Elements of Modern Physics
350
characteristic radiation. For example, traces of cobalt may be detected
by observing the radiation from cobalt isotope
60
Co formed on absorption
of neutrons.
3. In place of x-rays, the more energetic gamma rays from radioactive
isotopes may be used to detect flaws in metals, in medicine for the
treatment of some diseases such as cancer, for preservation of food
materials, for crop mutations in agriculture and in various industries.
The commonly used γ rays are from the radioactive
60
Co.
A particularly interesting application is radioactive
14
C dating based on a
nuclear reaction taking place in the atmosphere. Neutrons produced in the
atmosphere by cosmic rays, collide with nitrogen nuclei, producing
14
C and
protons
14
N + n →
14
C + p
(9.108)
14
C is radioactive an decays by β-emission,
14
C →
14
N + e + v
(9.109)
with a half-life of 5730 years. This radioactive carbon is assimilated by plants
in photosynthesis, so that living organisms contain a small fraction of
14
C. When
the organism dies, the intake of
14
C stops stops and because of the decay of
14
C,
its concentration relative to
12
C begins to decrease. Hence, a measurement of
the concentration of
14
C in the remains of the organism (e.g. wood, bones, etc.),
gives the data when it died. This is known as radioactive dating and permits us
to determine the age of organic relics which may be thousands of years old.
Two important applications of fission and fusion reaction, which lead to
the extraction of energy from nuclear processes, are considered in the next two
sections.
9.7 FISSION REACTORS
It was noted in Sec. 9.5, that it is energetically favourable [see Eq. (9.80)] for a
heavy nucleus to break into two nearly equal parts. Qualitatively, this is due to
the fast that the binding energy per nucleon is about 7.6 MeV for nuclei with
A ~ 230, whereas it is about 8.5 MeV for nuclei with A ~115. This means that
the fission of a nucleus with A ~ 230 into two equal parts would release an
energy of about 0.9 × 230 = 2078 MeV. However, the fission products must
pass through intermediate states of high energy provided by the Coulomb barrier,
similar to the situation in Fig. 9.6(b). The fission can take place by tunnelling
through the barrier, but with a rather long lifetime (for
238
U it is about 10
16
years).
The fission of a nucleus can be induced by bombarding the nucleus with
neutrons. Consider, for example, the capture of a slow neutron by a nucleus of
235
U. This leads to the formation of the compound nucleus
236
U in which the
small kinetic energy and the binding energy of the neutron are released. The
350
characteristic radiation. For example, traces of cobalt may be detected
by observing the radiation from cobalt isotope
60
Co formed on absorption
of neutrons.
3. In place of x-rays, the more energetic gamma rays from radioactive
isotopes may be used to detect flaws in metals, in medicine for the
treatment of some diseases such as cancer, for preservation of food
materials, for crop mutations in agriculture and in various industries.
The commonly used γ rays are from the radioactive
60
Co.
A particularly interesting application is radioactive
14
C dating based on a
nuclear reaction taking place in the atmosphere. Neutrons produced in the
atmosphere by cosmic rays, collide with nitrogen nuclei, producing
14
C and
protons
14
N + n →
14
C + p
(9.108)
14
C is radioactive an decays by β-emission,
14
C →
14
N + e + v
(9.109)
with a half-life of 5730 years. This radioactive carbon is assimilated by plants
in photosynthesis, so that living organisms contain a small fraction of
14
C. When
the organism dies, the intake of
14
C stops stops and because of the decay of
14
C,
its concentration relative to
12
C begins to decrease. Hence, a measurement of
the concentration of
14
C in the remains of the organism (e.g. wood, bones, etc.),
gives the data when it died. This is known as radioactive dating and permits us
to determine the age of organic relics which may be thousands of years old.
Two important applications of fission and fusion reaction, which lead to
the extraction of energy from nuclear processes, are considered in the next two
sections.
9.7 FISSION REACTORS
It was noted in Sec. 9.5, that it is energetically favourable [see Eq. (9.80)] for a
heavy nucleus to break into two nearly equal parts. Qualitatively, this is due to
the fast that the binding energy per nucleon is about 7.6 MeV for nuclei with
A ~ 230, whereas it is about 8.5 MeV for nuclei with A ~115. This means that
the fission of a nucleus with A ~ 230 into two equal parts would release an
energy of about 0.9 × 230 = 2078 MeV. However, the fission products must
pass through intermediate states of high energy provided by the Coulomb barrier,
similar to the situation in Fig. 9.6(b). The fission can take place by tunnelling
through the barrier, but with a rather long lifetime (for
238
U it is about 10
16
years).
The fission of a nucleus can be induced by bombarding the nucleus with
neutrons. Consider, for example, the capture of a slow neutron by a nucleus of
235
U. This leads to the formation of the compound nucleus
236
U in which the
small kinetic energy and the binding energy of the neutron are released. The