Introduction to Radiobiology Lesson 1milotti/Didattica/...Edoardo Milotti - Radiobiology 3 Aim of...

Introduction to RadiobiologyLesson 1

Master of Advanced Studies in Medical Physics A.Y. 2019-20

Edoardo MilottiPhysics Dept. – University of Trieste

Edoardo Milotti - Radiobiology 2

Radiation damages all kinds of human tissues – both healthy and diseased – as well as other materials

An area of ulceration on the hand, caused by exposure to radiation therapy


Aim of radiotherapy: destroy cancer cells, limit damage to healthy tissues

The purpose of these lessons is twofold:

1. gain a basic knowledge of the phenomenology of radiation damage to tissues

2. understand the basics of therapy optimization, based on the concept of maximum damage to cancer cells, minimum damage to healthy tissues


What is meant by understanding the basic mechanisms? Tissues are difficult, material science is easy, so let’s start with materials. Consider graphite in nuclear reactors

The Windscale (Sellafield) nuclear power plant, where the worst nuclear accident in the UK took place in 1957. The accident was due to uncontrolled energy release from the graphite in the reactor.


Nuclear reactors and the Wigner EffectThe Windscale accident was due to uncontrolled energy release from graphite in the nuclear reactor.

• Wigner energy occurs in graphite under neutron irradiation because atoms are displaced from their normal lattice positions into configurations of higher potential energy (on average this corresponds to ~ 25 eV per displaced atom).

Graphite unit cell

Edoardo Milotti - Radiobiology 6R&D TECHNICAL REPORT P3-080/TR

27

Figure 2.2 The structure of graphite and the formation of interstitials (from Simmons 1965 and Kelly 1981)

The hexagonal structure of graphite

a

b

a

b

A single

Di-interstitial (C2)

(C2)2 interstitials

Equilibrium positions of di-interstitials


R&D TECHNICAL REPORT P3-080/TR

26

Vacant Lattice sites X Displaced atoms Figure 2.1 Distribution of displaced atoms and vacant lattice sites (from Simmons 1965)

Primary knock-on atom

Fast neutron

• Fast neutrons undergo a series of collisions and produce displacement cascades

• A 1 MeV neutron produces on average about 900 displacements

• Not all displacements produce defects, as a displaced C can fill a vacancy

• The interstial atom-vacancy pairs are called Frenkel defects



29

Figure 2.4 Schematic annealing spectra for graphite irradiated at various temperatures (from Simmons 1965)

- 2 0 0 0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0

A n n e a l i n g t e m p e r a t u r e ( ° C )

Ene

rgy

rele

ase

with

tem

pera

ture

I r r a d i a t i o n t e m p e r a t u r e - 1 9 5 ° C

- 2 0 0 0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0


Ene

rgy

rele

ase

with

tem

pera

ture

I r r a d i a t i o n t e m p e r a t u r e 3 0 ° C

- 2 0 0 0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0


Ene

rgy

rele

ase

with

tem

pera

ture

I r r a d i a t i o n t e m p e r a t u r e 2 0 0 ° C


29

Figure 2.4 Schematic annealing spectra for graphite irradiated at various temperatures (from Simmons 1965)

- 2 0 0 0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0


Ener

gy r

elea

se w

ith te

mpe

ratu

re

I r r a d i a t i o n t e m p e r a t u r e - 1 9 5 ° C

- 2 0 0 0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0


Ener

gy r

elea

se w

ith te

mpe

ratu

re

I r r a d i a t i o n t e m p e r a t u r e 3 0 ° C

- 2 0 0 0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0


Ener

gy r

elea

se w

ith te

mpe

ratu

re

I r r a d i a t i o n t e m p e r a t u r e 2 0 0 ° C

Energy released by irradiated graphite as temperature increases


• The quantity of accumulated stored energy is a function of fast neutron flux, irradiation time, and temperature.

• The higher the irradiation temperature, the lower is the amount of “stored” energy. In all cases, a saturation point may be achieved in terms of the total amount of stored energy for long periods of irradiation.

• The maximum amount of stored energy ever found in a graphite sample is ~2,700 J/g, which, if all released at once, could theoretically lead to a temperature rise of approximately 1500 °C assuming adiabatic conditions.

• The Wigner effect has been known for a long time, and in reactors that use graphite as a moderator there are established procedures to periodically release the stored energy with annealing cycles.


What have we gained?

• There is a problem that has led to severe accidents in nuclear power plants.

• The physics has been understood, the culprit has been found.

• As a result, annealing cycles have been introduced to mitigate the problem, and, eventually, graphite has been replaced with other moderators in nuclear reactors.


Radiation damage in materials-428- Journal of the Korean Physical Society, Vol. 51, No. 1, July 2007

Fig. 3. Typical pictures of etched track pits caused by twodi↵erent particles. (a) 5.4-MeV ↵ particles (b) ⇠0.9-MeVprotons.

polyester, and di↵erent target thicknesses between 1 µmand 50 µm were used to generate proton with di↵erentenergies.

The Thomson parabola spectrometer is based uponthe superposition of an electric field and a magnetic fieldand can be used to analyze the kinetic energy and thecharge of particles at various the positions. An electricfield of E = 1.5 kV and a magnetic field of B = 8.47 kGinside a gap of 5 mm was applied along a 5-cm length.The pinhole of 400 µm was installed in front of the TPSto improve the energy resolution of the spectrum, anda CR39 detector was placed 15 mm away from the endof the TPS. This setup enbled us to investigate the de-pendences of the energies, the incident angles, and thecharges of the particles on di↵erent etching conditions.

IV. RESUTLS AND DISCUSSION

Figure 3 presents pictures of typical etched track pitscaesed by 5.4-MeV alpha particles and ⇠0.9-MeV pro-tons etched at 70 �C in 6N NaOH for 6 hours. Sincealpha particles are emitted in random directions from asurface of �35 mm diameter coated by 210Po, their trackpits are randomly cluttered with various shapes. A roundshape indicates normal incidence on the detector surfacewhile an elliptical shape corresponds to oblique incidencetoward the direction of the major axis. The measured de-tection e�ciency was about 40 % in our case. In contrastto the 210Po source, the shapes of etched track pits ofprotons generated by using a 10-TW laser were almostround, which meant most of the protons were incidentperpendicular to the detector surface.

The bulk etch rate was measured by using the weightloss method. Its mean value for a 6-hour etching 70 �C in6N NaOH is 1.396 µm/h, which is slightly greater thanother measurements [11]. The optimal etching conditiondepends on the energies and the kinds of particles. Inthe case of our experiments using a 10-TW laser sys-tem, a few MeVor less protons are the main source to beoptimized.

A TPS produces di↵erent particle trajectories, de-pending on the energy, the mass and the charge of ions,so di↵erent parabolic traces are recorded in the nucleartrack detector for protons and other ions. A horizontal

Fig. 4. Typical spectrogram taken with protons and ionsin a CR39 detector after a Thomson Parabolic Spectrometer.

displacement of tracks in the plastic detector correspondsto a decrease in the particle energy, and a verticle direc-tion is related to the charge-to-mass ratio, Z/m. Fig-ure 4 presents a typical spectrogram taken with protonsand ions generated by high-intensity laser irradiation ofa 13-µm polyester target. When the detector was prop-erly etched, all traces taken with protons and ions wereclearly distiguishable and countable. We can see fromFigure 4 that tracks for 0.1-MeV protons are deformeddue to over-etching, but they are still countable usingthe program ImageJ [12].

Four plastics were placed 15 mm behind the TPS andwere exposed to protons and light ions produced by usinga 6-µm polyester film target. After etching the four de-tectors in the same container for 3, 6, 9 and 12 hours, re-spectively, we measured the depth, H and the diameter,D, of a track pit at di↵erent positions (which is relatedto the energy) as shown in Figure 5. If a good spectrumof protons is to be obtained, the visibility and the count-ability over a wide energy range are important. Afterpassing the optimal etching time, tracks are over-etchedso that a deep V -shaped track becomes more rounded,wider, and shallower with the etching time. From thesedata, we can observe the development of track pits withetching time and the dependence of the track etch rateon the energy of the protons. The accuracy of measuredtrack etch rate is limited by the resolution of the micro-scope and the etching condition. A deeper track depthenhances the contrast ratio, and a size of ⇠10 µm can beresolved using the Omax microscope. The track depthwas the deepest for a 6-hour etching over the etchingenergy range (see Figure 5(a)) with countable sizes of7.5 ⇠ 9 µm (see Figure 5(b)). With increasing the etch-ing time, the absolute variation of the etch rate ratioand the diameter were reduced (see Figure 5(c)). Thetrack depths etched for 9 and 12 hours were shallowerthan that etched for 6 hours while their diameters werelarges. These results indicate that the tracks are over-etched after 6 hours. Furthermore, less background [13]

Radiation damage in CR-39 plastic

CR-39 dosimeter


Radiation damage to plastic scintillators


Radiation damage to human tissues is different from damage in inert material

1. Damage mechanisms are different

2. Cells and tissues have (limited) self-repair capabilities

In these lessons we are going to learn about both topics


RadiationEffectsDamage - 1 - K. E. Holbert

RADIATION EFFECTS AND DAMAGE The detrimental consequences of radiation are referred to as radiation damage. To understand the effects of radiation, one must first be familiar with the radiations and their interaction mechanisms. Further, the fundamental characteristics of the material(s) being irradiated must also be understood. A brief summary of the characteristics of radiation is first presented below. This is followed by a general discussion of the effects of radiation, along with some specific examples, with an emphasis toward the ionizing effects.

1. Ionizing Radiations The radiations of concern here include charged particles such as electrons (beta particles), protons, alphas and fission fragment ions, and the neutral radiations including photons (gamma and X rays) and neutrons. Table I compares some key characteristics of the radiations, including charge, mass, and range in air. For a kinetic energy of 1 MeV, the electron is relativistic (0.94c). For the same energy, the heavier particles are slower, stopped easier and deposit their entire energy over a shorter distance. The passage of radiation through tissue is depicted in Figure 1.

Table I: Comparison of Ionizing Radiation

Radiation (EK = 1 MeV)

Characteristic Alpha (D) Proton (p) Beta (E) or

Electron (e) Photon

(J or X ray) Neutron (n)

Symbol �242 HeorD �11

1 Horp Eore01� J00 n1

0 Charge +2 +1 –1 neutral neutral Ionization Direct Direct Direct Indirect Indirect Mass (amu) 4.001506 1.007276 0.00054858 — 1.008665 Velocity (cm/sec) 6.944×108 1.38×109 2.82×1010 c=2.998×1010 1.38×109 Speed of Light 2.3% 4.6% 94.1% 100% 4.6% Range in Air 0.56 cm 1.81 cm 319 cm 82,000 cm* 39,250 cm* * range based on a 99.9% reduction

Alpha particle: easily stopped least penetrating

Beta particle: very much smallermore penetrating

Gamma ray and X-ray:pure energy with no massmost penetrating

� neutral atom/moleculez ion

Figure 1. Radiation paths in tissue.

Ionizing radiation


Alpha particle (He nucleus)easily stopped, small penetration, very damaging

Beta particle (electron)longer penetration, less ionization, less damaging

Gamma ray and X-raylocalized ionization, less damaging


Energy loss by ionization/excitation – dE/dx


4 33. Passage of particles through matter

with mean M0. Ne is either measured in electrons/g (Ne = NAZ/A) or electrons/cm3

(Ne = NA !Z/A). The former is used throughout this chapter, since quantities of interest(dE/dx, X0, etc.) vary smoothly with composition when there is no density dependence.

Muon momentum

1

10

100M

ass s

topp

ing

pow

er [M

eV c

m2 /

g]

Lind

hard

-Sc

harf

f

Bethe Radiative

Radiativeeffects

reach 1%

Without δ

Radiativelosses

βγ0.001 0.01 0.1 1 10 100

1001010.1

1000 104 105

[MeV/c]100101

[GeV/c]100101

[TeV/c]

Minimumionization

Eµc

Nuclearlosses

µ−µ+ on Cu

Anderson-Ziegler

Fig. 33.1: Mass stopping power (= !"dE/dx#) for positive muons in copper as a functionof "# = p/Mc over nine orders of magnitude in momentum (12 orders of magnitude inkinetic energy). Solid curves indicate the total stopping power. Data below the break at"# $ 0.1 are taken from ICRU 49 [4], and data at higher energies are from Ref. 5. Verticalbands indicate boundaries between di!erent approximations discussed in the text. Theshort dotted lines labeled “µ! ” illustrate the “Barkas e!ect,” the dependence of stoppingpower on projectile charge at very low energies [6]. dE/dx in the radiative region is notsimply a function of ".

33.2.2. Maximum energy transfer in a single collision :

For a particle with mass M ,

Wmax =2mec2 "2#2

1 + 2#me/M + (me/M)2. (33.4)

In older references [2,8] the “low-energy” approximation Wmax = 2mec2 "2#2, valid for2#me % M , is often implicit. For a pion in copper, the error thus introduced into dE/dxis greater than 6% at 100 GeV. For 2#me & M , Wmax = Mc2 "2#.

At energies of order 100 GeV, the maximum 4-momentum transfer to the electron canexceed 1 GeV/c, where hadronic structure e!ects significantly modify the cross sections.

June 5, 2018 19:57


The Bragg peak

Bragg curve of 5.49 MeV alpha particles in air. This radiation is produced from the initial decay of radon (222Rn). Stopping power (which is essentially identical to LET) is plotted here versus particle range.

(Adapted from the Wikipedia article http://en.wikipedia.org/wiki/Linear_energy_transfer)

x(E) =

Z E0

E

��dx

dE

�� dE

��dE

dx

��


(adapted from http://en.wikipedia.org/wiki/Bragg_peak and http://en.wikipedia.org/wiki/Proton_therapy )

http://en.wikipedia.org/wiki/Bragg_peak

http://en.wikipedia.org/wiki/Proton_therapy


Track structure (example, low-energy electrons)


e !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!e2

c " f#e2max $ e2

c%p

i ! 1

ec#emax=ec%f i ! 2;

(

(29)

where f is a random number uniformly distributed between 0and 1. Afterwards, by using another random number, theobtained value of e in Equation (29) accepts if f < Fi.

In a homogenous target, there is no difference for energyloss in any direction. In accordance with elastic scattering,the projectile is rotated by an angle Dh after passing a thick-ness Dx0 through a matter. Thus, the total angle of the projec-tile becomes h" Dh with respect to the initial beamdirection. In this case, h is the incident angle of projectile inthe thickness Dx0. This process is stochastic so that Dhshould be obtained by random sampling from the PDF ofelastic scattering. According to the Moliere series43 and byignoring the small probability of large-angle scattering, theangle deviation can be analytically sampled as follows:29

Dh ! 60:3965

!!!!!!!!!!!!!!!!!!!!!!!!!!!!$ln fQ2BqDx0

p2b2A

s

; (30)

where n is a random number between 0 and 1; p and Bdenote the projectile momentum and the Moliere parameter,respectively. The variable Q is

!!!!!!!!!!!!!!!!!!Z#Z " 1%

pand Z for electron

and proton, respectively. The sign of angle deviation inEquation (30) can be determined by using another randomnumber f0 2 &0; 1'. Therefore, if f0 ( 0:5, the positive sign isconsidered; otherwise the negative sign is accepted. In orderto increase the accuracy of our previous study,29 the thick-ness Dx0 is calculated by

Dx0 !cb2A 1:13" 3:76Z2

b21372

!

8831qq: (31)

In the relation, q is given by

q ! Z " 1# %Z 13 for proton

Z43 for electron:

(

(32)

In this analysis, the parameter c is considered as a constantduring the passage of a projectile through the target.On the other hand, the Moliere parameter B can be obtainedfor c ) 100 with the associated error less than 3% byB ! 1:153" 2:583 log 10c.44 It is worth noting that the val-ues of thicknesses Dx0 and Dx in Equations (31) and (16) arenot equal. In this case, the values of the projectile energy onthickness Dx0 can be obtained by using an interpolationmethod.

FIG. 2. Trajectories for 100 protons (a)and 100 electrons (b) with the incidentenergy of 5 MeV in liquid water.

053120-5 M. R. Kia and H. Noshad Phys. Plasmas 23, 053120 (2016)

from M. R. Kia , and H. Noshad, Phys. Plasmas 23, 053120 (2016)


electrons in water

Ionizationsexcitations


α particles



Carbon ions



For indirect action of x rays the chain of events from the absorption of the incident photon to the final biological damage is as follows:

Incident x-ray photon

Fast electron or positron

Ion radical

Free radical

Breakage of bonds

Biological effect

Typical time scale involved in these 5 steps:

• (1) The physics of the processtakes of the order of 10-15 s.

• (2) The ion radicals have a lifetimeof the order of 10-10 s.

• (3) The free radicals have a lifetimeof the order of 10-5 s.

• (4) The step between the breakageof bonds and the biological effectmay take hours, days or years.

Water radiolysis and production of ROS (Reactive Oxygen Species)


Molecular oxygen and the superoxide anion

Oxygen molecule: double bond ”hides” the electrons

Superoxide anion: added electron forces one of the atoms to “display” an unpaired electron.


Hund's rule states that

• Every orbital in a sublevel is singly occupiedbefore any orbital is doubly occupied.

• All of the electrons in singly occupied orbitalshave the same spin (to maximize total spin).

In the case of oxygen, the triplet statefits the rule and is the ground state.

This is clearly displayed in thebehavior of oxygen, which, whenliquid, is paramagnetic (electronswith aligned spinse)

However, three different states areactually possible, two with pairedelectrons.

Singlet oxygen is common, an easy way toproduce it is by mixing hydrogen peroxidewith sodium hypochlorite. It displays onlyresidual paramagnetism, associated withthe orbital angular momentum.

The Three Forms of Molecular Oxygen

Mlchael Lalngl California State University, Northridge, CA 91330

: Everyone is familiar with the oxygen in the air ( I ) , and most have oreoared a "oure" samole of this important ele- ment. here &e many ways of doing this, and onk of the best is to heat a mixture of 90 parts KCIO2and 10 parts MnOn (by mass) and collect the gas that is evolved in a gas j& by downward displacement of water (2).

I t is certain that pure oxygen gas is very reactive. Not only will a glowing splint burst into flame when dropped into oxygen, but heated iron filings will hurn when dropped into the pure gas. This latter reaction is of course close to that of iron rusting (3), although rusting requires oxygen, water, and an electrolyte to proceed (4).

On being cooled helow -183 O C oxygen condenses into a beautiful pale blue liquid with a remarkable property: it sticks to the poles of a magnet (5)! This property of heing attracted to a magnetic field, called paramagnetism, is found in any molecule or material that contains unpaired electrons. So these are a few of the facts about the behavior of elemental oxygen. The question is whether the bonding model for the pair of oxygen atoms in the diatomic molecule fits these facts.

The simple molecular orhital model for diatomic molecules works beautifully (6). Figure 1 shows the energy level diagram for the Oz molecule. Pairs of electrons are assigned to the a and the two r honding orbitals (BO), and one electron is assiened to each of the two r* antihondine orbitals (AB), the latter twoelectrons having their spins p&allel as reauired bv Hund's rule (7). These two electrons obev the "ma&num multiplicity, minimum energy" rule, andthey are clearly of parallel spin. Thus, the 0 2 molecule has two unpaired electrons and is paramagnetic. This explanation of the paramagnetism of oxygen was the great triumph of the molecular orbital model.

But what prevents us from assigning the two electrons to the same orhital hut with opposite spin (Fig. 2)? And what of keeping the two electrons in different r* orbitals but assigning opposite spins to them (Fig. 3)?

The three electron distributions described above are clearly different. The first of these, the ground state, has two unpaired electrons and is paramagnetic, while the other two have no unpaired electrons and are both diamagnetic. In other words, the simple molecular orhital picture of honding in diatomic molecules predicts that three forms of oxygen molecules could exist. The oxygen molecules with the electron configurations illustrated in Figures 2 and 3 have all electrons paired so they will not be attracted by a magnetic field. Therefore, they will differ from the paramagnetic form shown in Fieure 1 and so should he detectable. Furthermore. they shouldbave different chemical properties. Even though the two nuclei are identical in each case. the form with two unpaired electrons will differ in chemical reactivity from the ones in which all electrons are oaired. Also. because the ele~tronconfi~urationsarediftere~t, these three forms must differ in enerrv. Unfortunatelv, we cannot deduce their relative energies-&her than to say that the form with two unpaired electrons will he lowest in energy (Fig. 4), in keeping with Hund's rule (7).

, ' On leave from University of Natal, Durban, South Africa.

Flgve 1. Energy level diagram of the O2 molecule (ground state blplet form. 3Z)drawn to scale, wlth wbltal energies measured by photmlecbon spectroc- copy. Note the two unpaired electrons of parallel spin that occupy the two w' antibonding wbltals (AB). (Energies are In kJ Iml X 100).

Figwe 2. (lefl) Schematle energy level dlagam of me oxygen molecule in the more stable slnglet state, 'A. This form lies 94.7 kJ (7882 cm-', 1269 nm) in energy above the blplet ground state.

Figure 3. (rlgM) Smematloenergy level diagram of the oxygen molecule In the second (and less sable) singlet state '2. This state lies 158 kJ (13120 cm-'. 762 nm) in energy above the triplet ground state.

Figure 4. Schematic diagram showing Gle relative enargles of the highest occupied orbitals of the oxygen molecules in the three states: 32, 'A, '2.

We can also ponder on the 0-0 bond lengths in the three different electronic states: will they be the same or different? In each state there are six honding electrons and two antibonding electrons. Clearly the formal bond order in each case will he 2. We are therefore led to predict that the three forms would have similar 0-0 bond lengths, with the bond lengths in the forms with all electrons paired predicted to be somewhat longer than in the paramagnetic form.

Volume 66 Number 6 June 1969 453

The Three Forms of Molecular Oxygen

Mlchael Lalngl California State University, Northridge, CA 91330

: Everyone is familiar with the oxygen in the air ( I ) , and most have oreoared a "oure" samole of this important ele- ment. here &e many ways of doing this, and onk of the best is to heat a mixture of 90 parts KCIO2and 10 parts MnOn (by mass) and collect the gas that is evolved in a gas j& by downward displacement of water (2).

I t is certain that pure oxygen gas is very reactive. Not only will a glowing splint burst into flame when dropped into oxygen, but heated iron filings will hurn when dropped into the pure gas. This latter reaction is of course close to that of iron rusting (3), although rusting requires oxygen, water, and an electrolyte to proceed (4).

On being cooled helow -183 O C oxygen condenses into a beautiful pale blue liquid with a remarkable property: it sticks to the poles of a magnet (5)! This property of heing attracted to a magnetic field, called paramagnetism, is found in any molecule or material that contains unpaired electrons. So these are a few of the facts about the behavior of elemental oxygen. The question is whether the bonding model for the pair of oxygen atoms in the diatomic molecule fits these facts.

The simple molecular orhital model for diatomic molecules works beautifully (6). Figure 1 shows the energy level diagram for the Oz molecule. Pairs of electrons are assigned to the a and the two r honding orbitals (BO), and one electron is assiened to each of the two r* antihondine orbitals (AB), the latter twoelectrons having their spins p&allel as reauired bv Hund's rule (7). These two electrons obev the "ma&num multiplicity, minimum energy" rule, andthey are clearly of parallel spin. Thus, the 0 2 molecule has two unpaired electrons and is paramagnetic. This explanation of the paramagnetism of oxygen was the great triumph of the molecular orbital model.

But what prevents us from assigning the two electrons to the same orhital hut with opposite spin (Fig. 2)? And what of keeping the two electrons in different r* orbitals but assigning opposite spins to them (Fig. 3)?

The three electron distributions described above are clearly different. The first of these, the ground state, has two unpaired electrons and is paramagnetic, while the other two have no unpaired electrons and are both diamagnetic. In other words, the simple molecular orhital picture of honding in diatomic molecules predicts that three forms of oxygen molecules could exist. The oxygen molecules with the electron configurations illustrated in Figures 2 and 3 have all electrons paired so they will not be attracted by a magnetic field. Therefore, they will differ from the paramagnetic form shown in Fieure 1 and so should he detectable. Furthermore. they shouldbave different chemical properties. Even though the two nuclei are identical in each case. the form with two

unpaired electrons will differ in chemical reactivity from the ones in which all electrons are oaired. Also. because the ele~tronconfi~urationsarediftere~t, these three forms must differ in enerrv. Unfortunatelv, we cannot deduce their relative energies-&her than to say that the form with two unpaired electrons will he lowest in energy (Fig. 4), in keeping with Hund's rule (7).

, ' On leave from University of Natal, Durban, South Africa.

Flgve 1. Energy level diagram of the O2 molecule (ground state blplet form. 3Z)drawn to scale, wlth wbltal energies measured by photmlecbon spectroc- copy. Note the two unpaired electrons of parallel spin that occupy the two w' antibonding wbltals (AB). (Energies are In kJ Iml X 100).

Figwe 2. (lefl) Schematle energy level dlagam of me oxygen molecule in the more stable slnglet state, 'A. This form lies 94.7 kJ (7882 cm-', 1269 nm) in energy above the blplet ground state.

Figure 3. (rlgM) Smematloenergy level diagram of the oxygen molecule In the second (and less sable) singlet state '2. This state lies 158 kJ (13120 cm-'. 762 nm) in energy above the triplet ground state.

Figure 4. Schematic diagram showing Gle relative enargles of the highest occupied orbitals of the oxygen molecules in the three states: 32, 'A, '2.

We can also ponder on the 0-0 bond lengths in the three different electronic states: will they be the same or different? In each state there are six honding electrons and two antibonding electrons. Clearly the formal bond order in each case will he 2. We are therefore led to predict that the three forms would have similar 0-0 bond lengths, with the bond lengths in the forms with all electrons paired predicted to be somewhat longer than in the paramagnetic form.

Volume 66 Number 6 June 1969 453

singlet oxygen

triplet oxygen

The reactivity of molecular oxygen: "triplet oxygen" and "singlet oxygen"


Simple explanation of the reactivity of "singlet oxygen"

Atom A Atom B

Bond with paired electrons

Here it is difficult to insert an oxygen molecule with unpaired spins, but it is easy to insert singlet oxygen. Thus higher reaction rates for singlet oxygen than triplet oxygen!


Reactivity of atomic oxygen (adapted from Footie et al. (eds.) "Active Oxygen in Chemistry", Chapman & Hall, 1995)

Atomic oxygen, which is atomic number 8, has a total of eight electrons and is highlyreactive. Using the concept of atomic orbitals and the Pauli exclusion principle to fillthese orbitals with electrons, the placement of these eight electrons in the atomicorbitals of O is represented by the electronic configuration 1s22s22p4.

Since the 2p orbitals are only partially filled, there are three different ways toarrange the electrons in the 2px 2py and 2pz orbitals, and the ground state mustobey Hund’s rule.

2 Overview of the Energetics and Reactivity of Oxygen

The most abundant form of elemental oxygen is the gaseous diatomic molecule O2 (properly called" dioxygen" but frequently called" oxygen" in these chapters), which accounts for approximately 21 % by volume of dry air. The oxygen atoms in the atmosphere are composed of three iso-topes: oxygen-16, which makes up 99.759%, oxygen-17, 0.037%, and ox-ygen-18, 0.204% (Staschewski, 1974). The isotopes 170 and 180 and com-pounds containing them have proven to be very valuable aids in the elucidation of mechanisms of reactions involving oxygen, despite their low natural abundances, which make them quite expensive.

ENERGETICS AND CHEMICAL REACTIVITY OF ATOMIC OXYGEN AND DIOXYGEN

To understand the chemical reactivity of oxygen, it is necessary to discuss first the electronic configuration of oxygen. Atomic oxygen, which is atomic number 8, has a total of eight electrons. Using the concept of atomic orbitals and the Pauli exclusion principle to fill these orbitals with electrons, the placement of these eight electrons in the atomic orbitals of o is represented by the electronic configuration ls22s22p4. Since the 2p orbitals are only partially filled, there are three different ways to arrange the electrons in the 2px, 2py, and 2pz orbitals (Fig. 1-1). Hund's rule, which states that the ground-state configuration corresponds to an orbital oc-cupancy that gives the highest multiplicity, can be used to rule out either the second or the third configurations in Fig. 1-1 as the ground state, because each of these configuration has a multiplicity of 1 as compared to a multiplicity of 3 for the first configuration. The ground state of atomic oxygen therefore has two unpaired electrons, and is designated as the 3p ("triplet P") state. Of the two remaining configurations, the second is lower in energy based on Hund's second rule which states that, if the multiplicity is the same, the configuration with the highest total orbital angular momentum (L) will have the lower energy. Because the second configuration has the higher L value, it is lower in energy. This configuration is the first excited state of atomic oxygen, designated as

FIGURE 1-1 Three possible electron configurations in the partially filled 2p orbitals of atomic oxygen. Under each configuration is the corresponding term symbol.

t++-+- #++- +t+-+-3p

Preferredby Hund’s rule


The ground state of atomic oxygen therefore has two unpaired electrons, and isdesignated as the 3P ("triplet P") state.

The first excited state of atomic oxygen, is designated as the 1D ("singlet D") state. Thethird configuration is the second excited state, designated 1S. The situation is similar tothat found in oxygen molecules.

2 Overview of the Energetics and Reactivity of Oxygen

The most abundant form of elemental oxygen is the gaseous diatomic molecule O2 (properly called" dioxygen" but frequently called" oxygen" in these chapters), which accounts for approximately 21 % by volume of dry air. The oxygen atoms in the atmosphere are composed of three iso-topes: oxygen-16, which makes up 99.759%, oxygen-17, 0.037%, and ox-ygen-18, 0.204% (Staschewski, 1974). The isotopes 170 and 180 and com-pounds containing them have proven to be very valuable aids in the elucidation of mechanisms of reactions involving oxygen, despite their low natural abundances, which make them quite expensive.

ENERGETICS AND CHEMICAL REACTIVITY OF ATOMIC OXYGEN AND DIOXYGEN

To understand the chemical reactivity of oxygen, it is necessary to discuss first the electronic configuration of oxygen. Atomic oxygen, which is atomic number 8, has a total of eight electrons. Using the concept of atomic orbitals and the Pauli exclusion principle to fill these orbitals with electrons, the placement of these eight electrons in the atomic orbitals of o is represented by the electronic configuration ls22s22p4. Since the 2p orbitals are only partially filled, there are three different ways to arrange the electrons in the 2px, 2py, and 2pz orbitals (Fig. 1-1). Hund's rule, which states that the ground-state configuration corresponds to an orbital oc-cupancy that gives the highest multiplicity, can be used to rule out either the second or the third configurations in Fig. 1-1 as the ground state, because each of these configuration has a multiplicity of 1 as compared to a multiplicity of 3 for the first configuration. The ground state of atomic oxygen therefore has two unpaired electrons, and is designated as the 3p ("triplet P") state. Of the two remaining configurations, the second is lower in energy based on Hund's second rule which states that, if the multiplicity is the same, the configuration with the highest total orbital angular momentum (L) will have the lower energy. Because the second configuration has the higher L value, it is lower in energy. This configuration is the first excited state of atomic oxygen, designated as

FIGURE 1-1 Three possible electron configurations in the partially filled 2p orbitals of atomic oxygen. Under each configuration is the corresponding term symbol.

t++-+- #++- +t+-+-3p

Easier to pair spins when electron added, faster reaction rates

Slower reaction rate


The superoxide anion is highly reactive and toxic

• Human cells use the superoxide anion to kill bacteria.

• The enzymes of the complex NADPH oxidase (NOX) produce superoxide.

• The absence of NADPH oxidase leads to the chronic granulomatous diseases.

• The superoxide anion is toxic to human cells, and this requires mechanisms to get rid of it, like the enzyme superoxide dismutase.


Main types of ROS (Reactive Oxygen Species)

Electron structures of common reactive oxygen species. Each structure is providedwith its name and chemical formula. The • designates an unpaired electron.

This involves mostly the ionization

and the excitation of water molecules


Physical stage (time < 10-15 s)

�3.�Mechanisms�of�water�radiolysis��

The� radiolysis� of�water� is� usually� divided� in� three�more� or� less� overlapping� stages:� physical��(<10Ͳ15�s),�physicoͲchemical�stage� (a10Ͳ15Ͳ10Ͳ12�s)�and�nonͲhomogeneous�chemical�stage� (a10Ͳ12Ͳ10Ͳ6�s).�Although� this� time� division� is� controversial,� it� gives� a� convenient� way� to� describe� the�mechanisms�involved�in�water�radiolysis.��3.1�Physical�stage�(<10Ͳ15�s)��

The�physical�stage�is�the�absorption�of�ionizing�radiation�by�matter.�The�main�consequences�are�the�ionization�and�excitation�of�water�molecules.�An�ionization�event�is�the�removal�of�an�electron�from�the�water�molecule:�� (3)��Similarly,�an�excitation�is�the�transfer�of�an�electron�from�a�fundamental�state�to�an�excited�state:�� (4)�� There� are� several�molecular� orbitals� and� excitation� levels� in� the�water�molecule.� The� description� of�these�states�is�beyond�the�scope�of�this�text�and�is�not�necessary�for�the�discussion�that�follows.��3.2�PhysicoͲchemical�stage�(a10Ͳ15Ͳ10Ͳ12�s)��

The�ionized�and�excited�molecules�created�during�the�physical�stage�are�highly�unstable.�During�this� stage,� lasting�a10Ͳ12� s,� the� ionized� and�excited�water�molecules�dissipate� their�energy�by�energy�transfer� to�neighboring�molecules�and�bond� rupture.�The�sequence�of�events�of� the�physicoͲchemical�stage� is,� in� fact,� not� well� characterized� experimentally.� However,� some� important� physicoͲchemical�stage�events�worth�mentioning:�proton�transfer�to�a�neighboring�molecule,�dissociation�of�excited�water�molecule�and�electron�thermalization�and�solvatation.��The� proton� transfer� to� a� neighboring� water� molecule� is� very� important,� because� it� leads� to� the�

production�of�an�.OH�radical*:��

�x�x �o� OHOHOHOH 322 � (5)�

�

��*In�chemistry,�a� radical� (also� referred� to�as� free� radical)� is�an�atom,�molecule�or� ion�with�at� least�one�unpaired�electron.� The�unpaired� electron�usually� cause� them� to�be�highly� chemically� reactive.� The� radical� site� is�usually�

noted�by�putting�a�dot�on�the�atom�(ex.:�.OH)�






�x�x �o� OHOHOHOH 322 � (5)�

�



The ionized and excited molecules produced in the physical stage are highly

unstable, and they transfer their energy by dissipating it on neighboring

molecules and by breaking chemical bonds.

Proton transfer to a neighboring water molecule leads to the production of

·OH radicals (i.e., an ion with an unpaired electron; radicals are usually quite

reactive).


Physico-chemical stage (time ≈ 10-15 s – 10-12 s)






�x�x �o� OHOHOHOH 322 � (5)�

�



There are several pathways for the dissociation or the deexcitation of the excited water molecule


Physico-chemical stage (time ≈ 10-15 s – 10-12 s) /ctd.

They�are�several�channels�for�the�dissociation�of�an�excited�water�molecule:��

�OHHOH *

2xx �o

�(6a)

�

�)D(OHOH 1

2*

2 �o�

(6b)� �

�)P(OH2OH 3*

2 �o x

�(6c)�

�Where�O(1D)�and�O(3P)�are�the�singlet�and�triplet�state�of�the�atomic�oxygen,�respectively͘ �The�excited�water�molecule�can�also�return�to�its�fundamental�state�without�dissociation�(by�heat�loss):��

� OHOH 2*

2 o � (7)��

Most�secondary�electrons�have� low�energy6,�but�some�of�them�may�have�energy� in�the�keV�or�even� in� the�MeV� range.� These� electrons� lose� their� energy� into�medium� by� doing� further� ionization,�excitations� until� they� eventually� reach� thermal� equilibrium� with� the� liquid.� The� electron,� which� is�negatively�charged,�interacts�with�the�dipoles�of�the�surrounding�water�molecules�and�becomes�trapped�in� a� state� called� «� trapped� electron� ».� Finally,� this� electron� becomes� a� «� hydrated� electron� »,�which�behaves�like�chemical�specie.�This�rapid�sequence�of�events�can�be�written�as�follows:��

�� ooo aqtrth eeee � (8)�

�The� hydrated� (or� solvated)� electron� is� of� great� importance� in�water� radiolysis.� However,� its�

existence�has�been�proposed�only�in�the�1950’s�and�it�was�observed�experimentally�in�the�1960’s.��3.3�NonͲhomogeneous�chemical�stage�(a10Ͳ12Ͳ10Ͳ6�s)��

At�the�end�of�the�physicoͲchemical�stage,�the�species�H.,�.OH,�H2,�H2O2�are�created�in�very�high�concentration� in� the� spurs.�Other� species� such�as�O(3P)�may�also�be�present,� in� small�quantity.� �They�diffuse� in� the�medium�and�eventually�encounter�chemical� species�created� in�other� spurs,�which�gives�them�the�opportunity�to�react.�In�general,�the�radical�species�(such�as�H.,�.OH�and�eͲaq)�react�in�a1�Ps�to�form�the�molecular�species�H2�and�H2O2.�For�example,�H2O2� is�formed�by�the�reaction�.OH+.OHoH2O2.�Another�important�reaction�is�H.+�.OHo�H2O,�which�forms�back�water.��

Many� reactions� are� known� to�occur� in�pure,� irradiated� liquid�water;� the�most� important� are�given�in�the�following�table.��

atomic oxygen, singlet state

atomic oxygen, triplet state


�OHHOH *

2xx �o

�(6a)

�

�)D(OHOH 1

2*

2 �o�

(6b)� �

�)P(OH2OH 3*

2 �o x

�(6c)�


� OHOH 2*

2 o � (7)��







thermal de-excitation

Secondary electrons also behave as a new individual species and they become hydrated


Physico-chemical stage (time ≈ 10-15 s – 10-12 s) /ctd.


�OHHOH *

2xx �o

�(6a)

�

�)D(OHOH 1

2*

2 �o�

(6b)� �

�)P(OH2OH 3*

2 �o x

�(6c)�


� OHOH 2*

2 o � (7)��







At the end of the physico-chemical stage, the species H·, ·OH, H2, H2O2 are created in very high concentration in the spurs.

Other species such as O(3P) may also be present in small quantity. They diffuse in the medium and eventually encounter chemical species created in other spurs, which gives them the opportunity to react.

In general, the radicals such as H·, ·OH and e-aq react in ∼1 μs to form the molecular species H2 and H2O2. For example, H2O2 is formed by the reaction

·OH + ·OH → H2O2

Another important reaction is H· + ·OH → H2O, which forms water.


Non-homogeneous chemical stage (time ≈ 10-12 s – 10-6 s)


��

Chemical�reactions�table�

Reactions� � � �

H.+H.oH2�.OH+.OHoH2O2� H2O2+e

ͲaqoOHͲ+.OH� H++O2

.Ͳ�oHO2.�

H.+.OHoH2O�.OH+H2O2oHO2

.+H2O� H2O2+OHͲoHO2

Ͳ+H2O� H++HO2ͲoH2O2�

H.+H2O2oH2O+.OH� .OH+H2oH.+H2O� H2O2+O(

3P)oHO2.+.OH� H++O.Ͳo.OH�

H.+eͲaqoH2+OHͲ� .OH+eͲaqoOHͲ� H2O2+O

.ͲoHO2.+OHͲ� OHͲ+HO2

.oO2.Ͳ+H2O�

H.+OHͲoH2O+eͲaq�

.OH+OHͲoO.Ͳ+H2O� H2+O(3P)oH.+.OH� OHͲ+O(3P)oHO2

Ͳ�H.+O2�oHO2

.� .OH+HO2.oO2+H2O� H2+O

.ͲoH.+OHͲ� HO2.+O(3P)oO2+

.OH�H.+HO2

.oH2O2�.OH+O2

.ͲoO2+OHͲ� eͲaq+e

ͲaqoH2+2OH

Ͳ.� HO2.+HO2

.o�H2O2+O2�H.+O2

.ͲoHO2Ͳ� .OH+HO2

ͲoHO2.+OHͲ� eͲaq+H

+oH.� HO2.+O2

.Ͳo�HO2Ͳ+O2�

H.+O(3P)�o.OH� .OH+O(3P)oHO2.� eͲaq+O2oO2

.Ͳ� HO2Ͳ+O(3P)oO2

.Ͳ+.OH�H.+O.ͲoOHͲ� .OH+O.ͲoHO2

Ͳ� eͲaq+HO2.oHO2

Ͳ� O(3P)+O(3P)oO2��

At�the�end�of�the�nonͲhomogeneous�chemical�stage,�the�following�equation�for�the�radiolysis�of�water�can�be�written:�� (9)��3.3.1�Yields�of�radiolytic�species��

The�radiolytic�yield�of�the�species�X,�noted�G(X),�is�defined�as:��

� energy deposited eV 100destroyed)(or created species ofNumber G(X)

�(10)�

�The� units� of� the� radiolytic� yields� are�molec./100� eV.� In� SI� units,� 1�molec./100� eV� у� 0.10364�

Pmol/J.�An�equivalent�definition�of�G(X)�is�G(X)=(1/U)(d[X]/dD),�where�U�is�the�density�of�the�irradiated�medium,�[X]�is�the�concentration�of�X�and�D�is�the�dose.�It�is�usually�obtained�by�using�the�slope�of�the�graph� [X]� vs� D� at� origin.� If� D=It,� where� I� is� the� doseͲrate� and� t� is� the� time,� we� can� write�G(X)=(1/UI)(d[X]/dt).��

The�yield�of�the�radiolytic�species�at�the�end�of�spur�expansion,�at�a10Ͳ6�s,�is�called�primary�yield�and� is� noted� GX.� In� pure� liquid� water,� the� primary� yields� of� the� principal� radiolytic� species� are� (in�molec./100�eV)13:�� 50.2G

aqe � ;� 56.0G H x ;� 7.0G22OH ;� 45.0G

2H ;� 50.2G OH x�

(11)�

�Experimentally,�the�yield�values�can�be�obtained�by�pulsedͲradiolysis.��

The end result of the radiolysis of water leads to radiochemical species

��

Chemical�reactions�table�

Reactions� � � �

H.+H.oH2�.OH+.OHoH2O2� H2O2+e

ͲaqoOHͲ+.OH� H++O2

.Ͳ�oHO2.�

H.+.OHoH2O�.OH+H2O2oHO2

.+H2O� H2O2+OHͲoHO2

Ͳ+H2O� H++HO2ͲoH2O2�

H.+H2O2oH2O+.OH� .OH+H2oH.+H2O� H2O2+O(

3P)oHO2.+.OH� H++O.Ͳo.OH�

H.+eͲaqoH2+OHͲ� .OH+eͲaqoOHͲ� H2O2+O

.ͲoHO2.+OHͲ� OHͲ+HO2

.oO2.Ͳ+H2O�

H.+OHͲoH2O+eͲaq�

.OH+OHͲoO.Ͳ+H2O� H2+O(3P)oH.+.OH� OHͲ+O(3P)oHO2

Ͳ�H.+O2�oHO2

.� .OH+HO2.oO2+H2O� H2+O

.ͲoH.+OHͲ� HO2.+O(3P)oO2+

.OH�H.+HO2

.oH2O2�.OH+O2

.ͲoO2+OHͲ� eͲaq+e

ͲaqoH2+2OH

Ͳ.� HO2.+HO2

.o�H2O2+O2�H.+O2

.ͲoHO2Ͳ� .OH+HO2

ͲoHO2.+OHͲ� eͲaq+H

+oH.� HO2.+O2

.Ͳo�HO2Ͳ+O2�

H.+O(3P)�o.OH� .OH+O(3P)oHO2.� eͲaq+O2oO2

.Ͳ� HO2Ͳ+O(3P)oO2

.Ͳ+.OH�H.+O.ͲoOHͲ� .OH+O.ͲoHO2

Ͳ� eͲaq+HO2.oHO2

Ͳ� O(3P)+O(3P)oO2��

At�the�end�of�the�nonͲhomogeneous�chemical�stage,�the�following�equation�for�the�radiolysis�of�water�can�be�written:�� (9)��3.3.1�Yields�of�radiolytic�species��

The�radiolytic�yield�of�the�species�X,�noted�G(X),�is�defined�as:��

� energy deposited eV 100destroyed)(or created species ofNumber G(X)

�(10)�

�The� units� of� the� radiolytic� yields� are�molec./100� eV.� In� SI� units,� 1�molec./100� eV� у� 0.10364�

Pmol/J.�An�equivalent�definition�of�G(X)�is�G(X)=(1/U)(d[X]/dD),�where�U�is�the�density�of�the�irradiated�medium,�[X]�is�the�concentration�of�X�and�D�is�the�dose.�It�is�usually�obtained�by�using�the�slope�of�the�graph� [X]� vs� D� at� origin.� If� D=It,� where� I� is� the� doseͲrate� and� t� is� the� time,� we� can� write�G(X)=(1/UI)(d[X]/dt).��

The�yield�of�the�radiolytic�species�at�the�end�of�spur�expansion,�at�a10Ͳ6�s,�is�called�primary�yield�and� is� noted� GX.� In� pure� liquid� water,� the� primary� yields� of� the� principal� radiolytic� species� are� (in�molec./100�eV)13:�� 50.2G

aqe � ;� 56.0G H x ;� 7.0G22OH ;� 45.0G

2H ;� 50.2G OH x�

(11)�

�Experimentally,�the�yield�values�can�be�obtained�by�pulsedͲradiolysis.��


Time-dependent cross sections of the nonhomogeneous spatial distributions of the mainradiolytic species (eaq, .OH, H., H2, and H2O2) in liquid water exposed to 24-MeV 4He2+ ions from 1 ps to 10 µs.

Adapted from I. Plante and J.-P. Jay-Gerin: “Monte-Carlo step-by-step simulation of the early stages of liquid water radiolysis: 3D visualization of the initial radiation track structure and its subsequent chemical development”, Journal of Physics: Conference Series 56 (2006) 153-155


13.4 Examples of Calculated Charged-Particle Tracks in Water 403

Fig. 13.1 Chemical development of a 4-keVelectron track in liquid water, calculated byMonte Carlo simulation. Each dot in thesestereo views gives the location of one of theactive radiolytic species, OH, H3O+, e–

aq, or H,at the times shown. Note structure of trackwith spurs, or clusters of species, at early

times. After 10–7 s, remaining species continueto diffuse further apart, with relatively fewadditional chemical reactions. (Courtesy OakRidge National Laboratory, operated by MartinMarietta Energy Systems, Inc., for theDepartment of Energy.)

schemes (13.4)–(13.10) can thus be used to carry out the chemical development ofa track.

Three examples of calculated electron tracks at 10–12 s in liquid water were shownin Fig. 6.5. The upper left-hand panel in Fig. 13.1 presents a stereoscopic view ofanother such track, for a 4-keV electron, starting at the origin in the upward direc-tion. Each dot represents the location of one of the active radiolytic species, OH,H3O+, e–

aq, or H, shown in Table 13.2, at 10–12 s. There are 924 species present ini-tially. The electron stops in the upper region of the panel, where its higher linearenergy transfer (LET) is evidenced by the increased density of dots. The occurrenceof species in clusters, or spurs, along the electron’s path is seen. As discussed inSection 6.7, this important phenomenon for the subsequent chemical action of ion-izing radiation is a result of the particular shape and universality of the energy-lossspectrum for charged particles (Fig. 5.3). The passage of time and the chemical

Chemical development of a 4-keV electron track in liquid water, calculated by Monte Carlo simulation. Each dot in these stereo views gives the location of one of the active radiolytic species, OH, H3O+, e–aq, or H, at the times shown. Note structure of track with spurs, or clusters of species, at early times. After 10–7 s, remaining species continue to diffuse further apart, with relatively few additional chemical reactions. (Adapted from James E. Turner: “Atoms, Radiation, and Radiation Protection, 3rd ed.” Wiley 2007)


Track of a 300 MeV 12C6+ ion, from ~10-12 to ~10-6 s, front view

Each dot represents a radiolytic species. The changes in color indicate chemical reactions.

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Track of a 300 MeV 12C6+ ion, from ~10-12 to ~10-6 s, side viewEach dot represents a radiolytic species. The changes in color indicate chemical reactions.

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G value: number of a given species produced per 100 eV of energy loss by the original charged particle and its secondaries, on the average, when it stops in the water.

Table extracted from Turner: “Atoms, Radiation, and Radiation Protection”



Table extracted from Turner: “Atoms, Radiation, and Radiation Protection”


Exercise:

If a 20-keV electron stops in water and an average of 352 molecules of H2O2 are produced, what is the G value for H2O2 for electrons of this energy?



Exercise:

If a 20-keV electron stops in water and an average of 352 molecules of H2O2 are produced, what is the G value for H2O2 for electrons of this energy?

Answer:

20 keV/100 eV = 200 therefore G = 352/200 = 1.76



Electrons, protons, and alpha particles all produce the same species in local track regions at 10-15 s: H2O+, H2O∗, and subexcitation electrons.

The chemical differences that result at later times are presumably due to the different spatial patterns of initial energy deposition that the particles have.


13.5 Chemical Yields in Water 407

Table 13.3 G Values (Number per 100 eV) for Various Species inWater at 0.28 µs for Electrons at Several Energies

Electron Energy (eV)

Species 100 200 500 750 1000 5000 10,000 20,000

OH 1.17 0.72 0.46 0.39 0.39 0.74 1.05 1.10H3O+ 4.97 5.01 4.88 4.97 4.86 5.03 5.19 5.13e–

aq 1.87 1.44 0.82 0.71 0.62 0.89 1.18 1.13H 2.52 2.12 1.96 1.91 1.96 1.93 1.90 1.99H2 0.74 0.86 0.99 0.95 0.93 0.84 0.81 0.80H2O2 1.84 2.04 2.04 2.00 1.97 1.86 1.81 1.80Fe3+ 17.9 15.5 12.7 12.3 12.6 12.9 13.9 14.1

the other species, such as H2O2 and H2, increase with time. As mentioned earlier,by about 10–6 s the reactive species remaining in a track have moved so far apartthat additional reactions are unlikely. As functions of time, therefore, the G valueschange little after 10–6 s.

Calculated yields for the principal species produced by electrons of various ini-tial energies are given in Table 13.3. The G values are determined by averaging theproduct yields over the entire tracks of a number of electrons at each energy. [Thelast line, for Fe3+, applies to the Fricke dosimeter (Section 10.6). The measuredG value for the Fricke dosimeter for tritium beta rays (average energy 5.6 keV),is 12.9.] The table indicates how subsequent changes induced by radiation can bepartially understood on the basis of track structure—an important objective in ra-diation chemistry and radiation biology. One sees that the G values for the fourreactive species (the first four lines) are smallest for electrons in the energy range750–1000 eV. In other words, the intratrack chemical reactions go most nearly tocompletion for electrons at these initial energies. At lower energies, the number ofinitial reactants at 10–12 s is smaller and diffusion is more favorable compared withreaction. At higher energies, the LET is less and the reactants at 10–12 s are morespread out than at 750–1000 eV, and thus have a smaller probability of subsequentlyreacting.

Similar calculations have been carried out for the track segments of protons andalpha particles. The results are shown in Table 13.4. As in Fig. 7.1, pairs of ionshave the same speed, and so the alpha particles have four times the LET of theprotons in each case. Several findings can be pointed out. First, for either type ofparticle, the LET is smaller at the higher energies and hence the initial density ofreactants at 10–12 s is smaller. Therefore, the efficiency of the chemical developmentof the track should get progressively smaller at the higher energies. This decreasedefficiency is reflected in the increasing G values for the reactant species in the firstfour lines (more are left at 10–7 s) and in the decreasing G values for the reactionproducts in the fifth and sixth lines (fewer are produced). Second, at a given velocity,the reaction efficiency is considerably greater in the track of an alpha particle thanin the track of a proton. Third, comparison of Tables 13.3 and 13.4 shows some


Homework

A 50 cm3 sample of water is given a dose of 50 mGy from 10-keV electrons.

If the yield of H2O2 is G = 1.81 per 100 eV, how many molecules of H2O2 are produced in the sample?


The radiolysis of water is known to damage metal pipes, but how do the radiolytic species act in cells and organisms?

• Radiobiology is a branch of science which combines basic principles of physics and biology and is concerned with the action of ionizing radiation on biological tissues and living organisms.

• Ionizing radiation acts at the molecular and cellular level, while in this Master’s course we are interested in the medical issues: in this Radiobiology course we try to understand how the action of radiation at the microscopic level affects human health

Introduction to Radiobiology Lesson 1milotti/Didattica/...Edoardo Milotti - Radiobiology 3 Aim of...

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