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ß and ? decays, Radiation Therapies and
Diagnostic, Fusion and Fission

• This Lecture Radioactivity, Nuclear decay
  Radiation damage, radiation therapies and
  diagnostic
• Evaluations for Prof. T. Montaruli today
• Previous lecture nuclear physics

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Final Exam

• Fri, Dec 21, at 745-945 am in Ch 2103
• About 40 on new material
• 2 sheets allowed (HAND WRITTEN!)
• The rest on previous materials covered by MTE1
  MTE2 MTE3.

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New material not covered by MTE1,2,3

• Ch 40.4-5 particle in a box wave functions,
  energy levels, photon absorption and emission,
  40.10 tunneling
• Ch 41.1-3 H-atom quantum numbers and their
  meaning, wave functions and probabilities,
  electron spin
• Ch 41.4-6 Pauli exclusion principle,
  multi-electron atoms, periodic table, emission
  and absorption spectra
• Ch 41.8 Stimulated emission and Lasers
• Ch 42.1-3 Nuclear structure, atomic mass,
  isotopes, binding energy, the strong force
• Ch 42.5 Radioactivity, Ch 42.6 Nuclear decay, Ch
  42.7 Biological applications

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Women Nobel Prizes

• The only 2 female Nobel Prizes in Nuclear Physics!

1903 Marie Curie (with Pierre) in recognition of
the extraordinary services they have rendered by
their joint researches on the radiation phenomena
discovered by Professor Henri Becquerel
Maria Goeppert-Mayer 1963 Shell Model of Nucleus
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Nuclear Physics

• Strong force attractive force keeping p and n in
  nucleus (short range)
• It is convenient to use atomic mass units to
  express masses
• 1 u 1.660 539 x 10-27 kg
• mass of one atom of 12C 12 u
• Mass can also be expressed in MeV/c2
• From rest energy of a particle ER mc2
• 1 u 931.494 MeV/c2
• Binding energy mnucleus lt Zmp (A-Z)mn Zmp
  Nmn
• The energy you would need to supply to
  disassemble the nucleus into nucleons Ebinding
  (ZmpNmn-mnucleus)c2 (ZmpZmeNmn
  -Zme-mnucleus)c2 (ZmH Nmn - matom) c2

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Fission and Fusion
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Stable and Unstable Isotopes

• Isotope same Z
• Isotone same N
• Isobar same A

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Stability of nuclei

• Dots naturally occurring isotopes.
• Blue shaded region isotopes created in the
  laboratory.
• Light nuclei are most stable if NZ
• Heavy nuclei are most stable if NgtZ
• As of p increases more neutrons are needed to
  keep nucleus stable
• No nuclei are stable for Zgt83

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Radioactivity

• Discovered by Becquerel in 1896
• spontaneous emission of radiation as result of
  decay or disintegration of unstable nuclei
• Unstable nuclei can decay by emitting some form
  of energy
• Three different types of decay observed
• Alpha decay ? emission of 4He nuclei (2p2n)
• Beta decay? electrons and its anti-particle
  (positron)
• Gamma decay? high energy photons

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Penetrating power of radiation

• Alpha radiation barely penetrate a piece of paper
  (but dangerous!)
• Beta radiation can penetrate a few mm of Al
• Gamma radiation can penetrate several cm of lead

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Is the radiation charged?

• Alpha radiation positively charged
• Beta radiation negatively charged
• Gamma radiation uncharged

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The Decay Rate

• probability that a nucleus decays during ?t
• number of decays (decrease) NxProbrN?t
  Nnumber of independent nuclei

Constant of proportionality r decay rate (in
s-1)
The number of decays per second is the activity
time constant
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The half-life

• After some amount of time, half the radioactive
  nuclei will have decayed, and activity decreases
  by a factor of two.
• This time is the half-life

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Units

• The unit of activity, R, is the curie (Ci)
• The SI unit of activity is the becquerel (Bq)
• Therefore, 1 Ci 3.7 x 1010 Bq
• The most commonly used units of activity are the
  millicurie and the microcurie

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An Example

• 232Th has a half-life of 14 x109 yr
• Sample initially contains N0 106 232Th atoms
• Every 14 billion years, the number of 232Th
  nuclei goes down by a factor of two.

N0
N0/2
N0/4
N0/8
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Radiocarbon dating

• 14C (Z6) has a half-life of 5,730 years,
  continually decaying back into 14N (Z7).
• In atmosphere very small amount! 1 nucleus of 14C
  each 1012 nuclei of 12C

After death, no exchange with atmosphere. Ratio
changes as 14C decays
If material alive, atmospheric carbon mix
ingested (as CO2), ratio stays constant.
So can determine time since the plant or animal
died (stopped exchanging 14C with the atmosphere)
if not older than 60000 yr
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Carbon dating

• A fossil bone is found to contain 1/8 as much 14C
  as the bone of a living animal. Using T1/25,730
  yrs, what is the approximate age of the fossil?

1. 7,640 yrs
2. 17,190 yrs
3. 22,900 yrs
4. 45,840 yrs

Factor of 8 reduction in 14C corresponds to three
half-lives. So age is 5,730 x 3 17,190 yrs
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Decay processes a 4He
Heavy nucleus spontaneously emits alpha particle

• nucleus loses 2 neutrons and 2 protons.
• It becomes a different element (Z is changed)
• Example

Alpha particle
92 protons146 neutrons
90 protons144 neutrons
2 protons2 neutrons
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A quantum process

• This is a quantum-mechanical process
• It has some probability for occurring.
• For every second of time, there is a probability
  that the nucleus will decay by emitting an
  a-particle.
• This probability depends on the width of the
  barrier
• The a -particle quantum-mechanically tunnels out
  of the nucleus even if
• energy is not gt energy barrier

Coulomb repulsion dominates
Nuclear attraction dominates
Potential energy of a in the daughter nucleus vs
distance
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Disintegration Energy

• In decays energy-momentum must be conserved
• The disintegration energy appears in the form of
  kinetic energy of products
• MXc2 MYc2 KY Mac2 Ka ? ?EKY Ka (Mx
  My Ma)c2
• Textbook neglect KY since
• MaltltMY? ?EKa (Mx My Ma)c2
• It is sometimes referred to as the Q
• value of the nuclear decay

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Decay sequence of 238U
Number of protons
a decay
Number of neutrons
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Radon
Zone 1 Highest Potential (greater than 4 pCi/L)

• Radon is in the 238U decay series
• Radon is an a emitter that presents an
  environmental hazard
• Inhalation of radon and its daughters can ionize
  lung cells increasing risk of lung cancer
• Madison is in Zone 1!
• In USA 20000 people die but a Geiger can help to
  identify problem in houses
• Also used to predict Earthquakes!

Zone 2 Moderate Potential (from 2 to 4 pCi/L)
http//www.radonwisconsin.com/
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Activity of Radon

• 222Rn has a half-life of 3.83 days.
• Suppose your basement has 4.0 x 108 such nuclei
  in the air. What is the activity?

We are trying to find number of decays/sec. So we
have to know decay constant to get RrN
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Radiation damage

• The degree and type of damage caused by radiation
  depend on
• Type and energy of the radiation
• Properties of the absorbing matter
• Radiation damage in biological organisms is
  primarily due to
• ionization effects in cells that disrupts their
  normal functioning

Alpha particles cause extensive damage, but
penetrate only to a shallow depth Gamma rays can
cause severe damage, but often pass through the
material without interaction Other kind of
radiations eg. neutrons penetrate deeper and
cause more damage.
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Radiation Poisoning Killed Ex-Russian Spy
The British authorities said today that A. V.
Litvinenko, a former Russian Federal Security
Service liutenant-colonel, and later dissident,
died of radiation poisoning due to a rare and
highly radioactive isotope known as Polonium 210.

Highly radioactive metalloid discovered by M.
Curie A N Isotopic T1/2
Activity mass (u) (d) (uCi) 210Po 84
126 209.98 140 0.1
Produced by bombarding bismuth-209 with neutrons
in nuclear reactors. In the decay 210P
creates 140 W/g so 1/2 a gram reaches 500 C.
Considered to power spacecrafts. Used in many
daily applications eg anti-static brushes in
photographic shops Dangerous only if ingested
because it is an a emitter.
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Radiation Levels
RBE (relative biological effectiveness of
rads of X or gamma radiation that produces the
same biological damage as 1 rad of the radiation
being used rem (radiation equivalent in man)
dose in rem dose in rad x RBE
rad (radiation absorbed dose) amount of
radiation that increases the energy of 1 kg of
absorbing material by 1 x 10-2 J
Ground 0.30 rem/yr Mercury 9 60.6 rem/yr
Apollo 14 146.2 rem/yr MIR Station 34.9
rem/yr Space Station 36.5 rem/yr
Upper limit suggested by US gov 0.50 rem/yr
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Beta decay

• Nucleus emits an electron or a positron
• Must be balanced by a positive or negative charge
  appearing in the nucleus.

This occurs as a n changing into a p or a p into
a n
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Example of ß-decay

• 14C (radioactive form of carbon) decays by
  ß-decay (electron emission).
• Carbon Z 6, 14C has (14-6)8 neutrons.
• A new element with Z 7

Beta decay decreases number of neutrons in
nucleus by one increases number of protons in
nucleus by one We do not see it, but to explain
this decay an anti-neutrino is needed
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The Positron and Antimatter

• Every particle now known to have an antiparticle.
• Our Universe seems to contain more matter (we are
  lucky otherwise everything would annihilate into
  photons!)

Positron 1st detection in cosmic rays through
bending in a B-field and a bubble chamber
(Anderson 1932)
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Decay Quick Question

• 20Na decays in to 20Ne, a particle is emitted?
  What particle is it?
• Na atomic number Z 11
• Ne Z 10
• Alpha
• Electron beta
• Positron beta
• Gamma

20Na has 11 protons, 9 neutrons20Ne has 10
protons, 10 neutronsSo one a proton ( charge )
changed to a neutron (0 charge) in this decay. A
positive particle had to be emitted.
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Nuclear Medicine diagnostic

• Basic Idea
• Inject patient with radioactive isotope (tracer)
  that decays in a positron
• Positrons annihilate with electrons into gamma
  rays
• Reconstruct the 3-D image

Positron Emission Tomography image showing a
tumor
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Positron Emission Tomography - PET
Gamma Photon 1
Nucleus (protonsneutrons)

• Basic Idea
• A short-lived radioactive tracer isotope emits a
  positron
• Positron collides with a nearby electron and
  annihilates
• e e- ? 2?
• Two 511 keV gamma rays are produced
• They fly in opposite directions (to conserve
  momentum)

e-e-???
electrons
Gamma Photon 2
Isotope Max. Positron Range (mm)
18F 2.6
11C 3.8
68Ga 9.0
82Rb 16.5
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Emission Detection
Ring of detectors

• If detectors receive gamma rays at the approx.
  same time, we have a detection
• Nuclear physics sensor and electronics

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Image Reconstruction

• Each coincidence event represents a line in space
  connecting the two detectors along which the
  positron emission occurred.
• Coincidence events can be grouped into
  projections images, called sinograms.
• Sinograms are combined to form 3D images

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Cancer Radiation Therapy

• 50-60 of cancer patients treated with radiation
• Radiation destroys the cancer cells' ability to
  reproduce and the body naturally gets rid of
  these cells.
• Although radiation damages both cancer cells and
  normal cells, most normal cells can recover from
  the effects of radiation and function properly.
• Ionization (stripping atomic electrons) makes
  nuclear radiation dangerous
• Used radiations
• X and ?-rays (60Co) from 20 KV to 25 MV
• Pion Therapy under study, less
• invasive then photons
• Neutrons,protons,..

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Gamma decay

• Both a and ß-decays can leave the nucleus in
  excited state
• The nucleus can decay to a lower energy state (eg
  the ground state) by emitting a high energy
  photon (1 MeV-1 GeV)

The X indicates a nucleus in an excited state
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Decay Question?
Which of the following decays is NOT allowed?
1
2
3