decay. w. udo schröder, 2007 nuclear decay 2 decay types there are many unstable nuclei - in nature...
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Decay
General Features & Kinetics
Nu
clear
Deca
y
W. Udo Schröder, 2007
2
Decay Types
There are many unstable nuclei - in nature Nuclear Science began with Henri Becquerel’s discovery (1896) of uranium radioactivity
and man-made:
+30 30 30 J oliot &Al( ,n) P Si ,1934
Th source
Curi
, E
e
6 MeV
Types of decay:
1 1
1 1 1
A A 4Z N Z 2 N 2
A AZ N Z 1 N 1 e
A AZ N Z 1 N 1 e
A AZ N Z 1 N 1 e
A A A x yAZ N Z N Z Z y N x
decay : X Y
decay : X Y e
decay : X Y e
e capture : X Y ( e )
Fission : X F F xn yp
Various rare heavy particle(cluster ) decays
“weak” decays
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Domains of Nuclear Decay Modes
N=126
Isotones
Z=82 Isotopes
A
Neutron Dripline
Bn = 0
SHE Z=118 discovered (?)
Proton Dripline Bp = 0
Ef = 0
Segré Chart
stable nuclide
A = 132 Isobars
Stable nuclides
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Example: ThB (212Pb) Decay Scheme
212Pb ground state decays spontaneously by e- emission (b- decay)
212Bi ground state has branched (a and g ) decays
208Pb ground state is stable
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The 4 Natural Decay Series
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Chain Parent t1/2 (a) Final
Thorium 232Th 1.4·1010 208Pb
Neptunium 237Np 2.1·106 209Bi
Uranium 238U 4.5·109 206Pb
Actinium 235U 7.0·108 207Pb
238U Decay Chain
Np chain is not found on Earth, t1/2 age of Earth
Dominantly chain of a and b decays
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The 4 Natural Decay Series
W. Udo Schröder, 2007
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Chain Parent t1/2 (a) Final
Thorium 232Th 1.4·1010 208Pb
Neptunium 237Np 2.1·106 209Bi
Uranium 238U 4.5·109 206Pb
Actinium 235U 7.0·108 207Pb
Np chain is not found on Earth, t1/2 age of Earth
Th Series Th Series
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Observing a Finite Lifetime of the 198Au g.s.
E. Norman et al., http://ie.lbl.gov/radioactivedecays/page2
411.8 keV
411.8 keV
Spectrum of b delayed 198Au g-rays
Spectrum of b delayed 198Au g-raysg decay of 198Hg exc. state is prompt: t g tb
11 measurementsEach spectrum ran for 12 hours real time#11 taken 5 days after #1
# 1
# 11
Pri
nci
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s M
eas
W. Udo Schröder, 2004
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Measuring “Decay Curves”: Fast-Slow Signal Processing
Radiation
Source
Slow
Fast
PreAmp
Amp
Produce timing signal electron. Clock
(TAC)
Data Acquisition System
Energy
DE-Tag
Produce analog signal Binary
data to computer
EnergyDiscriminator
TimeTrigger
Start
Stop
External Time reference signal t0
Detector
Measured: Energy and time of arrival Dt=t-t0 (relative to an external time-zero t0) for radiation (e.g., g-rays), energy discriminator to identify events (DA) in a certain energy interval DE by setting an identifier “tag.”
Calibrate Dt axis channel # time units (s, y,..)Watch that Dt-channel t.
0 100 200 300 400.0.01
0.1
1
i
Dt
Act
ivit
y D
A(D
t)/D
A(t
0)
Dt (Channel #)
tA( t ) exp
Kinetics of Nuclear Decay: Logarithmic Decay Law
2.303
:
# /
( )
( 2.1828..)
( ) ( 0)
( 10)
( ) 1( 0)
( 2)
( 0
0
( )
1
)
t
t
e l
First order process
Activity of decays unit time
dA N N t N
dt
exponential law base e
N t N t
exponential law base
N t N t
exponential law b
ife time
ase
N t N t 0.69312
t
0 100 200 300 4001 .10 2
0.1
1
i
t
0 100
200
300
400
0
0.2
0.4
0.6
0.8
1
Disintegration of Radioactive Sample
i
ti
Sam
ple
Act
ivit
y A
(t)/
A(0
)
time t
time t
:Decay width
1/ 2
0.6931
Half life t
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Sum Radioactivity
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0
Genetically independent species: Sample with 2 components (N1, N2) same type of radiation (g-rays)
(N1)
(N2)
(l1)
(l2)1 2
1 2
( ) (0) ( 1,2)
:
( ) (0) (0)
tii i
t t
A t A e i
Total activity
A t A e A e
Decompose total decay curve l1, l2.
Simultaneous fit or deduce constant l2
for “shallow” decay first
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Branching Decay
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1
Genetically dependent species: Sample depopulated by 2 decay paths (l1, l2)
1 2
1 2
1 2
1 2
( ) tt
" level width"
dN(t )N(t ) N(t )
dtN(t ) N(0) e N(0) e
l1
l2
G
1 2( ) ( ) (0) ( ) ( )
:
( ) (0) ( 1,2)
t
ti i
A t N t N e A t A t
Partial activities
A t N e i
Partial decay constants/half lives:
( ) ( )( ) ( )i i iA t N t
A t N t
1 20.693
ii
t
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Activation and Decay
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2
Competition production/decay for a species with N(t) members
t
t
PN(t ) 1 e
A(t ) P 1 e
dN(t )N(t ) P
dt
Irradiation of sample produces unstable species N.Constant rate of production PConstant decay rate l
Gain- Loss Equation
t
For long times, t
A(t ) P 1 e P
Irradiation inefficient for t 3 t
lN
N
PIrradiation of Sample
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Activation and Decay
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3
Irradiate 51V with thermal neutrons, daughter b-decays to 52Cr*
A(t)/P vs. t
51 52 5223 23 24V n V Cr e
Fit Curve
52Cr* de-excites by g emission
tA(t ) P 1 e 1
g intensity activity
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Genetically Related Decay Chain
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4
l2
l1
N1
N2
N3
ii 1 i 1 i i
dN (t )N (t ) N (t )
dt
Gain and loss for i-th daughter
1
1 2
m
t1 11
t t2 21 22
kt
k kmm 1
N (t ) c e P( parent )
N (t ) c e c e P(1.daughter )
N (t ) c e P((k 1).daughter )
Coupled DEq. For populations Ni of nuclei in chain
i 1ij i 1, j
i j
Recursion Relations
c c
i i1 i2 ii
ii
Boundary condition
N (0) c c ... c
determines c
1
1 2
t1 1
t t12 2
2 1
: N (t ) N (0) e
N (t ) N (0)
k
e e
2
Check by differentiation
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Examples of Genetically Related Decay Chains
W. Udo Schröder, 2007
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5
1
1 2
t1 1
t t12 2
2 1
: N (t ) N (0) e
N (t ) N (0)
k
e e
2
Decay
Applications of Nuclear Radiation
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Biological Effects-Radiation Safety
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Radio-Activity/Units
1
10
Number of nuclei in sample : N N(t ) changes in time
Differential probability for a nucleus to decay (dimension time )
Activity A(t ) : N(t )
Units of activity : 1Bq(Becquerel ) 1disintegration / s
Old : 1Ci (Curie) 3.7 10 di sintegr
226
3
ations / s ( 1g Ra)
radiation energy abs.Absorbed dose : D
mass of material m
Unit [D] 1Gy (Gray ) 100 rad 1J / kg
Old : 1R(Roentgen) 8.8 10 J / kg in air (material dependent )
Bio log ically equivalent dose H weight D
unit [H] 1Sv (
2
Sievert ) 1 J / kg
Old unit 1rem 10 Sv
19
18
1eV 1.602 10 J
1 J 6.242 10 eV
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9
Average Radiation Exposure
From Lilley, Nuclear Physics, Principles and Applications, J. Wiley & Sons, Ltd., 2001
(238U, 232Th, 40K)
(219Rn, 220Rn, 222Rn)
Tobacco absorbs Rn 210Pb, 210Po“hot spots” in lungs cancer risk
Note unit: m Sv
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0
Biological EffectsAnn. ICRP 26, 1994
Heavy charged particles:High ionization density, localized: maximum near end of range (Bragg peak)
Electrons (+Bremsstrahlung):Long range, diffuse multiple scattering, low ionization density, delocalized absorption
Neutrons:Indirect ionization, capture H(n, g) for En<100 eV, keV-neutrons scatter elastically (np), 2-MeV neutrons have l = 6 cm to thermalization and high ionization density. Photons:Like electrons, low ionization density, Compton scattering + photoelectric absorption, delocalized absorption
Indirect chemical effects:Free radicals (neutral atom or molecule with an unpaired e-)
2 2
2 2
2 2
2
2
RH OH
H O rad H O e
H O e H O
H O H OH
H O H OH
R organic
RH H R H
R O RO peroxy radical
2 2
Oxygen Effect (Chain Re ac
RO RH R
tion)
O H R
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1
Biologically Relevant Dose Weighting Factors
Type Energy Range
Weighting wR
, g e± all 1
neutrons < 10 keV 5
10-100 keV 10
100 keV – 2 MeV
20
2 - 20 MeV 10
>20 MeV 5
protons < 20 MeV 5
a, FF, clusters
20
tissue radiation tissue,radiation
T R T ,R
T R T ,RR
T TT
Biol. equivalent dose (Damage due to energy deposition)
H w D
Brief : H w D
Combination of different rads,H w D
Combination of different tiss. Equivalent dose E w H
Tissue Weight wT
Gonads 0.20
Red bone marrow 0.12
Colon 0.12
Lungs 0.12
Stomach 0.12
Bladder 0.05
Breast 0.05
Liver 0.05
Oesophagus 0.05
Thyroid 0.05
Skin 0.01
Bon surface 0.01
All remaining tissue 0.05
Ann. ICRP 26, 1994
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2
Effect on Complex Molecules
Enzyme deoxyribonuclease (DNAse)
Splits DNA
Rad exposure decreases activity exponentially with dose
• High DNAse concentrations: expect more direct hits, direct damage of molecule
• Low DNAse concentration: expect fewer direct hits, less direct damage.Observation due to more free OH. and H. radicals from H2O dissociation.
DNAse in Water
Recovery: DNA molecules can repair themselves after moderate damage by X rays and minimum ionizing radiation.
Approximately total recovery after small doses, no accumulation of effects
More damage and less recovery after irradiation with neutrons
X-rays, Assay at t0
t0+5hrs
Neutrons Assay at t0
t0+5hrs
DNA Survival Rate
After Lilley, Nuclear Physics, Principles and Applications, J. Wiley & Sons, Ltd., 2001
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Risk Factors
Tissue Effect Probability/Sv
Breast Cancer 2.0 x 10-3
Red bone marrow Leukemia 5.0 x 10-3
Lung Cancer 8.5 x 10-3
Thyroid Cancer 8.0 x 10-4
Bone surface Cancer 5.0 x 10-4
Other tissue Cancer 3.4 x 10-2
Whole body Cancer effects 5.0 x 10-2
After Lilley, Nuclear Physics, Principles and Applications, J. Wiley & Sons, Ltd., 2001
W. Udo Schröder, 2007
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Applications of Nuclear Instruments and Methods
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Halflives of Radio-Isotopes for Dating
years Age of Earth
Nucl. Synth.
, , a b b- : particles measured to identify fractional abundance of radioactive isotope,
K: K electron capture R : measure series of several decay products
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Carbon Dating of Organic Objects
4 1
1 / 2
0.6931 0.69311.21
5730a10 a
t
12
12C 12C
t14C 14C
t14C
12C1.3 10
N (t ) N (t 0)
N (t ) N (t 0) e
N (t )R(t ) R(t 0) e
N (t )
" ag1 R(0)
t nR(
e"t )
n
14 2 1
14 12 12
1 2
Now :
N( C ) 2.5 cm s
C C 1.5 10
t 5730 a
Conventional method: b counting
Direct 14C counting method: Accelerator Mass Spectroscopy R
10 -16 (10 5 a)
Measure 14C/12C ratio
of sample at t
14
t 0 :
time of death
No further
C intake
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Calibration of 14C Dating Methods
(a) CE
t-dependent flux of cosmic rays (solar
cycles) t-dependent 14C
production and intake
Calibration:14C-analyze yearly rings in trees of different ages (number and widths of
rings), connect to fossils
Errors in very old samples lead to
underestimation of age (few hundred years).
Variation in 14C Production
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Rb/Sr Dating of Rocks/Age of the Earth
0 m( ) xy y t
Undisturbed by erosion/transmutation
All rocky objects (planets, asteroids, meteorites) of solar system crystallized ≈ simultaneously
(t=0) out of interstellar dust/nebula (supernova
remnants).87 87
87
tP P R R
D P P D
tD P D
tP
Rm
x
P P D
D
R
y
Parent P Rb, daughter D Sr
Re ference R Rb ( stable)
N (t ) N (
N (0) N (t )
0) e N (t ) N (0)
N (t ) N (0) N (t ) N (0)
N
N (t )
N (t )N
(t ) N (t ) e
but unk
1 N (0)
N (t )e 1
N (t )(t
now
)
n!
0
D
R
y
N (0)N (0)
R
Different minerals in meteorite containing
different amounts of NP different x
Construct isochron
1 2
9
t
4.7 10 a
1t n m 1
Age of rock (since formation)
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Age of the Earth
Terrestrial volcanic activity dated: produces younger rocks
Age of Earth = 4.5·109 aMoon has similar age