9.117)
which for Z 1 = Z 2 = 1 and r 1 + r 2 = 2 fm has a value of about 0.7 MeV. Thus, each
of the two nuclei must have an energy of about 0.35 MeV. A temperature of
about 2 × 10
9
K would provide an average thermal energy of about 0.3 MeV,
and hence promote the fusion reaction. However, the fusion reaction can proceed
even at lower temperatures. This is due to the fact that (i) the energies of the
nuclei at a given temperature have Maxwell-Boltzmann distribution so that
there are always some nuclei with enough energy to overcome the Coulomb
barrier, (ii) nuclei can tunnel through the potential barrier. Therefore, and
appreciable amount of fussion takes place at temperatures of about 10
7
K. Since
the reaction is induced by high temperatures, it is known as thermonuclear
fusion.
Controlled Fusion
To have controlled fusion reactions, it is necessary to maintain nuclei at a
temperature of about 10
7
– 10
8
K in a confined region, so that nuclear reactions
can take place. At such high temperature, the atoms are ionized into positively
charged ions and electrons, forming what is known as a plasma state. The two
main problems in achieving controlled fusion are the containment of the plasma
within a suitable volume, and the heating of the plasma to the required high
temperatures.