Download Note 2e - Decay Processes

PHY583 – Note 2e – Decay Processes
DECAY PROCESSES
Alpha Decay
When a nucleus emits -particle, it loses 2 protons & 2 neutrons.
...................13.12
X is parent nucleus & Y is daughter nucleus.
E.g.
Another e.g.:
-decay processes release energy because the decay product, especially the -particle, are more
tightly bound than the parent nucleus.
Fig. 13.6 depicts the spontaneous decay of
.
General rule:
1. The sum of mass number A must be the same for both sides of the equation.
2. The net charge must be the same on both sides of the equation.
3. The total relativistic energy & momentum must be conserved.
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PHY583 – Note 2e – Decay Processes
Fig. 13.16 -decay of radium.
Disintegration energy Q:
Q = (MX  MY  M)c2 ..................13.15
MX is the atomic mass of the parent.
MY is the mass of the daughter.
M is the mass of -particle.
Note: the atomic mass rather than the nuclear mass can be used here, because
the electronic masses cancel in an evaluation of the mass differences.
The unit of Q is joules (J) if the masses are in kg & c in 3.00 × 108 m/s.
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PHY583 – Note 2e – Decay Processes
Q value of the nuclear reaction in MeV, if the masses are given in atomic mass
unit u.
Q = (MX  MY  M)
.............13.16
As illustrated in Fig. 13.16, lighter -particle recoils with a much higher speed
than the daughter nucleus.
Generally, light particles carry off most of the energy in nuclear decays.
By applying conservation of energy & momentum to the -decay:
Q = KY + K .............13.17
pY = p ..............13.18
Y stands for the daughter nucleus.
From eqn. 13.17 & 13.18, we can show that:
...............13.19
MY & M are the atomic masses of the daughter nucleus &  particle.
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PHY583 – Note 2e – Decay Processes
Mechanism of  decay
Imagine that an -particle is formed within the nucleus.
Fig. 13.17 is a plot of potential energy vs distance r from the nucleus for a
typical  particle-nucleus system, where R is the range of the nuclear force.
The curve represents the combined effects of
1. The repulsive force which gives the positive peak for r > R.
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PHY583 – Note 2e – Decay Processes
2. The nuclear attractive force, which causes the curve to be negative for r
< R.
The disintegration energy Q when radium decays is  5 MeV, which is the
approximate kinetic energy of the  particle.
Since the potential barrier in Fig. 13.17 is 30 MeV, therefore according to
classical physics the  particle will be trapped in the potential well.
How then it can ever escape the nucleus?
From quantum mechanics point of view, there is always some probability that
the particle can penetrate (tunnel through) the barrier.
Recall: the probability of locating the particle depends on its wavefunction
the probability of tunnelling is measured by
&
.
Fig. 18.18 is a sketch of a wavefunction for a particle of energy E meeting a
square barrier of finite height, a shape that approximate the nuclear barrier.
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PHY583 – Note 2e – Decay Processes
Note: The wavefunction exists both inside & outside the barrier. Although the amplitude is much
smaller outside the barrier, there is still a finite probability for the particle to penetrate the barrier.
The probability for the particle to escape the barrier increases as:
1. The energy of the particle increases
2. The width of the barrier decreases
Beta Decay
When a radioactive nucleus undergoes - decay, the daughter nucleus has the same number of
nucleons as the parent nucleus, but the atomic number is changed by 1:
................13.20
....................13.21
The nucleon number & total charge are conserved in eqn. 13.20 & 13.21.
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PHY583 – Note 2e – Decay Processes
In  decay, a neutron changes into protons or vice versa.
However, eqn. 13.20 & 13.21 violate conservation of energy as illustrated by
the following results of experiment:
It is found that  particle from a single type of nucleus are emitted with
a continuous range of kinetic energies up to a maximum value, Kmax (Fig.
13.9).
Kinetic energy of the system = decrease in mass-energy
after the decay
of the system (i.e. Q value)
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PHY583 – Note 2e – Decay Processes
Because all parent nuclei of a given type have the same initial mass, the
Q value must be the same for each decay.
Since the daughter nucleus carry off very little kinetic energy, all the
emitted  particles should have a single kinetic energy.
However, Fig. 13.9 shows that the  particles have many different kinetic
energies including, Kmax which equals Q-value.
Conservation of energy is violated.
Hence, there must be other particle emitted together with the 
particles to account for the “missing” energy.
It turns out that the linear momentum & angular momentum are also violated,
and a third particle is needed in order for both momenta to be balanced
before & after the  decay
Later, Pauli in 1930 proposed a third particle, he called neutrino (), that must
be present in -decay to account for the “missing” energy & momentum.
Neutrino was finally detected experimentally in 1956.
Properties of neutrino:
1. Zero electric charge.
2. The rest mass is much smaller than that of electron  2.8 eV/c2.
3. A spin of , which satisfies the law of conservation of angular
momentum.
4. Very weak interaction with matter, very difficult to detect.
General form of -decay:
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PHY583 – Note 2e – Decay Processes
...............13.22
..............13.23
is the antineutrino, which is the antiparticle to the neutrino.
In
decay neutron is converted to proton and antineutrino is emitted
In
decay proton is converted to neutron and neutrino is emitted
A process that competes with e+ decay is called electron capture.
This occurs when a parent nucleus captures one of its own orbital atomic
electrons & emits a neutrino.
The final product after decay has a charge of Z  1:
..............13.24
In most cases it is the inner K-shell electron that is captured, where it is
referred to as K-capture.
E.g. K-capture when
captures an electron to become
.
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PHY583 – Note 2e – Decay Processes
Q values for
decay & electron capture: Q = (MX  MY) c2
Q values for
decay: Q = (MX  MY  2me ) c2
MX & MY are masses of neutral atoms.
Gamma Decay
Very often, a nucleus that undergoes radioactive decay is left in an excited
energy state.
The nucleus can then undergo a second decay to a lower energy state, perhaps
to the ground state, by emitting high-energy photons called gamma rays.
..........13.25
X* is nucleus in an excited state.
The typical half-life of an excited nuclear state is 1010 s.
Energy range of gamma rays, 1 MeV to 1 GeV, is very high relative to the
energy of visible light ( 1eV).
Recall: energy of photons emitted (absorbed) by an atom equals the difference
in energy between the two electronic states involved in the transition.
Similarly, gamma ray photons has an energy hf that equals the energy
difference E between two nuclear energy levels.
When a nucleus decays by emitting a gamma ray, the nucleus doesn’t change
its atomic mass A or atomic number Z.
A nucleus may reach an excited state after a violent collision with another
particle.
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PHY583 – Note 2e – Decay Processes
It is also very common for a nucleus to be in an excited state after undergoing
an  or  decay.
A typical sequence of events in which gamma decay occurs:
..............13.26
.................13.27
Fig. 13.20 shows the decay scheme of
.
It undergoes beta decay with a half-life of 20.4 ms to either of two levels of
:
1. Decay directly to the ground state of
or
2. Undergoes e decay to an excited state of
by emitting 13.4 MeV electron
, followed by decay to
the ground state which results in emission of 9.0 MeV electron & 4.4
MeV photon.
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PHY583 – Note 2e – Decay Processes
Table 13.4 summarizes the pathways by which a radioactive nucleus can
undergo decay
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PHY583 – Note 2e – Decay Processes
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