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
Final Exam
• Fri, Dec 21, at 7:45-9:45 am in Ch 2103
• About 40% on new material
• 2 sheets allowed (HAND WRITTEN!)
• The rest on previous materials covered by
MTE1 MTE2 MTE3.
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
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
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
12
C
6
• Binding energy: mnucleus < Zmp + (A-Z)mn = Zmp + Nmn
• The energy you would need to supply to disassemble the nucleus
into nucleons Ebinding = (Zmp+Nmn-mnucleus)c2 = (Zmp+Zme+Nmn+
-Zme-mnucleus)c2 =(ZmH + Nmn - matom) c2
5
Fission and Fusion
6
Stable and Unstable Isotopes
Isotope = same Z
Isotone = same N
Isobar = same A
Stability of nuclei
• Dots: naturally occurring isotopes.
• Blue shaded region: isotopes
created in the laboratory.
• Light nuclei are most stable if N=Z
• Heavy nuclei are most stable if
N>Z
• As # of p increases more neutrons
are needed to keep nucleus stable
• No nuclei are stable for Z>83
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 (2p+2n)
Beta decayelectrons and its anti-particle (positron)
Gamma decayhigh energy photons
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
Is the radiation charged?
• Alpha radiation positively charged
• Beta radiation negatively charged
• Gamma radiation uncharged
The Decay Rate
• probability that a nucleus decays during Δt
Prob(in t)  rt
Constant of proportionality r = decay rate (in s-1)
• number of decays (decrease)= NxProb=rNΔt

N=number of independent nuclei
N
 rN
t
rt
N(t)  N0e
# radioactive
nuclei at time t
# rad. nuclei
at t=0
The number of decays per second is the activity

N
R
 rN
t
1

r
time constant
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
N0
N(t1/ 2 ) 
 N0ert1/2
2
ln2
  ln2  0.693
 t1/ 2
r

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
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
N(t1/ 2 ) 
 N0ert1/2
2
N0

N0/2
N0/4
N0/8
Radiocarbon dating
•
14C
(Z=6) has a half-life of 5,730 years, continually
decaying back into 14N (Z=7).
• In atmosphere very small amount! 1 nucleus of 14C each
1012 nuclei of 12C
If material alive,
atmospheric
carbon mix
ingested (as CO2),
ratio stays
constant.
After death, no exchange
with atmosphere. Ratio
changes as 14C decays
So can determine time since the plant or animal died
(stopped exchanging 14C with the atmosphere) if not
older than 60000 yr
Carbon dating
A fossil bone is found to contain 1/8 as much
14C as the bone of a living animal. Using
T1/2=5,730 yrs, what is the approximate age
of the fossil?
A. 7,640 yrs
B. 17,190 yrs
Factor of 8 reduction in 14C
corresponds to three half-lives.
C. 22,900 yrs
So age is 5,730 x 3 =17,190 yrs
D. 45,840 yrs
Decay processes:  = 4He
Heavy nucleus spontaneously
emits alpha particle
• nucleus loses 2 neutrons and 2 protons.
• It becomes a different element (Z is changed)
Alpha particle
• Example:
238
4
234
92
2
90
U  He 
92 protons
146 neutrons
2 protons
2 neutrons
Th
90 protons
144 neutrons
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  particle.
• This probability depends on the width of the
barrier
Coulomb repulsion
• The  -particle quantum-mechanicallydominates
tunnels out
of the nucleus even if
energy is not > energy barrier
Nuclear attraction dominates
Potential energy of  in
the daughter nucleus vs
distance
Disintegration Energy
• In decays energy-momentum must be conserved
• The disintegration energy appears in the form of kinetic energy
of products
MXc2 = MYc2 + KY + M c2 + K EKY K = (Mx – My – M )c2
Textbook: neglect KY since
M <<MYE=K ~ (Mx – My – M )c2
• It is sometimes referred to as the Q
value of the nuclear decay
Number of protons
Decay sequence of
238U
 decay
Number of neutrons
Radon
Zone 1 Highest Potential (greater than 4 pCi/L)
uic kTimpre™
and
a
TI FF (QUncom
essed
) decom
pr esso r
ar e needed t o see t his pict u r e.
• Radon is in the 238U decay
series
uic kTimpre™
and
a
TI FF (QUncom
essed
) decom
pr esso r
ar e needed t o see t his pict u r e.
Zone 2 Moderate Potential (from 2 to 4 pCi/L)
• Radon is an  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!
uic kTimpre™
and
a
TI FF (QUncom
essed
) decom
pr esso r
ar e needed t o see t his pict u r e.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
• In USA 20000 people die but a
Geiger can help to identify
problem in houses
• Also used to predict
Earthquakes!
http://www.radonwisconsin.com/
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 R=rN
r
0.693
0.693

 2.09 106 s
t1/ 2
3.83days 86,400s /day
dN
 rN  2.09 106 s  4.0 108 nuclei 836decays/s
dt
1Ci
R  836 decays/s 
 0.023Ci
10
2.7 10 decays/s
R
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.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
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
mass (u)
210Po 84 126 209.98
T1/2 Activity
(d) (uCi)
140 0.1
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
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  emitter.
Radiation Levels
rad (radiation absorbed dose) =
amount of radiation that increases
the energy of 1 kg of absorbing
material by 1 x 10-2 J
Ground
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
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
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TIFF (Uncompressed) decompressor
are needed to see this picture.
Upper limit
suggested by US
gov
0.50 rem/yr
Beta decay
• Nucleus emits an electron or a positron
• Must be balanced by a positive or negative
charge appearing in the nucleus.
A
Z
A
Z 1
X Y  e

A
Z
A
Z 1

X Y 'e
This occurs as a n
changing into a p or
a p into a n
Example of -decay
(radioactive form of carbon) decays by decay (electron emission).
• Carbon Z = 6, 14C has (14-6)=8 neutrons.
• A new element with Z = 7
•
14C
14
6

C 14
N
e
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 antineutrino is needed
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!)
Quic kT ime™ and a
T IFF (Uncompres sed) decompres sor
are needed to s ee this picture.
Positron 1st detection in cosmic
rays through bending in a Bfield and a bubble chamber
(Anderson 1932)
Decay Quick Question
20Na
decays in to 20Ne, a particle is emitted? What
particle is it?
Na atomic number Z = 11
Ne Z = 10
A.
B.
C.
D.
Alpha
Electron beta
Positron beta
Gamma
20Na
has 11 protons, 9 neutrons
20Ne has 10 protons, 10 neutrons
So one a proton (+ charge ) changed to a
neutron (0 charge) in this decay.
A positive particle had to be emitted.
p  n  e   e
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
Positron Emission Tomography PET
Gamma Photon #1
Nucleus
(protons+neutrons)
e+-e-
electrons
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
Gamma Photon #2
Isotope
Max. Positron Range (mm) • They fly in opposite directions
(to conserve momentum)
18F
2.6
11C
3.8
68Ga
9.0
82Rb
16.5
Emission Detection
Ring of detectors
• If detectors receive gamma rays at the approx. same time, we
have a detection
• Nuclear physics sensor and electronics
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
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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are needed to see this picture.
Gamma decay
• Both  and -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
Decay Question?
Which of the following decays is NOT allowed?



U Th  
1
238
92
234
90
2
214
84
210
82
3
14
6
4
2
Po Pb He
C N  
14
7
238 = 234 + 4
92 = 90 + 2
214 = 210 + 4
84 = 82 + 2
14 = 14+0
6 < 7+0