Radioactive Decay

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Radioactive Decay

• Professor Jasmina Vujic
• Lecture 3
• Nuclear Engineering 162
• Department of Nuclear Engineering
• University of California, Berkeley

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Spontaneous Nuclear Transformation - Radioactivity

• Only certain combinations of protons and neutrons
  form a stable nucleus
• Unstable nuclei undergo spontaneous nuclear
  transformations, with a formation of new elements
  and emission of charges and/or neutral particles
• These unstable isotopes are called radioactive
  isotopes, and the spontaneous nuclear
  transformation is called radioactivity.

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Types of Radioactive Decay

• The type of radioactive decay depends on the
  particular type of nuclear instability (whether
  the neutron to proton ratio is either too high or
  too low) and on the mass-energy relationship
  among the parent nucleus, daughter nuclear, and
  emitted particle.

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Types of Radioactive Decay

• Usually, radioactive decays are classified by
  types of particles that are emitted during the
  decay
• Alpha decay
• Beta decay
• Gamma decay
• Electron capture (EC)
• Internal conversion (IC)
• Spontaneous fission
• Isomeric transition (IT)
• Neutron emission

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Four types of radioactive decay
1) alpha (a) decay - 4He nucleus (2p 2n)
ejected 2) beta (?) decay - change of nucleus
charge, conserves mass 3) gamma (g) decay -
photon emission, no change in A or Z 4)
spontaneous fission - for Z92 and above,
generates two smaller nuclei
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Induced Nuclear Transformations - Nuclear
Reactions

• An event in which, because of interaction with a
  particle or radiation (a projectile), a nucleus
  (target) is changed in mass, charge or energy
  state, and particles or radiation is emitted.

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The Conservation Laws in Nuclear Transformations
(NT)

• Conservation of Charge - the number of elementary
  positive and negative charges must be equal
  before and after NT
• Conservation of the number of nuclides - A is the
  same before and after NT
• Conservation of mass/energy - the total energy
  (rest mass energy plus kinetic energy) is the
  same before and after NT
• Conservation of linear momentum
• Conservation of angular momentum

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Alpha Decay

• Heavy nuclei with mass numbers higher than 150
  can disintegrate by emission of an ALPHA
  PARTICLE.
• Alpha particle is a nucleus of helium containing
  two neutrons and two protons
• Example

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a decay
- involves strong and coloumbic forces - alpha
particle and daughter nucleus have equal and
opposite momentums (i.e. daughter experiences
recoil)
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Alpha Decay
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Beta Decay

• Beta minus decay
• Neutron ?proton (p) electron (e-)
  antineutrino
• Beta plus decay
• Proton (p) ? neutron positron (e) neutrino

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? decay - two types
1) ?- decay
- converts one neutron into a proton and
electron - no change of A, but different
element - release of anti-neutrino (no charge, no
mass)
2) ? decay
- converts one proton into a neutron and a
positron - no change of A, but different
element - release of neutrino
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Beta Decay
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Gamma Decay

• Sometimes the newly formed isotopes (after alpha
  or beta decay) appear in the excited state (with
  a surplus of energy). Excited nuclides have
  tendency to release the excess of energy by
  emission of gamma rays (Photons) and return to
  their ground state.

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Beta-EC-Gamma Decay
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Beta-Gamma Decay
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Beta-Gamma Decay
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Orbital Electron Capture (EC)

• In addition, an X-ray characteristic of the
  daughter element is emitted as an electron from
  an outer shell falls into K-shell.
• Internal Conversion (IC)
• Is an alternative mechanism in which an excited
  nucleus may rid itself of the excitation energy
  from the nucleus by ejecting a tightly bound
  electron (K or L shell).

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Electron Capture
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Spontaneous Fission

• This is another type of decay that heavy nuclei
  can undergo they decay by splitting into two
  lighter nuclei with the release of several
  neutrons
• In addition, large amount of energy is released
  per fission event. Similar process called INDUCED
  FISSION is used in nuclear reactor.

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g decay
- conversion of strong to coulombic E - no change
of A or Z (element) - release of photon - usually
occurs in conjunction with other decay
Spontaneous fission
- heavy nuclides split into two daughters and
neutrons - U most common (fission-track dating)
Fission tracks from 238U fission in old zircon
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Isomeric Transition (IT)

• A nuclide formed after a nuclear transformation
  may be a long-lived metastable or isomeric state.
  The decay of isomeric state by emission of gamma
  rays is called isomeric transition (IT).
• Mo-99 decay by beta(-) decay into Tc-99m
  metastable state of Tc-99. It decays by gamma ray
  emission into Tc-99 ground state with 6 hr
  half-life.

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Neutron Emission

• There are nuclides which undergo a spontaneous
  transformation with emission of neutrons
• Br-87 (55.6 s), I-137 (22.0 s), Br-88 (15.5 s)

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The Radioactive Decay Law

• The rate at which a radioactive isotope
  disintegrates is defines by the following DECAY
  LAW
• Where
• N Number of atoms of a radioactive isotope at
  time t
• N0 Number of atoms at time zero
• ? Decay constant (each isotope has different )
• tH Half-life (each isotope has different
  half-life)

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The Radioactive Decay Law
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Radioactive Decay
- a radioactive parent nuclide decays to a
daughter nuclide - the probability that a decay
will occur in a unit time is defined as l (units
of y-1) - the decay constant l is time
independent the mean life is defined as ?1/l
N0
t1/2 5730y
5730
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The Radioactive Decay Law
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Derivation
The solution is easily found using an integrating
factor
Where N0 is the number of nuclei at t 0.
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Derivation of Decay Law
If there is no source (Q 0), the result is
simple exponential decay
Activity is then defined as
Probability of decay between t and (tdt) is
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The Mean Lifetime
The probability density function (pdf) for
radioactive decay is defined as
The mean lifetime of radionuclide is defined as
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The Half-life
Units of activity
1 Ci (curie) 3.7 x 1010 dis/s
1 Bq (becquerel) 1 dis/s
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Activity calculations
- SA (Specific activity) disintegrations per
sec per g of parent atom) - usually reported in
Bq (disintegrations per sec), example
(calculate SA of 14C) ? Bq / gram C
- because activity is linearly proportional to
number N, then A can be substituted for N in
the equation
Example calculation
How many 14C disintegrations have occurred in a
1g wood sample formed in 1804AD? T200y t1/2
5730y so l 0.693/5730y 1.209e-4
y-1 N0A0/l so N0(13.56dpm60m/hr24hr/day36
5days/y) /1.209e-4 5.90e10 atoms N(14C)N(14C)0
e-(1.209e-4/y)200y 5.76e10 atoms decays
N0-N 2.4e9 decays
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Serial Radioactive Decay (Chain Decay)

• A simple case of chain decay is the decay of a
  radionuclide (Parent) to a second radionuclide
  (Daughter), which then decays to a stable
  element

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Serial Radioactive Decay (Chain Decay)
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General Cases for Chain Decay

• There are three general cases for formulating
  chain decay
• Secular Equilibrium, Tp gtgt Td
• Transient equilibrium, Tp gt Td
• No equilibrium

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Decay chains and secular equilibrium
- three heavy elements feed large decay chains,
where decay continues through radioactive
daughters until a stable isotope is reached 238U
--gt radioactive daughters --gt 206Pb Also 235U
(t1/2) 700My And 232Th (t1/2)10By
After 10 half-lives, all nuclides in a decay
chain will be in secular equilibrium, where
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Secular Equilibrium
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Decay chains and secular equilibrium (cont)
Ex
where l1gtgtl2
The approach to secular equilibrium is dictated
by the intermediary, because the parent is
always decaying, and the stable daughter is
always accumulating.
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Transient Equilibrium