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Radioactive Decay. Professor Jasmina Vujic Lecture 3 Nuclear Engineering 162 Department of Nuclear Engineering University of California, Berkeley. Spontaneous Nuclear Transformation - Radioactivity. Only certain combinations of protons and neutrons form a stable nucleus

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Radioactive decay l.jpg

Radioactive Decay

Professor Jasmina Vujic

Lecture 3

Nuclear Engineering 162

Department of Nuclear Engineering

University of California, Berkeley


Spontaneous nuclear transformation radioactivity l.jpg
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 Z=92 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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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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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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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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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

    • λ: Decay constant (each isotope has different )

    • tH: Half-life (each isotope has different half-life)



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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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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 (t+dt) 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?

T=200y

t1/2 = 5730y so l = 0.693/5730y = 1.209e-4 y-1

N0=A0/l so N0=(13.56dpm*60m/hr*24hr/day*365days/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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General Cases for Chain Decay

  • There are three general cases for formulating chain decay:

    • Secular Equilibrium, Tp >> Td

    • Transient equilibrium, Tp > Td

    • No equilibrium


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234Th

24d

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 --> radioactive daughters --> 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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Decay chains and secular equilibrium (cont)

Ex:

where l1>>l2

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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