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Decay Mechanisms
1. Alpha Decay
An alpha particle is a helium-4 nucleus. This is a very stable entity and alpha emission
was, historically, the first decay process to be studied in detail. Almost all naturally
occurring alpha emitters are heavy elements with Z > 82. This is the only way a heavy
nucleus can reduce its nucleon number, A.
The laws of conservation of charge and of nucleons require that for alpha decay,
A
Z
P→
A− 4
Z −2
D + 24 He + Q
3.1
where Q is the energy release in the decay, the disintegration energy.
An example is
212
83
Bi →
Tl + 24 He
208
81
If the radioactive parent is taken to be initially at rest, the conservation laws of energy
and of linear momentum yield
MPc2 = (MD + Mα)c2 + KD + Kα
3.2
MDvD = Mαvα
3.3
where the M’s are the atomic rest masses of the parent, daughter, and helium atom, and
the K’s and v’s are the kinetic energies and velocities of the daughter and α particle.
Since the kinetic energies KD and Kα can never be negative, α decay is energetically
possible only if
MP > M D + M α
If this inequality is not satisfied, α decay simply cannot occur. In other words, decay is
energetically possible only for Q > O.
Q = KD + Kα = (MP – MD - Mα)c2
3.4
In an α decay, it’s the energy of the α particle, Kα, that is usually measured, for example
by measuring its radius of curvature in a magnetic field. So, how is Kα related to Q?
Squaring the masses in the kinetic energy equation above (3.2), and multiplying each side
by ½ gives:
MD(½MDvD2) = Mα(½Mαvα2)
1
MDKD = MαKα
In atomic mass units, the daughter and the α masses are approximately A – 4 and 4 u,
respectively. Then the equation above becomes
(A – 4)KD = 4Kα
But
4 ⎞
⎛
Q = Kα + KD = Kα ⎜1 −
⎟
A− 4⎠
⎝
and therefore
Kα =
A−4
Q
A
3.5
Since most alpha emitters are those with large A (i.e. A >> 4), Kα is only slightly less
than Q; nearly all the energy released in the decay is carried away as kinetic energy by
the light particle.
The equation above also shows that in two-particle emission from an initially unstable
nucleus at rest, the α particle emerges with a precisely defined energy; since Q has a
precise value, so does Kα.
This does not mean that all alpha emitters emit only one alpha energy. Some alpha
decays leave the daughter nucleus in one of a number of discrete excited states as well as
the ground state. This means that the emitter can emit a group of alpha particles all at
discrete energies.
Over 300 α emitters have been identified. The emitted α particles have discrete energies
from about 4 to 10 MeV, a factor of 2, but half-lives ranging from 10-6 to 1017 s, a factor
of 1023. Short-lived α emitters have the highest energies, and the contrary, as indicated
by the examples in the table below.
α emitter
238
92 U
Kα(MeV)
4.19
T ½ (s)
1.42 x 1017
λ (s-1)
4.9 x 10-18
212
83
Bi
6.09
3.64 X 103
1.90 X 10-4
215
85
At
8.00
10-4
104
Hazard:
Alpha particles have a very limited range, and can’t even penetrate the outer, dead layer
of skin. They therefore generally pose no direct external hazard to the body. However,
ingestion or inhalation of alpha-emitters can lead to damage to internal organs, such as
the inhalation of the daughters of radon gas. We’ll be discussing this in more detail later
in the course.
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Decay Schemes:
A decay scheme is a graphical or schematic representation of nuclear transformations
showing decay mode, energy transitions, and abundance (branching ratios). It consists of
a qualitative plot of energy (vertical axis) versus atomic number (horizontal axis).
Transitions leading to an increase in Z are indicated by an arrow slanting down and to the
right. Those leading to a decrease in Z are indicated by a downward arrow to the left.
Gamma emission, which results in no change in z, is indicated by a vertical wavy line.
Below is the decay scheme for radium-226 which decays by alpha decay to radon-222 by
one of two paths. One path is 94.4 % probable and leads directly to the ground state of
the daughter and leads to the emission of a 4.785 MeV alpha particle. The other pay is
5.5% abundant and leads to an excited state of the daughter nucleus via the emission of a
4.602 MeV alpha particle. The excited state of radon drops down to the ground state via
emission of a gamma ray within about 10-14 seconds. The gamma ray energy is equal to
the 4.785 – 4.602 = 0.186 MeV. [Note that gamma emission occurs only 3.3 % of the
time, indicating that 2.2 % of the time, the energy of excitation is lost via another process.
This is internal conversion, described on page 12.]
Beta (β) Decay
Beta decay can be defined as the radioactive decay process in which the charge of
the nucleus is changed without any change in the number of nucleons. There are three
types of beta decay: β− decay, β+ decay, and electron capture.
2. β− Decay
Nuclides with neutron excess lie to the right of the line of stability on the Z vs. N
plot and need to convert a neutron to a proton via the β− decay process. Again we will
invoke conservation of electric charge and conservation of nucleons in describing the
decay of the parent nucleus P into the daughter D:
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A
Z
P→
A
Z +1
D +
0
−1
0
e + 0ν
3.6
The symbol ν represents the neutrino, and ν represents its antiparticle, the antineutrino.
Neutrinos (and antineutrinos) are chargeless particles with little or no mass. They
interact extremely weakly with nuclei and are consequently very difficult to detect.
An example of beta minus decay is:
60
27
60
Co→ 28
Ni +
0
−1
0
e + 0ν
The cobalt nucleus has too many neutrons to be stable. The unstable cobalt nucleus
decays to a lower state by changing one of its nucleons from a neutron to a proton. This
changes the nucleus to a Ni nucleus, and, to conserve electric charge, one unit of negative
charge must be created. Since an electron cannot exist within the nucleus, the created
electron, or beta particle, must be emitted from the decaying nucleus.
What are the requirements for β− decay? We simply need the mass of the parent to
exceed the mass of the daughter, MP > MD. Let’s look at how that comes about.
Mass-energy conservation requires that the rest mass (energy) of the parent nucleus, MP –
Zme, exceed the rest masses (energies) of the daughter nucleus, MD – (Z +1)me, and the
electron me, where MP and MD are the neutral atomic masses of the parent and daughter.
Any excess energy Q, that is, energy released in the decay, appears as kinetic energy of
the particles emerging from the decay. Therefore,
MP – Zme = [MD – (Z +1)me] + me +
Mp = MD +
Q
c2
Q
c2
3.7
Thus β− decay is possible whenever MP > MD. Further, whenever β− decay can occur it ,
although the probability may be small and the half-life extremely long.
So, where does the disintegration energy go? (i.e. the energy released in going from the
less stable (60Co) to the more stable (60Ni) entity. The energy is shared between the
recoil 60Ni nucleus, the beta particle, and the antineutrino. Thus, beta particles are
emitted in a decay into three bodies which can share energy and momentum in a
continuum of ways, resulting in a spectrum of possible beta particle energies. [This is
unlike alpha particles which are emitted in a decay into two bodies which must share
energy and momentum in a unique way; this gives rise to discrete alpha energies.] A
typical beta-particle spectrum is shown below. Note that the maximum beta partilce
energy, Kmax, is observed when the anti-neutrino receives no kinetic energy and, since the
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mass of the daughter nucleus is so large, it receives negligible kinetic energy, and the
entire Q will be given to the beta particle.
It was the appearance of the beta particle spectrum that led Wolfgang Pauli to postulate
the existence of neutrinos and antineutrinos. If they didn’t exist, beta emission would
occur at discrete energies only (like alphas). The neutrino avoids what would otherwise
be a violation of the principles of the conservation of momentum, angular momentum and
energy. Further, without the neutrino the daughter nucleus and β− particle would move in
opposite directions, contrary to observation.
Below is the decay scheme for cobalt-60 which decays by β- decay, leading to the 2.505
MeV excited state of nickel-60. This 60Ni* nucleus immediately decays be a two-photon
gamma cascade.
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3. β+ Decay
Nuclides that are excessively proton rich lie to the left of the stability line on the Z vs. N
plot and can decay by positive electron (positron) emission. The nuclide attempts to gain
stability by increasing the N/Z ratio by conversion of a neutron to a proton.
P→ Z −A1 D + +10 e + ν
Let’s now look at the energetics involved: Again we want to include all electron masses:
A
Z
MP – Zme = [MD – (Z-1)me] + me +
Q
c2
We no longer see all electron masses canceling on both sides of the equation. Instead we
see that β+ is energetically possible only if the mass of the parent atom exceeds the mass
of the daughter atom by at least two electron masses (2 x .000549 u or its energy
equivalent, 1.02 MeV). MP > MD + Zme
MP = MD +2me +
Q
c2
3.8
Additional radiations are observed with positron decay. The positron, the anti-matter
equivalent of the electron, has only a limited lifetime. A positron will slow down in
matter and then combine with an atomic electron in the material (making ‘positroniuim’).
The positron-electron pair then annihilates, giving rise to two photons, each having
energy 0.511 MeV and travelling in opposite directions. This phenomenon (which we’ll
investigate in more detail later in the course) is the basis of Positron Emission
Tomography (PET imaging).
4. Electron Capture
Some nuclides are too neutron rich for stability, but positron emission is not possible
because the masses of the parent and daughter nuclides differ by less than 1.02 MeV. In
this situation the nuclide can undergo the process of electron capture which has the same
effect on the nucleus as β+ decay (reducing Z by one but leaving A unchanged) but has no
emissions from the nucleus. The general relation for electron capture is written:
0
−1
e + ZA P→ Z −A1 D + ν
In electron capture, an orbital electron is captured by the parent nucleus, and the products
are the daughter nucleus and a neutrino.
Mass energy is conserved when the energy Q released in the decay equals the sum of the
rest masses entering the reaction minus the sum of the rest masses leaving the reaction.
Therefore,
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me + (MP – Zme) = [MD – (Z – 1)me] +
MP = MD +
Q
c2
Q
c2
3.9
Thus, electron capture is possible if MP > MD.
In an electron-capture decay, energy is released. Where does it go? Unlike β+ and β−
decay, electron capture produces only two particles. By momentum conservation, the
neutrino and the daughter nucleus must move in opposite directions with the same
momentum magnitude; the sum of their kinetic energies is the disintegration energy Q.
Because only two particles appear in electron capture, each has a precisely defined
energy. The neutrino’s rest mass is (probably) zero; therefore, almost all the energy is
carried by a virtually unobservable neutrino, and the nucleus recoils with an energy of
only a few electron volts. Nevertheless, some very delicate experiments have confirmed
that the recoiling nuclei are monoenergetic and their energy is precisely the amount
required to satisfy the laws of momentum and energy conservation. Without the
accompanying neutrino in electron capture, this decay process is completely inexplicable.
The most common electron capture process is one in which the nucleus captures a K shell
electron. This is because the K shell electrons are closest to the nucleus; the electron
cloud can even overlap the nucleus. Thus, although capture of electrons from other shells
is possible, electron capture is sometimes referred to as “K-capture”.
Shown below is the decay scheme for 22-sodium. The energy levels are drawn relative to
the ground state of 22Ne as having zero energy. This nuclide decays by both positron
emission and electron capture. In (a) we see the positron decay illustrated, showing that
the daughter nucleus, neon-22, is left in an excited state. This energy of excitation is
given off immediately in the form of a gamma ray. Positron emission is 89.8 % possible
and the accompanying gamma ray is given off with every positron decay. In (b) we see
the electron capture decay illustrated. This process occurs 10.2 % of the time and leaves
the neon daughter in the same excited state. In (c) the complete decay scheme for 22Na is
shown. The starting EC level is 2mc2 higher than the starting level for positron decay.
[You should ask yourself why an energy difference of two electron masses is shown.]
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Electron capture always leaves the atom with an orbital vacancy in an inner shell. These
inner shells are higher energy shells than those farther from the nucleus and so the atom
will rearrange its electron structure so as to get to a lower energy state. It will do this by
allowing an electron in an outer (lower energy) shell to drop down into the inner (high
energy) shell. When this happens the difference in energy is given off as electromagnetic
radiation, i.e. a photon. This photon (as you already know) is called fluorescence.
So, while there are no detectable radiations emitted by the nucleus during electron
capture (the neutrino is really not detectable), there is atomic radiation detected. Note
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however, that since the electron capture results in a new nuclide and the orbital
rearrangement occurs in that nuclide, the fluorescent photons are representative of the
daughter, not the parent.
When the K-shell vacancy is filled by an electron from the L shell, the M shell, and so
on, the photons are called Kα, Kβ etc. Similarly, if an L-shell vacancy is filled the
photons are designated Lα, Lβ etc.
The diagram below illustrates the phenomenon of fluorescence as well as the competing
process of Auger electron emission.
Auger Electrons
There is another process that competes with fluorescence. That is, an atom in which an
L-shell electron makes a transition to fill a K-shell electron does not always emit a
photon, especially if the element is low Z. A different transition can occur in which an L
electron is ejected from the atom, thereby leaving two vacancies in the L shell. The
ejected electron is called an Auger electron.
The fluorescence yield of an element is defined as the number of photons emitted per
vacancy. Fluorescence yield varies from essentially zero for the low Z elements to
almost 1.0 for high Z, as shown in the plot below. Thus, Auger electron emission is
favored over photon emission for light elements.
Note that orbital vacancies can arise from a number of processes. We’ve seen the
consequences of vacancies caused by electrons hitting the atom and knocking out orbital
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electrons (cathode ray tubes) and vacancies cause by electron capture. They can also be
caused by internal conversion (see below) or by ejection of electrons by photoelectron
absorption of a photon ( a topic to be covered later in the course).
Note that emission of an Auger electron increases the number of vacancies in the atomic
shells by one unit. Often we see Auger cascades in relatively heavy atoms as inner-shell
vacancies are successively filled by the Auger process with simultaneous ejection of the
more loosely bound atomic electrons. An original, singly charged ion with one innershell vacancy can thus be converted into a highly charged ion by an Auger cascade. This
phenomenon is being studied in radiation research and therapy. Auger emitters can be
incorporated into DNA and other biological molecules. For example, 125I decays by
electron capture. The ensuing cascade can release some 20 electrons, depositing a large
amount of energy (~ 1 keV) within a few nanometers. A highly charged 125Te ion is left
behind. A number of biological effects can be produced, such as DNA strand breaks,
chromatid aberrations, mutations, bacteriophage inactivation, and cell killing.
5. Gamma Decay
All stable nuclides are ordinarily in their lowest, or ground, states. If such nuclei are
excited and gain energy by photon or particle bombardment, they may exist in any one of
several excited, quantized energy states. Excited nuclei can emit their energy excitation
as a photon. A photon emitted from the nucleus in an excited state is called a gamma ray.
[This distinguishes such photons from ‘x-rays’ which is the term used to refer to photons
emitted from the atomic structure. Two examples of ‘x-rays’ are the fluorescent
radiations (“characteristic x-rays”) observed when inner vacancies are filled, and the
photons produced when an electron undergoes a change in acceleration in the field of a
nucleus (bremsstrahlung – see notes from Lecture 1 page 5).
0.492 MeV _________________________________
0.472 MeV _________________________________
0.327 MeV _________________________________
γ
γ
γ
γ
γ
0.040 MeV _________________________________
0 _________________________________
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Alpha or beta decay often leaves the daughter nucleus in an excited state instead of the
ground state. This is often represented by an asterisk beside the symbol of the nuclide,
e.g. AZ*
Z → AZ + γ
A *
Gamma decay is very rapid, occurring with a half-life on the order of 10-14 seconds.
A few gamma decaying nuclides have much longer half-lives, for example greater than
10-6s and thus relatively easy to measure. These nuclides are given the name “isomers”.
An isomer is not chemically distinguishable from the lower-energy nucleus into which it
slowly decays.
6. Internal Conversion
A process that competes with gamma emission from an excited nucleus is internal
conversion. In this process the nucleus transfers its energy of excitation to one of the
inner atomic electrons. This electron, originally bound to the atom with binding energy
Eb, leaves the atom with a kinetic energy, Ke, equal to:
Ke = E*- Eb
where E*is the energy of excitation of the nucleus.
The internal conversion coefficient α for a nuclear transition is defined as the ratio of the
number of conversion electrons Ne and the number of competing gamma photons Nγ
for that transition:
Ne
α=
.
Nγ
The conversion coefficient α increase as Z3, the cube of the atomic number, and
decreases with E*. Internal conversion is thus prevalent in heavy nuclei, especially in the
decay of low-lying excited states (small E*). Gamma decay predominates in light nuclei.
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This concludes our discussion of decay mechanisms. You need to make sure you
understand both what a decay scheme is showing you, and how to construct one given
emission and energy data.
Example: work out the decay scheme for 137Cs which undergoes β- decay using the
following information:
Q = 1.174 MeV
βmax: 1.174 MeC (5%)
βmax: 0.512 MeC (95%)
γ : 0.662 (85%, 137mBa), Ba X-rays
e- : 0.624, 0.656
Beta minus decay of cesium-137 leads to a nucleus with the same A but with a Z
increased by one, therefore the daughter is Barium-137. From the radiation emission
information given, we can see that 5 % of the time, beta decay leads directly to the
ground state of the barium nucleus since the maximum beta energy is the same as the Q
for this decay. We can illustrate this on a decay scheme by drawing a line downward to
the barium daughter, and slanting to the right, indicating an increase in Z. 95 % of the
time beta decay occurs via a different path. This beta has a lower maximum energy,
indicating the decay leads to an excited state of the daughter. The energy of the daughter
in this case is 1.174 - 0.512 MeV=0.662 MeV. A photon of this energy occurs with 85%
frequency. Therefore, internal conversion occurs in 95-85 = 10% of the decays, giving
rise to conversion electrons, e-. The conversion electron energies reflect the excitation
energy, 0.662 MeV, minus the binding energies of two different orbital shells, most likely
the K, and L shells. Characteristic Ba X-rays are emitted following the inner-shell
vacancies created in the atom by internal conversion.
The plot below shows the spectrum of electron energies from cthe decay of cesium-137.
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