radioactive decay l.
Skip this Video
Loading SlideShow in 5 Seconds..
Radioactive Decay PowerPoint Presentation
Download Presentation
Radioactive Decay

Loading in 2 Seconds...

play fullscreen
1 / 43

Radioactive Decay - PowerPoint PPT Presentation

  • Uploaded on

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

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

PowerPoint Slideshow about 'Radioactive Decay' - flora

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
radioactive decay

Radioactive Decay

Professor Jasmina Vujic

Lecture 3

Nuclear Engineering 162

Department of Nuclear Engineering

University of California, Berkeley

spontaneous nuclear transformation radioactivity
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.
types of radioactive decay
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.
types of radioactive decay4
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

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

induced nuclear transformations nuclear reactions
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.
the conservation laws in nuclear transformations nt
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
alpha decay
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

a decay

- involves strong and coloumbic forces

- alpha particle and daughter nucleus have equal and opposite momentums

(i.e. daughter experiences “recoil”)

beta decay
Beta Decay
  • Beta minus decay:
  • Neutron →proton (p+) + electron (e-) + antineutrino
  • Beta plus decay:
  • Proton (p+) → neutron + positron (e+) + neutrino

 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

gamma decay
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.
orbital electron capture ec
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).
spontaneous fission
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.

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

isomeric transition it
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.
neutron emission
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)
the radioactive decay law
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)

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


t1/2 = 5730y



The solution is easily found using an integrating factor:

Where N0 is the number of nuclei at t = 0.

derivation of decay law
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

the mean lifetime
The Mean Lifetime

The probability density function (pdf) for radioactive decay is defined as:

The mean lifetime of radionuclide is defined as

the half life
The Half-life

Units of activity

1 Ci (curie) = 3.7 x 1010 dis/s

1 Bq (becquerel) = 1 dis/s


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?


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

serial radioactive decay chain decay
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:
general cases for chain decay
General Cases for Chain Decay
  • There are three general cases for formulating chain decay:
    • Secular Equilibrium, Tp >> Td
    • Transient equilibrium, Tp > Td
    • No equilibrium



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


Decay chains and secular equilibrium (cont)


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.