117/18/20077/18/2007

General Physics (PHY 2140)

Lecture 19Lecture 19Modern Physics

Nuclear PhysicsNuclear ReactionsMedical ApplicationsRadiation Detectors

Chapter 29

http://www.physics.wayne.edu/~alan/2140Website/Main.htm

227/18/20077/18/2007

Lightning ReviewLightning Review

Last lecture:

1.1. Nuclear physicsNuclear physicsNuclear propertiesNuclear propertiesBinding energyBinding energyRadioactivityRadioactivityThe Decay ProcessThe Decay ProcessNatural RadioactivityNatural Radioactivity

Review Problem: An alpha particle has twice the charge of a beta particle. Why does the former deflect less than the latter when passing between electrically charged plates, assuming that both have the same speed?

AZ X 1/3

0r r A=

Mass: The alpha particle is 7344 times as massive as the beta particle. Recall:

2r mEqB

=

Nuclear density ~ 2.3 x 1017 Kg/m3

337/18/20077/18/2007

QUICK QUIZ 29.2

The activity of a newly discovered radioactive isotope reduces to 96% of its original value in an interval of 2 hours. What is its half- life?

(a) 10.2 h (b) 34.0 h (c) 44.0 h (d) 68.6 h

Radioactive Decay:

447/18/20077/18/2007

QUICK QUIZ 29.2 ANSWER

(b). If the original activity is R0 =λN0

, the activity remaining after an elapsed time t is R = R0 e-λt

= R0 e-(0.693/T1/2)t . Solving for the half-life yields

T1/2 = [-0.693/ln(R/R0 )]t.

If R = 0.96R0 at t = 2.0 hr, the half-life is:

T1/2 = [-0.693/ln(0.96)](2.0 h) = 34 h.

557/18/20077/18/2007

29.6 Nuclear Reactions29.6 Nuclear Reactions

Structure of nuclei can be changed by bombarding them Structure of nuclei can be changed by bombarding them with energetic particleswith energetic particles

The changes are called The changes are called nuclear reactionsnuclear reactions

As with nuclear decays, the atomic numbers and mass As with nuclear decays, the atomic numbers and mass numbers must balance on both sides of the equationnumbers must balance on both sides of the equation

667/18/20077/18/2007

Problem

Which of the following are possible reactions?

(a) and (b). Reactions (a) and (b) both conserve total charge and total mass number as required. Reaction (c) violates conservation of mass number with the sum of the mass numbers being 240 before reaction and being only 223 after reaction.

ΔA= -17, ΔZ=0

777/18/20077/18/2007

Q ValuesQ Values

Energy must also be conserved in nuclear reactionsEnergy must also be conserved in nuclear reactionsThe energy required to balance a nuclear reaction is The energy required to balance a nuclear reaction is called the called the Q valueQ value of the reactionof the reaction

An An exothermicexothermic reactionreactionThere is a mass There is a mass ““lossloss”” in the reactionin the reactionThere is a release of energyThere is a release of energyQ is positiveQ is positive

An An endothermicendothermic reactionreactionThere is a There is a ““gaingain”” of mass in the reactionof mass in the reactionEnergy is needed, in the form of kinetic energy of the incoming Energy is needed, in the form of kinetic energy of the incoming particlesparticlesQ is negativeQ is negative

887/18/20077/18/2007

Problem: nuclear reactionsProblem: nuclear reactions

Determine the product of the reaction What is the Q value of the reaction?

7 43 2 ?Li He n+ → +

997/18/20077/18/2007

Determine the product of the reaction What is the Q value of the reaction?

Given:

reaction

Find:

Q = ?

In order to balance the reaction, the total amount of nucleons (sum of A-numbers) must be the same on both sides. Same for the Z-number.

7 4 1 10X X+ = + ⇒ =

The Q-value is then

( ) ( )7 4 102 2 2.79nLi He B

Q m c m m m m c MeV= Δ = + − − = −

3 2 0 5Y Y+ = + ⇒ =Number of nucleons (A): Number of protons (Z):

Thus, it is B, i.e. 7 4 10 13 2 5 0Li He B n+ → +

7 43 2 ?X

YLi He n+ → +

Endothermic ⇒ Need to put in energy = >2.79 MeV

10107/18/20077/18/2007

Threshold Energy in Endothermic ReactionsThreshold Energy in Endothermic Reactions

To conserve both momentum and energy, incoming particles must To conserve both momentum and energy, incoming particles must have a minimum amount of kinetic energy, called the have a minimum amount of kinetic energy, called the threshold threshold energyenergy

m is the mass of the incoming particlem is the mass of the incoming particleM is the mass of the target particleM is the mass of the target particle

If the energy is less than this amount, the endothermic reactionIf the energy is less than this amount, the endothermic reaction cannot occurcannot occur

QMm1KEmin ⎟⎠⎞

⎜⎝⎛ +=

11117/18/20077/18/2007

QUICK QUIZ

If the Q value of an endothermic reaction is -2.79 MeV, the minimum kinetic energy needed in the reactant nuclei if the reaction is to occur must be (a) equal to 2.79 MeV, (b) greater than 2.79 MeV, (c) less than 2.79 MeV, or (d) precisely half of 2.79 MeV.

(b). In an endothermic reaction, the threshold energy exceeds the magnitude of the Q value by a factor of (1+ m/M), where m is the mass of the incident particle and M is the mass of the target nucleus.

QMm1KEmin ⎟⎠⎞

⎜⎝⎛ +=

12127/18/20077/18/2007

Radiation Damage in MatterRadiation Damage in Matter

Radiation absorbed by matter can cause damageRadiation absorbed by matter can cause damageThe degree and type of damage depend on many factorsThe degree and type of damage depend on many factors

Type and energy of the radiationType and energy of the radiationProperties of the absorbing matterProperties of the absorbing matter

Radiation damage in biological organisms is primarily due to Radiation damage in biological organisms is primarily due to ionization effects in cellsionization effects in cells

Ionization disrupts the normal functioning of the cellIonization disrupts the normal functioning of the cell

13137/18/20077/18/2007

Types of DamageTypes of Damage

Somatic damageSomatic damage is radiation damage to any cells except is radiation damage to any cells except reproductive onesreproductive ones

Can lead to cancer at high radiation levelsCan lead to cancer at high radiation levelsCan seriously alter the functional characteristics of specific Can seriously alter the functional characteristics of specific organismsorganisms

Genetic damageGenetic damage affects only reproductive cellsaffects only reproductive cellsCan lead to defective offspringCan lead to defective offspring

14147/18/20077/18/2007

Units of Radiation ExposureUnits of Radiation Exposure

RoentgenRoentgen [R] is defined as[R] is defined asThat amount of ionizing radiation that will produce 2.08 x 10That amount of ionizing radiation that will produce 2.08 x 1099 ion ion pairs in 1 cmpairs in 1 cm33 of air under standard conditionsof air under standard conditionsThat amount of radiation that deposits 8.76 x 10That amount of radiation that deposits 8.76 x 10--33 J of energy J of energy into 1 kg of airinto 1 kg of air

RadRad ((RRadiation adiation AAbsorbed bsorbed DDose)ose)That amount of radiation that deposits 10That amount of radiation that deposits 10--22 J of energy into 1 kg J of energy into 1 kg of airof air

15157/18/20077/18/2007

More UnitsMore Units

RBERBE ((RRelative elative BBiological iological EEffectiveness)ffectiveness)The number of rad of xThe number of rad of x--radiation or gamma radiation that radiation or gamma radiation that produces the same biological damage as 1 rad of the produces the same biological damage as 1 rad of the radiation being usedradiation being usedAccounts for type of particle which the rad itself does notAccounts for type of particle which the rad itself does not

RemRem ((RRoentgen oentgen EEquivalent in quivalent in MMan)an)Defined as the product of the dose in RAD and the RBE Defined as the product of the dose in RAD and the RBE factorfactor

Dose in REM = dos in RAD X RBEDose in REM = dos in RAD X RBE

16167/18/20077/18/2007

RBE for several types of RadiationRBE for several types of Radiation

RadiationRadiation RBE factorRBE factor

XX--rays and gamma raysrays and gamma rays 1.01.0

Beta particlesBeta particles 1.01.0--1.71.7

Alpha particlesAlpha particles 1010--2020

Slow neutronsSlow neutrons 44--55

Fast neutrons and protonsFast neutrons and protons 1010

Heavy ionsHeavy ions 2020

17177/18/20077/18/2007

Radiation LevelsRadiation Levels

Natural sources Natural sources –– rocks and soil, cosmic raysrocks and soil, cosmic raysBackground radiationBackground radiationAbout 0.13 rem/yrAbout 0.13 rem/yr

Upper limit suggested by US governmentUpper limit suggested by US government0.50 rem/yr0.50 rem/yrExcludes background and medical exposuresExcludes background and medical exposures

OccupationalOccupational5 rem/yr for whole5 rem/yr for whole--body radiationbody radiationCertain body parts can withstand higher levelsCertain body parts can withstand higher levelsIngestion or inhalation is most dangerous Ingestion or inhalation is most dangerous (Ingested, 1 (Ingested, 1 mCimCi 9090Sr can yield 1000 Sr can yield 1000 remrem dose! )dose! )

LDLD5050 = 400= 400--500 500 remrem whole bodywhole body

18187/18/20077/18/2007

Applications of RadiationApplications of Radiation

SterilizationSterilizationRadiation has been used to sterilize medical equipmentRadiation has been used to sterilize medical equipmentUsed to destroy bacteria, worms and insects in foodUsed to destroy bacteria, worms and insects in foodBone, cartilage, and skin used in graphs is often irradiated Bone, cartilage, and skin used in graphs is often irradiated before graftingbefore grafting

19197/18/20077/18/2007

Applications of Radiation, contApplications of Radiation, cont

TracingTracingRadioactive particles can be used to trace chemicals Radioactive particles can be used to trace chemicals participating in various reactionsparticipating in various reactions

Example, Example, 131131I to test thyroid actionI to test thyroid action

CAT scansCAT scansCComputed omputed AAxial xial TTomographyomographyProduces pictures with greater clarity and detail than traditionProduces pictures with greater clarity and detail than traditional al xx--raysrays

20207/18/20077/18/2007

Other Medical UsesOther Medical Uses

Radionuclide ImagingRadionuclide ImagingImaging the distribution of radioactively labeled substances in Imaging the distribution of radioactively labeled substances in the bodythe bodyRecent improvement is to use computed tomography techniques Recent improvement is to use computed tomography techniques PET scanning (PET scanning (PPositron ositron EEmission mission TTomography)omography)

Studying retention, turnover or clearance rates of various Studying retention, turnover or clearance rates of various substances in the body substances in the body –– labeled vitamins, thyroid labeled vitamins, thyroid uptake and othersuptake and others

21217/18/20077/18/2007

Therapeutic Applications of RadiationTherapeutic Applications of Radiation

Cancer TreatmentCancer TreatmentVarious types of methods to get ionizing radiation to cancer celVarious types of methods to get ionizing radiation to cancer cellslsExternal beam External beam –– CobaltCobalt--60 or linear accelerators produce 60 or linear accelerators produce gamma rays (photons) in the range of a few gamma rays (photons) in the range of a few MeVMeV to tens of to tens of MeVMeVBrachytherapyBrachytherapy –– radioactive seeds such as radioactive seeds such as 125125I and I and 103103Pd Pd ( photons in the ( photons in the keVkeV range) to range) to 137137Cs and Cs and 192192Ir (< 1MeV) are Ir (< 1MeV) are placed in close proximity to the cancer cellsplaced in close proximity to the cancer cellsProton and ion beams Proton and ion beams –– treatment of Ocular melanoma, treatment of Ocular melanoma, radiosurgicalradiosurgical procedures, brain procedures, brain metastaismetastais, Parkinson, Parkinson’’s and s and others.others.Neutron beamsNeutron beams

22227/18/20077/18/2007

Image of Image of BrachytherapyBrachytherapy seeds in placeseeds in place

23237/18/20077/18/2007

More Applications of RadiationMore Applications of Radiation

MRIMRIMMagnetic agnetic RResonance esonance IImagingmagingWhen a nucleus having a When a nucleus having a magnetic moment is placed in magnetic moment is placed in an external magnetic field, its an external magnetic field, its moment processes about the moment processes about the magnetic field with a magnetic field with a frequency that is proportional frequency that is proportional to the fieldto the fieldWeak oscillating field applied Weak oscillating field applied perpendicular to DC fieldperpendicular to DC fieldTransitions between energy Transitions between energy states can be detected states can be detected electronicallyelectronically

24247/18/20077/18/2007

Radiation DetectorsRadiation Detectors

A A Geiger counterGeiger counter is the most is the most common form of device used to common form of device used to detect radiationdetect radiationIt uses the ionization of a medium as It uses the ionization of a medium as the detection processthe detection processWhen a gamma ray or particle enters When a gamma ray or particle enters the thin window, the gas is ionizedthe thin window, the gas is ionizedThe released electrons trigger a The released electrons trigger a current pulsecurrent pulseThe current is detected and triggers a The current is detected and triggers a counter or speakercounter or speaker

25257/18/20077/18/2007

Detectors, 2Detectors, 2

Semiconductor Diode DetectorSemiconductor Diode DetectorA reverse biased pA reverse biased p--n junctionn junctionAs a particle passes through the junction, a brief pulse of currAs a particle passes through the junction, a brief pulse of current is ent is created and measuredcreated and measuredCan be used to measure particle energyCan be used to measure particle energy

Scintillation counterScintillation counterUses a solid or liquid material whose atoms are easily excited bUses a solid or liquid material whose atoms are easily excited by y radiationradiationThe excited atoms emit visible radiation as they return to theiThe excited atoms emit visible radiation as they return to their ground r ground statestateWith a With a photomultiplierphotomultiplier, the photons can be converted into an electrical , the photons can be converted into an electrical signalsignalCan also be used to measure particle energyCan also be used to measure particle energy

26267/18/20077/18/2007

Detectors, 3Detectors, 3

Track detectorsTrack detectorsVarious devices used to view the tracks or paths of charged Various devices used to view the tracks or paths of charged particlesparticles

Photographic emulsionPhotographic emulsionSimplest track detectorSimplest track detectorCharged particles ionize the emulsion layerCharged particles ionize the emulsion layerWhen the emulsion is developed, the track becomes visibleWhen the emulsion is developed, the track becomes visible

Cloud chamberCloud chamberContains a gas cooled to just below its condensation levelContains a gas cooled to just below its condensation levelThe ions serve as centers for condensationThe ions serve as centers for condensationParticles ionize the gas along their pathParticles ionize the gas along their pathTrack can be viewed and photographedTrack can be viewed and photographed

27277/18/20077/18/2007

Detectors, 4Detectors, 4

Track detectors, contTrack detectors, cont

Bubble ChamberBubble ChamberContains a liquid near its boiling pointContains a liquid near its boiling pointIons produced by incoming particles leave tracks of bubblesIons produced by incoming particles leave tracks of bubblesThe tracks can be photographedThe tracks can be photographed

Wire ChamberWire ChamberContains thousands of closely spaced parallel wiresContains thousands of closely spaced parallel wiresThe wires collect electrons created by the passing ionizing partThe wires collect electrons created by the passing ionizing particleicleA second grid allows the position of the particle to be determinA second grid allows the position of the particle to be determinededCan provide electronic readout to a computerCan provide electronic readout to a computer

28287/18/20077/18/2007

Not all Radiation is badNot all Radiation is bad

An accidental contamination of construction steel with An accidental contamination of construction steel with discarded cobaltdiscarded cobalt--60 sources led to the exposure of 60 sources led to the exposure of 10,000 persons to chronic low levels of gamma radiation.10,000 persons to chronic low levels of gamma radiation.

The results of a The results of a study suggest study suggest that long term that long term exposure to exposure to radiation at a radiation at a dose rate of 5 dose rate of 5 remrem/year greatly /year greatly reduces cancer reduces cancer mortality.mortality.

29297/18/20077/18/2007

Idealized Dose Response CurveIdealized Dose Response Curve

Too much Too much oror too too little ionizing little ionizing radiation may not radiation may not be healthy.be healthy.

10 rad

Ref: Journal of American Physicians and Surgeons, 9(1) Spring 2004