Decay. W. Udo Schröder, 2007 Nuclear Decay 2 Decay Types There are many unstable nuclei - in nature Nuclear Science began with Henri Becquerel’s discovery

Decay

General Features & Kinetics

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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


5

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


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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

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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


1

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


1

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


1

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


1

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


1

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


1

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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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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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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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


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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

Documents

Decay. W. Udo Schröder, 2007 Nuclear Decay 2 Decay Types There are many unstable nuclei - in nature Nuclear Science began with Henri Becquerel’s discovery