The Nucleus
343
(∆E) max > E c
(9.82)
On using Eqs. (9.80) and (9.81) with R ≈ 12(A/2)
1/3
fm, the inequality reduces
to
Z
2
> 65 A
(9.83)
This condition is not satisfied even in the case of the heaviest known nucleus
2 6 2
1 0 5 Ha (hahnium) for which Z
2
/A ≈ 42. Thus all the observed fission processes
are expected to produced by tunnelling through the potential barrier.
A fission process is initiated by bombarding a nucleus with neutrons, giving
an excited initial state such as
236
U*, and forms the basis of nuclear fission
reactors used for tapping large nuclear energies.
Gamma Decay
A nucleus may be found in an excited state if it is one of the products in an
alpha or a beta decay. The excitation energy here is provided by the higher mass
of the decaying particle. Alternatively, the excitation may take place as a result
of a collision in which the projectile excites the nucleus by transferring to it
some of its kinetic energy. In either case, the excited nucleus usually undergoes
transition to a lower state by emitting a photon,
Z* → Z + γ
(9.84)
An example of γ-decay is the de-excitation of
208
Tl discussed earlier. The
energy of the photon emitted is
hv ≈ E* – E
(9.85)
i.e. the difference in the energies of the number states.
The lifetimes for γ-decay are usually of the order of 10
–14
s. However,
selection rules may inhibit some of these decays leading to mush longer lifetimes
of the excited states are sufficiently long so as to be directly measurable, the
nuclei are known as isomers. An example of extreme isomerism is
91
Nb* which
has a lifetime of about 87 days.
Radioactive Series
In nature one observes several decays of radioactive elements some of which
were created in the early stages of the evolution of the universe, others which
are continuously formed by the bombardment of cosmic rays (see Sec. 10.6).
Of special interest are the ones which form what are known as the radioactive
series.
All nuclei with A > 209 are unstable and normally undergo either α-decay,
β-decay, or γ-decay. Since the changes in the number of nucleons A, are due
only to α-decay, the mass numbers A of the series of nuclei produced in a series
are related by
343
(∆E) max > E c
(9.82)
On using Eqs. (9.80) and (9.81) with R ≈ 12(A/2)
1/3
fm, the inequality reduces
to
Z
2
> 65 A
(9.83)
This condition is not satisfied even in the case of the heaviest known nucleus
2 6 2
1 0 5 Ha (hahnium) for which Z
2
/A ≈ 42. Thus all the observed fission processes
are expected to produced by tunnelling through the potential barrier.
A fission process is initiated by bombarding a nucleus with neutrons, giving
an excited initial state such as
236
U*, and forms the basis of nuclear fission
reactors used for tapping large nuclear energies.
Gamma Decay
A nucleus may be found in an excited state if it is one of the products in an
alpha or a beta decay. The excitation energy here is provided by the higher mass
of the decaying particle. Alternatively, the excitation may take place as a result
of a collision in which the projectile excites the nucleus by transferring to it
some of its kinetic energy. In either case, the excited nucleus usually undergoes
transition to a lower state by emitting a photon,
Z* → Z + γ
(9.84)
An example of γ-decay is the de-excitation of
208
Tl discussed earlier. The
energy of the photon emitted is
hv ≈ E* – E
(9.85)
i.e. the difference in the energies of the number states.
The lifetimes for γ-decay are usually of the order of 10
–14
s. However,
selection rules may inhibit some of these decays leading to mush longer lifetimes
of the excited states are sufficiently long so as to be directly measurable, the
nuclei are known as isomers. An example of extreme isomerism is
91
Nb* which
has a lifetime of about 87 days.
Radioactive Series
In nature one observes several decays of radioactive elements some of which
were created in the early stages of the evolution of the universe, others which
are continuously formed by the bombardment of cosmic rays (see Sec. 10.6).
Of special interest are the ones which form what are known as the radioactive
series.
All nuclei with A > 209 are unstable and normally undergo either α-decay,
β-decay, or γ-decay. Since the changes in the number of nucleons A, are due
only to α-decay, the mass numbers A of the series of nuclei produced in a series
are related by