Radiochemistry & Imaging Science

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Radiochemistry & Imaging Science

Roger Alberto, Jason P. Holland, Henrik BrabandDepartment of ChemistryUniversity of Zürich

CHE 438

Course overview

1. Short Historical Background2. The Atomic Nucleus

• General features• Nuclear stability, modes of decay• Nuclear forces• Nuclear states

3. Unstable Nuclides• Chart of isotopes• Law of decay• Types of decay• a-decay• b--decay / b+-decay / e-capture• g-radiation / iosomeric transitions• Internal conversion IC / Auger electrons• Other decays• Natural decay series 2

Course overview

4. Laws of Radioactive Decays• Parent-daughter relationships• Transient and secular equilibria• Radionuclide Generators

5. Interaction of Ionizing Radiation with Matter• Ionization with electrons• Bremsstrahlung• Photo effect• Compton scattering• Pair formation

6. Biological Action of Ionizing Radiation• Dose / Doserate• Shielding / Calculations• Dose calculations

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Course overview

7. 99m-Technetium• Chemistry / Radiochemistry

8. Synthesis of Elements• Synthesis of transactinides / super heavy elements• Synthesis of the chemical elements: Nucleosynthesis

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Historical Background

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Atomic theory

Leukipp (about 450 b.C.): creates the expression „atomos“

Demokrit (ca 460 – 400 b. C.): Atomic theory

“Nur der Meinung nach gibt es süss, bitter, warm, kalt, Farbe, in Wahrheit gibt es Atome und leeren Raum”

“Atoms and Void“


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“Ausserdem sind die kompakten Atomkörperchen, aus welchen die Stoff-zusammensetzungen entstehen und in welche sie sich auflösen, unerfasslichin Bezug auf die Verschiedenheit ihrer Formen......”

“Die Atome bewegen sich fortwährend,......die einen schweben dabei weitauseinan der, die anderen führen eine Schwingung am Ort aus, wenn sieetwa in einer Stoffverbindung verflochten und eingeschlossen sind.....”

Epikur (341 – 271 b.C): summarized Demokrit‘s theses (letter to Herodot)

J.C. Magien (1590 – 1679): Revival of Demokrit

Oft beobachtet, dass ein Weihrauchkorn durch Verbrennen das 8x108-fache seines Volumen (von Erbsengrösse auf Zimmergrösse) gleichmässig mit Duft erfüllt. Einerbsengrosses Volumen könnte mechanisch in ca. 103 noch sichtbare Teilchen geteiltwerden, jedes dieser Teilchen besteht sicher noch aus mindestens 106 Atomen.Beigleichmässiger Verteilung muss das Weihrauchkorn aus 8x108x103x106 ³ 8x1017

Atomen bestehen.


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W.C. Röntgen (1896): X-rays

“MM. les Drs. Oudin et Barthélemy communiquent unephotographie des os de la main, obtenue à l’aide des “X-Strahlen” de M. le professeur Röntgen.”

c. r. 122, 1896, 150, séance du lundi 20 janvier 1896

A.H. Becquerel (1852 - 1908): Uranium rays

“...l’origine de ces expériences avait été l’idée de rechercher si les corps phosphor-escents, après avoir été excités par la lumière, émettaient des rayons pénétrants.”

In contrast to Röntgen‘s X-rays, the report of Becquerel did not find any interestand Becquerel stopped publishing anything for a long time!


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Within 3 months, Becquerel found that K2SO4UO2SO4, a phosphorescingsubstance (t1/2 = 0.01 s) emits invisible, strongly penetrating radiation

“On doit donc conclure de ces expériences que la substance phophorescenteen question émet des radiations qui traversent le papier opaque à la lumièreet réduisent les sels d’argent.”

“On peut vérifier très simplement que les radiations émises par cette substance, quand elle est exposée au soleil ou à la lumière diffuse du jour, traversent, non seulement des feuilles de papier noir, mais encore divers métaux....”



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... and then that sunlight is not necessary at all !

“J’insisterai particulièrement sur le fait suivant, qui me paraît tout à fait important et en dehors des phénomènes que l’on pouvait s’attendre à observer: Les mêmes lamellescristallines...mais à l’abri de l’excitation des radiations incidentes et maintenues à l’obscurité produisent encore les mêmes impressions photographiques....Quelques-unes avaient été préparées le mercredi 26 et le jeudi 27 février et, commeces jours-là, le soleil ne s’est montré que d’une manière intermittante, j’avaisconservé les expériences.... dans le tiroir d’un meuble, en laissant en place les lamel-les du sel d’uranium. Le solei ne s’étant montré de nouveau les jours suivants, j’aidéveloppé les plaques photographiques le ler mars, en m’attendant à trouver des images très faibles. Les silhouettes apparurent, au contraire, avec une grandeintensité.“



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In contrast to Röntgen‘s experiment‘s, reproduction of Becquerel‘s was rare.

“Hence the writer ventures to give to the new phenomenon thus independently observed by M. Becquerel and by himself the name of hyperphosphorescence. A hyperphosphorescent body is one which, after due stimulus, exhibits a persistent emission of invisible rays not included in the hitherto recognized spectrum.”

1. Die Angaben Becquerels bezüglich der physikalischen Eigenschaften der dunkeln, von Uransalzen ausgehenden Strahlen fanden wir, soweit wir sie prüften, durchweg bestätigt.

2. Die Energiequelle der diese Strahlen entstammen ist noch vollständig dunkel. Monatelanges Aufbewahren des Salzes unter Lichtabschluss vermindert die Strahlungsintensität nicht merklich.”

S. P. Thompson, On hyperphosphorescence, Phil. Mag. (5) 42, 1896, 128-135J. Elster, H. Geitel, Versuche über die Hyperphosphoreszenz10. Jahresber. Ver. Naturw. Braunschweig 10, 1897, 157


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The first new elements 1898

“Nous croyons donc que la substance que nous avons retirée de la pechblende contient un métal se confirme, nous proposons de ’appeler polonium, du nom du pay d’origine du l’un de nous.”

“On réalise ainsi une source de lumière, à vrai dire très faible, mais qui fonctionnnesans source dénergie. Il y a là une contradiction, tout au moins apparente, avec le principe de Carnot.”

Accumulation of radium from pitchblend was very tedious, unknown problems emerged

- radioactivity of fresh samples increases steadily- nearby compounds start becoming radioactive

Polonium 4n+2 Po-210 138.38 d

Radium 4n+2 Ra-226 1600 y


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F. Giesel (1852 – 1927): Excellent experimentalist

- fresh solid radium compounds increase in activity, solution activity decreases

- formation of coloured centers in crystals after irradiation

- physiological action of radiation

“Ich habe 0.27g Radium-Baryum-Bromid in doppelter Celluloidkapsel 2 Stunden auf die Innenfläche des Armes gelegt. Anfangs war nur eine schwache Rötung vorhanden; nach 2-3 Wochen stellte sich starke Entzündung mit Pigmentierung und schliesslich....Abstossung der Oberhaut ein, worauf bald Heilung erfolgte.”

“Als bequeme Kontrolle der fortschreitenden Reinigung benutzt man die Färbung der Bunsenflamme.”


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Actinium 4n+3 Ac-227 21.77 y

Debierne finds a new activity (1899), chemically related to lanthanum

Giesel confirms finding 1902 (it produces emanation) and called it „Emanium“

Debierne wins, hence, the name „Actinium“ remains

Emanation and induced radioactivity

Emanation: Rn-222 4n+2 3.825 d U-238Rn-219 4n+3 3.96 s U-235Rn-220 4n 55.6 s Th-222


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The nature of emanation remains mysterious:

Owens and Rutherford (1899): “It was very early observed that the radiation from thorium oxide was not constant, but varied in a most carpicious manner. This was the more peculiar as the sulphate and the nitrate were fairly constant. All the compounds of uranium give out a radiation which remains remarkably constant..... The sensitiveness of thorium oxide to slight currents of air is very remarkable and made it difficult to work with... A large number of experiments of various kinds have been tried, but so far, no clue has been obtained as to why this action should be so manifest in thorium oxide......”

Giesel (1903): “Legt man ein Filter mit einigen Centigrammen der Substanz auf den Schirm, so verbreitet sich die Emanation auf grössere Strecken desselben und erzeugt ein durch den leisesten Luftstrom hin- und herwogendes Phosphorescenzlicht.”

“Ein Gas scheint die Emanation jedenfalls nicht zu sein, wenigstens wurde unter Wasser keine Gasentwicklung von der Substanz bemerkt.

E. Rutherford, R. B. Owens, Thorium and uranium radiation, Trans. Roy. Soc. Canada (3) 2, 1899, 9-12F. Giesel Über Radium und radioaktive Stoffe Ber. 35, 1902, 3608 1

The Atomic Nucleus

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neutrons and protons ® Baryonselectrons and neutrinos ® Leptons

p+ and p- Mesons are responsible for the attractive forces betweenp and n or n and p respectively.

p- / p+ Meson: 0.15 a.u. @ 273 em t½ = 2 ·10-8 spO Meson: 0.145 a.u. t½ = 10-16 s

p-Mesonen have been detected in cosmic radiation.

exchange forces explain, why neutrons have a magnetic moment.

The Atomic Nucleus

16http://commons.wikimedia.org/wiki/File:%C3%9Cbersicht_einiger_Hadronen.svg

The Atomic Nucleus

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The structure of the nucleus is almost a sphere.

range of radii: 3 ·10-15 - 16 · 10-15 m (3 fm – 16 fm)

Original determination by Rutherford with a-particle scattering experiments

The Atomic Nucleus

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Newer definition through the extremely short range nuclear forces

The potential energy of a p+ approaching the nucleus increases strongly.

At a certain distance (radii of nuclei) nuclear forces start and Epot decreases.

empirical relation: R = ro (9.1 fm für A = 222)

with A = number of nucleous and ro = 1.4 fm (radius of nucleons)

3 A

Atomic Radius

The Atomic Nucleus

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The density of the nucleus is about 1.5 · 1017 kg/m3

Compare mass of earth: 5.972 · 1024 kg

for A > 16 charge density constant over a certain range

Atomic density

The Atomic Nucleus

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The mass and charge distribution are constant

Layer of decreasing density (dn ~ 2.5 fm) follows Fermi statistics

For nuclear reactions, a charged nucleon needs to reach that distance to overcome the Coulomb potential.

Charge distribution

The Atomic Nucleus

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The wall potential can be calculated from Ec if the radius is known.

The wall is 14.7 MeV for a proton

(226Ra, 9Be) C-12 226Ra = 4.8 MeV

Epot(Be) = = 4.25 MeV

first neutron sources !!

Potential wall

Epot = = 29.5 MeV (r = 9.1 fm)

Natural a-particles don‘t have such high energies but nuclear reactions with lighter elements are possible

The Atomic Nucleus

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follows within a nucleus also the Coulomb potential

nuclear forces go to saturation but Coulomb forces increases

Nucleon-nucleon interactions

Considering 2 p+ with d ~ 3fm

and EC = Þ EPP ~ 0.5 MeV

Þ instability of heavy nuclei

The Atomic Nucleus

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strong Gluon 1electromagnetic Photon 10-2

weak Boson 10-5

gravitation Graviton 10-40

interaction mediating particle force constant

further fundamental particles

Comparison of the 4 principal forces in nature

Name Symbol Rest mass[u]

Electric charge [units]

Correspondingantiparticle(a)

Up u 0.33 + 2/3

Down d 0.33 - 1/3

Charm c 1.6 + 2/3

Strange s 0.54 - 1/3

Top t 24.2 + 2/3

Bottom b 5.3 - 1/3(a) Electric charge and quantum numbers are opposite to those of the corresponding particles.

The Atomic Nucleus

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The nucleon-nucleon interaction shown previously resembles the Morse potential for chemical bonds

nucleon interacts with essentially one partner

Binding energies

the mean binding energy is about constant

The Atomic Nucleus

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E = mc2, 1 u @ 931.5 MeV

with dM = Þ the higher EB, the more stable the nucleus

Empirical calculation of binding energy

Binding energies

MZ,N= Z·M(1H) + N·M(n) - dM

The Atomic Nucleus

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fission of 238U to 2 equal nuclei of same mass should deliver about 200 · 1 MeV = 200 MeV which is the amount experimentally found

Exact masses are knownfrom high resolution MS

®

7.01822 < 4.0026 + 3.017012 doesn‘t work

® does work

8.0053 > 2 x 4.0026

Binding energies

Stability of a nucleus in respect of a decay can be predicted (as in chemistry)

The Atomic Nucleus

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Semi-empirical calculation of binding energy

Bohr compared the nucleus with a incompressibel drop of liquidÞ the larger the drop, the less stable it is

Bethe-Weizsäcker: EB = EV + EC + EF + ES + EG

EB = total binding energy of all nucleous

EV = Volume energy = aV·A aV = 15.8 MeV

EC = mutual repulsion = -aC· aC = 0.71 MeV

EF = surface energy = -aF· aF = 17.8 MeV

ES = symmetry energy = -aS· aS = 23.7 MeV

+ 33.6 MeV eeEG = considers ee / oo nucleii = aG/A-3/4 aG = 0 MeV oe / eo

- 33.6 MeV oo

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2

A

Z

32

A

Binding energies

The Atomic Nucleus

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The B-W Formula allows calculation of all BE for A > 15 within 1%

example: calculated experimental

235U + 1n ® 236U: binding energy of neutron 6.81 MeV 236U „ ® 237U: „ 5.51 MeV237U „ ® 238U: „ 6.56 MeV 238U „ ® 239U: „ 5.31 MeV

97.947 97.943

51.959 51.956

Binding energies

Þ very useful for unknown nuclides

The Atomic Nucleus

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The high potential of the B-W Formula can be seen from EB within nuclides with equal A (Isobares)

which yields a parabolic curve (for oe/eo)

the larger A, the flatter the potential pot

if A is kept constant: MZA – M = g (z – z0)2

with g

Binding energies

the more stable nuclides

The Atomic Nucleus

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This explains:

For even mass numbers we receive two parabolas,

separated by

Z N A type numberse e e ee 162e o o eo 55o e o oe 50o o e oo 5

Statistic of stable nuclides:

Binding energies

why ee nuclides are particularly stableand oo nuclides not

The Atomic Nucleus

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Binding energiesThe most stable nuclides are close to the maximum EB

Nuclides with odd mass number have only one stable nuclidesThe others along the slope are b- or b+ unstable

1. Rule of Mattauch

The Atomic Nucleus

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More complex situation with even A (ee and oo nuclides)

2. Rule of Mattauch

Binding energies

depending on the shape of the parabolas, more than one stable nuclide is possible

Nuclides with even mass number frequently have two or three stable Isotopes which atomic numbers must be separated by 2.

The Atomic Nucleus

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Inspection of isotope chart confirms the rules and explains...

... why 43Tc has no stable nuclides

... why 61Pm has no stable nuclides

and why oo nuclides may decay

with either b- or b+.

K1940

K1940

Ca2040

Ar1840

(stable)

(stable)

0.01%natural abundancet1/2 = 1.28·109y

Binding energies

The Atomic Nucleus

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Þ most stable nuclides are found for Z = 26 or 28

Inspecting the valley of stability, it looks like a smooth landscape

Binding energies

The stability of a nuclide depends on the sum of Z and N and their relative ratio

The Atomic Nucleus

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The valley of b-stability

The Atomic Nucleus

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Dark blue line:

A=N+Z

ZN=Z

Electron capture

b- emission


Valley of b-stability

The Atomic Nucleus

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Source: http://ie.lbl.gov/toi


The Atomic Nucleus

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The Atomic Nucleus

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The Atomic Nucleus

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The Atomic Nucleus

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The Atomic Nucleus

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The Atomic Nucleus

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The Atomic Nucleus

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The Atomic Nucleus

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closer look shows that the energy landscape is rather bumpy with local minima along

Z / N = 2, 8, 20, 28, 50, 82, 126 and

theoretically predicted Z = 114 N = 184


These numbers are called „magic numbers“

The Atomic Nucleus

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unstable double magic nuclides have a relatively long t½ compared to their neighbors

Magic numbers

elements with magic Z have many stable Isotopes (Sn = 10 Isotopes)

elements with magic N have many stable Isotones

so called „double magic“ nuclides are particularly stable and abundant (Pb – 208, Ca – 40)

The Atomic Nucleus

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Magic numbers

The observation of particularly stable numbers can be explained with a shell model (similar to electrons).

Filled shells are more stable than partly filled ones.

Unstable Nuclides

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DE = DM×c2 = [MA-(MB-MX)]c2

If an atomic nucleus is along the wall of the Epot parabola, it canenergetically relax to a lower state according to

An activation barrier has to be surmounted or crossed by quantum mechanical tunneling

A sort of activation energy comparable to chemical first order kinetics

Unstable Nuclides

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Chart of nuclides

The chart of the nuclides lists all known nuclei together with most important decay data (energy, decay type, daughter nuclide, etc.)

Unstable Nuclides

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Example 102Rh (oo)-nuclide

left column

metastable nuclidee ³ 95%

conversion electrons £ 5%

right column

ground state nuclide95% £ b+ < 50%5% £ b- < 50%

Rh 102

2,9 a 207 de e

g 475 b+ 1,3631; b- 1,2697... g 475lg (42); e- 628...

Chart of nuclides

Unstable Nuclides

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Example a-emitter: Pa-230 (oo) nuclide

* The exact numbers are known

less than 5% * (0.003%)5% < e, b+ < 95% * (90%)5% < b- £ 50% * (10%)

Pa 230

17,4 d

Î; b- 0.5...a 5,345; 5,32g 952; 919, 455;899; 444...; sf 150

Chart of nuclides

Unstable Nuclides

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Vertical green bar: Excited states decay exclusively by spontaneous fission

Cf 252

2,645 a

a 6,118; 6,076...sf

g (43...); e-

s 20; sf 32

Am 241

432,2 a

sf a 5,486; 5,443...

sf; g 60; 26...

e-; gs 50 + 570; sf 3,1

Chart of nuclides

Green: Spontaneous fission in the ground state with emission of neutrons

Unstable Nuclides

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Radionuclides decay with a first order rate law

A(t) = AO· e-lt

l = decay constant or the probability to decay per unit time

a radionuclide has a certain probability l to decay per unit time

N(t) – N(t + Dt) = N(t) × l × Dt

Law of decay

AO = activity at time t = 0

Unstable Nuclides

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and if Dt ® 0, we receive

simple first order kineticsN(t) = NO × e-lt

telling us how many „active“ atoms are still around at a certain time point

slightly rearranged gives with e =

and from 1st order kinetics

corresponds to the number of half life times

Law of decay

4.4·10-8 (1:23 millions) better play lotto !!!

Unstable Nuclides

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l is the important constant

Examples: 99mTc (6h) l = 3.21×10-5 sec-1

3H (12.3y) l = 1.78×10-9 „

14C (5730y) l = 9.66×10-12 „

238U (4.47×109y) l = 4.92×10-18 „

137Cs (30y) l = 7.33×10-10 „

if we look at one single C atom, the probability for its decay in 1 min is

Law of decay

Unstable Nuclides

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Switching from nuclides to activity: activity = number of decays per time

A(t) =

one of the most useful relationships

A = l×N

1 decay / sec = 1 Bq

Dt ® 0

Law of decay

3.7×1010 Bq = 1 Ci = 37 GBq

Unstable Nuclides

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l = decay const [sec-1]1st order rate law: NdtdN l=-

integrated: N(t) = NO × e-l×t

compare to activity:

t1/2 = ll69.02ln

=

or N = NO t* = number of half-lives

1280AÞ after 7 t1/2 < 0.1% after 10 t1/2

Law of decay

A(t) = AO × e-l×t and A = l×N

Unstable Nuclides

average life time: ò¥

=×=00

11l

t dtNN

after t:eNN 0=

Law of decay

Unstable Nuclides

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mass of radioactive nuclidesAVNMNm ×

=

if radioactive nuclides are diluted with inactive isotopes

]/[ gBqmAAS =the specific activity AS is then

for some specific applications, no carrier added radionuclides are required

Specific activity

1 MBq 32P = 10-10 g1 MBq 99mTc = 5× 10-12 g

carrier added radionuclides (geträgert)

no carrier added means only radionuclides are present and the specific activity reaches a maximum

Unstable Nuclides

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Survey for the most important decay modes

Types of decay

Unstable Nuclides

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Types of decayUnstable nuclides may transform by:

emission of nucleons (a, b-, b+)

leads to an excited state of daughter nuclides0.16

0.04962+

4+

g(0.1105)g(0.1105)

g(0.0496)

Th(24.1d)234

g(0.1105)

a(4.04) 0.23%

a(4.15) 23%

a(4.20) 77%

O U(4.47 1 )× 0 g

0+

0+238 9

0

If „forbidden“, long lived metastable states occur

rarely p or n

capture an electron from the shell

Relaxation with emission of g-rays (< 10-13 sec)

Unstable Nuclides

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a-Decay

consider: the a-particle has an unusual high binding energy of ~ 28.3 MeV

The total energy of an a-decay is represented by:

DE = (MX - MY - )×c2

EB of is only 2.2 MeV ® „endothermic“ process

chemically spoken, a very stable compound with high DGf°(such as CO2)

Unstable Nuclides

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Observed for Z > 83 and some nuclides far away of b-stability line

Spontaneous fission starts for high Z (> 92) and begins prevailing for Z > 96 since fission barrier is high, a-decay is still dominant for Z > 106

Bild vorhanden

a-Decay

b-- and b+-decay is observed throughout the nuclide chart

Conditions for e electron capture see later

Unstable Nuclides

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written in a slightly different way

gives an expression for the decay energy

law of momentum conservation

Z×mpusing

with Q = Ea + EY; EY = Energy of recoiling nucleus

a-Decay

ma × ca = mY × cY

Unstable Nuclides

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since DE = Ea and ma << mY

the a-particle obtains ~ 98% of the full energy Q

consider that i.e. 2% of 4 MeV is still 80 keV

compounds are completely destroyed after decay due to recoil (compare to b- decay later)

a-Decay

this is much larger than any chemical bond energies

Unstable Nuclides

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Geiger and Nuttall (1911): empirical relationship between Q and decay constant l

and log l = a logQ + bl =

increasing decay energy leads to increased decay constant and strongly decreasing t1/2

Q varies by a factor of ~ 2,

a-Decay

(a, b constant)

t1/2 by 24 log units

Unstable Nuclides

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To understand this relationship we must have a look into theory of a-decays

The a-particle is surrounded by a high Potential barrier Epot

much larger than Ea = 4.2 MeV

Epot is!

!

!rZe22

41

×pe

3 A

3 A

= 28.1 MeV for

and R =

Epot = 0.96 × z · Z

a-Decay

Unstable Nuclides

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Typical a-energies are 4 – 10 MeV

Gamow and Gurney wave mechanics:

EC = 28.0 MeV but Ea » 4.8 MeV

the a-particle has to overcomeFor the reaction

a-Decay

the Coulomb wall, which is about

According to classical physics, not possible

There is a certain probability to find the a-particle outside the pot

Unstable Nuclides

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Tunneling is the answer

with Epot (r) = potential energy at distance r

from Schrödinger equation:

P decreases with increasing height and extension of the pot

drErEmh

ER

Rpotò -- a

p )(24

P = e

reduced formula: P = e-2gg = e-2G G = Gamow factor

b

rglp2

=a

gEEC=

CC EE

EE aa -- 1, across

lb = de Broglie Wellenlänge for EC and EC = Coulombbarriere

with l = f × P, the decay constant can calculated with f = n/2R = number of collisions with the Potential pot f is usually ~1020 s-1

a-Decay

m = reduced mass- a-particle-recoil nucleus

Unstable Nuclides

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coming back to Geiger-Nuttall rule

log l = a × log R + b or log t1/2 = - logEa

we can also approximate from the Gamow rule by log l = a - baE

Z22-

a-Decay

Unstable Nuclides

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a-Spectra

General decay schemes

Excited states are drawn above the ground states of the corresponding element

Daughter products with decreased atomic number A are drawn on the left, with increased A to the right

Unstable Nuclides

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no third particles are involved for ee nuclides, we frequently find one single line

Consider, that for the true decay energy the recoil energy of the nuclide must be added

a-Spectra

a-spectra show distinct lines since the change of nuclear angular momentumchanges by integers

Unstable Nuclides

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More complex spectra:

a-Spectra

Decay leads to excited states

Excited states decay very rapidly (<10-10 sec) to ground state

Unstable Nuclides

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One major decay line and some more weak ones of much higher energy

The mother nuclide possesses some excited states from which decay to ground state of daughter occurs

a-Spectra

Unstable Nuclides

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Three different b-decays are known:

b-: electron (+ antineutrino)

b+: positron (+ neutrino)

e: electron capture (+ neutrino)

if A is odd, then I = ,...25,

23,

21

Since A doesn‘t change (b-decay) and the electron e- carries away s = 1/2,something else (n) takes the other s = 1/2

b-Decay

Neutrino and antineutrino have different helicity

Neutrino and antineutrino had to be postulated due to the energy conservation laws

In addition: nuclear spin depends on A

if A is even, then I = integer: 0, 1, 2, ...

Unstable Nuclides

76

DE = [M1 – Z1× me – M2 + (Z1 + 1) × me – me]c2

Since neutrino has no mass:

> + meMAZ MAZ 1-

21MA

Z-1MAZ + Z× me > + me +(Z-1) × me

M1 > M2 + 2me

This means, that b+ is only possible if DE = 2×me× c2 ³ 1.022 MeV

b-Decay

Energy conditions for b--decay

= (M1 – M2) c2

taking the masses of nuclides

M1 > M2 + me

Energy conditions for b+-decay

Unstable Nuclides

77

from higher shells ® more energetic, characteristic X-rays

If DE is < 1.022 MeV: we find electron capture e

Energy conditions

b-Decay

for which the same conditions as for a b--decay apply

and >MAZ MAZ 1-DE = (M1 – M2)·c2

some nuclides do both, e and b+

the captured e- from the K-shell are replaced by e-

Unstable Nuclides

78

which is very small compared to DE

Emax = Ee + En

b-Spectra

Emax = Ee + En + EN EN = recoil nucleusmore precise

since Mn >>Me, En is neglectable (for Mn) > 5 u, DE – Emax ~ 0.01%)

for e decay, Ee is the binding energy in the shell

the n gets all the energy

Unstable Nuclides

79

maximum betweendtdN

31

21

Emax and Emax

b-Spectra

The coulomb field of nucleus accelerate b+ Þ low energy b+ particles are rare

b- are attracted by the nucleus Þ many low energy b- particles

Unstable Nuclides

80

The simplest case for b- decay is DE = 0.78 MeVt1/2 = 889 s-1

which is allowed since mn > mH

b- decays often result in excited daughter Þ prompt g-emission might follow

b-Spectra

Unstable Nuclides

81

The nucleus receives essentially no recoil

g-Radiation

g-radiation accompanies the b- (or b+) decay

the g-spectrum of a radionuclide represents its finger print

the nucleus might exist in excited states

The overall occurrence of g-transitions can be calculated

Unstable Nuclides

82

Upon emission of a g-quant, the angular momentum number changes by an integer l since g-quants also have an integer l

Dipolradiation l = 1Quadrapolradiation l = 2Oktopolradiation l = 3

g-Radiation

g-Energies are between 10 keV and 18 MeV.

The probability for a transition depends on the energy of the excited state on the numbers of nucleus and the multipole order of the radiation

Unstable Nuclides

83

between t½ of the excited state and the energy

g-Radiation

for an allowed g-transition there is a relationship (=selection rule)

Unstable Nuclides

84

g-Radiation

Unstable Nuclides

85

If the change between Ia and Ie is large, the probability for the transition is low and t½ long

Such long lived isomeric states are very important for medicinal application

Tc 99

6,0 h 2,1×105 a

lg 141... b- 0,3...e- g (90)b- b- 1,2

s 20g (322...)

Isomeric transition (IT)

Unstable Nuclides

86

The t½ of isomeric states can be precisely calculated from a formula developed by Weisskopf et al.

Type of Change of the orbital spin Change ofradiation quantum number, DL the parity

Half-life (s) at energies of

1 MeV 0.2 MeV 0.05MeV

E1 1 Yes 2 × 10-16 3 × 10-14 2 × 10-12

M1 1 No 2 × 10-14 2 × 10-12 2 × 10-10

E2 2 No 1 × 10-11 3 × 10-8 3 × 10-5

M2 2 Yes 9 × 10-10 3 × 10-6 3 × 10-3

E3 3 Yes 7 × 10-7 6 × 10-2 9 × 102

M3 3 No 7 × 10-5 5 8 × 104

E4 4 No 8 × 10-2 2 × 105 4 × 1010

M4 4 Yes 7 1 × 107 4 × 1012

Isomeric transition (IT)

Unstable Nuclides

87

excited nuclides can transfer the full energy „Eg“ to one of the electrons in the shell which is then emitted

IC electrons are monoenergetic Ee = Eg – EK,L,

99mTc [99Tc]+

Such an electron is called a conversion electron

Internal conversion (IC)

Instead of emitting a g-quant:

IC and g-emission compete

Unstable Nuclides

88

Since the electron density increases near the nucleus,IC with K electrons are more likely then with L, M, etc.

The magnitude depends on the shell (K, L, ...)

g

aNNe=


The ratio between Ng and NIC is called: Conversion coefficient

Unstable Nuclides

89

Internal conversion is not an internal photo effect

X-ray emission

by emitting further e- from higher shells with low energy „Auger electrons“ or an „Auger cascade“

http://commons.wikimedia.org/wiki/File:Atom_model_for_Auger_process_DE.svg


After IC, the „hole“ in the inner shells is filled with e- from outer shells

or

Unstable Nuclides

90

4th decay series has been reactivated by the artificial production of plutonium in nuclear reactors

Cosmic Radiation

Without decay series

20 Radioactive primordial nuclides

Long half-life times

Most important representative 40K

Terrestrial Radiation

From decay series

232Th ® 208Pb235U ® 207Pb238U ® 206Pb241Pu ® 209Bi

Natural RadioactivityProtons (93 %)

a-Particles (6.3 %)

Heavier nuclides (0.7 %)

Unstable Nuclides

91

Secondary radiation 14C: Formation pCnN 11

146

10

147 +®+

Decay eNC 0

1147

146 -+®

3H: Formation CHnN 126

31

10

147 +®+

Decay eHeH 0

132

31 -+®

Energy of the protons can be up to 1014 MeV

Initialization of nuclear reactions 3H, 7Be, 14C, 22Na

t1/2 = 5730 y

t1/2 = 12.32 y

Cosmic RadiationProtons (93 %)

a-Particles (6.3 %)

Heavier nuclides (0.7 %)

Unstable Nuclides

92

Radioactive nuclides without decay series

Electron capture

Nuclide T1/2 Decay Isotopic abundance

187Re 5 x 1010 y ß- 62.60 115In 4.4 x 1014 y ß- 95.7 123Te 1.24 x 1013 y K 0.908 87Rb 4.8 x 1010 y ß- 27.8 113Cd 9.3 x 1015 y ß- 12.2

Other examples

20 Radioactive nuclides

From primordial resources

Very long half-lives

Most important: is 40K (T1/2 = 1.28 x 109 y)

Terrestrial Radiation

Unstable Nuclides

93

232Th ® 208Pb (Thorium family 4n)235U ® 207Pb (Actinium family 4n+3)238U ® 206Pb (Uranium family 4n+2)241Pu ® 209Bi (Neptunium family 4n+1)

Pu/Bi series was decayed in nature due to the relatively short half-life of 237Np (t1/2 = 2.144 ∙106 a)

Cascades of radioactive decays which origin from a certain radioactive nuclide and ends with a certain stable nuclide (lead or bismuth)

Decay series include a-, ß- and g-decays

They can have branches but always end with the same final product

Four natural decay series were established

Natural decay series

Unstable Nuclides

94

232Th ® 208Pb235U ® 207Pb238U ® 206Pb241Pu ® 209Bi

Thorium family Actinium family Neptunium familyUranium family

Crucial element:Radon, inert gascan leave the compartment

Natural decay series

Unstable Nuclides

95

Daughterisotopes in the air

Daughterisotopes in the walls

Daughterisotopes in the soil

Radon is a main source of natural radioactivity

228Rn, 224Rn, 220Rn from 232Th

226Rn, 222Rn from 238U

219Rn from 235U (227Ac series)

Radon is a mobile radioelement

Formation from decay series:

Radon

Unstable Nuclides

96

Radon

Unstable Nuclides

97

Durchschnittliche Strahlenbelastung pro Jahr: 3,2 mSv9% kosmische

Strahlung

7% körperinnere Strahlung

13% terristische Strahlung

29% Rn-222 im Mauerwerk

42% Röntgenstrahlung

Mean radiation exposure per year: 3.2 mSv

42%

X-Ray

13% terrestrial

radiation

29% Rn in

building material

9% Rn cosmic

radiation7% internal

radiation

Mean radiation exposure to persons in industrial countries

Natural Radioactivity

Laws of Radioactive Decays

98

or substituted with t1/2

chemical reaction with no reversible steps

BdtdN

dtdB

×--= 21 l gives )( 210

112

12

tt eeNN ×-×- -×-

= ll

lll

úúû

ù

êêë

é÷øö

çèæ-

-=

- )1()2(

1)2/12/1

2/12/12

2/12/1

211

)1(/)2(1)1(/)2( tt

NttttN

Equilibrium N1 = N2 is achieved after a certain time, depending on t½(1) and t½(2)

Equilibria in decay series


99

For all cases t1/2(A) / t1/2(B) are important

)1( 201

2

1 teNN ll l

l --×= a normal exponential

a) t1/2(A) >> t1/2(B) this is called secular equilibrium

The N(A) / N(B) equation reduces to

http://www.epa.gov/radiation/understand/equilibrium.html



100

After t >> t1/2(2) equilibrium is achieved (~ 10 half lives of B)

and at equilibrium)1()2(

2/1

2/1

2

1

1

2

tt

NN

==ll

The activities of mother and all daughters are the same after some time if secular conditions applies

allows determination of very long half lives from daughter products. Explain!

calculation of mass ratios of radionuclides and other applications



101

If t1/2(A) » t1/2 (B) but ratio ³5 the equilibrium is called transient

and at equilibrium)()(

)(

2/12/1

2/1

1

2

BtAtBt

NN

-=

daughter activity2

1

22

21

2

1 1ll

ll

-=××

=NN

AA

now all terms have to be considered

http://www.epa.gov/radiation/understand/equilibrium.html



102

t1/2(A) < t1/2 (B)

no equilibrium is achieved!



103

A ® B ® C ® D ® ...

typically the natural decay series

...+×+×= ×-×- tB

tAn

BA ececN llthe decay law yields

with etc.0

11312

121

))()((...

An

nA Nc ×

---××

= -

lllllllll

úû

ùêë

é--

+--

+--

=---

))(())(())(( 313223211312

01213

321

llllllllllllll

lll ttt eeeNN

which can be rewritten

Successive transformations


104

If the mother is very long lived, secular equilibrium applies and

tn ecN ×-×= 1

1l 0

11

1 Ncn

×=ll

with

n

n

NN

ll1

1

=and (as shown before) and An = A1

Successive transformations

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