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General Physics (PHY 2140)

Lecture 37Lecture 37

Modern Physics

Nuclear PhysicsRadioactivityNuclear reactions

Chapter 29

http://www.physics.wayne.edu/~apetrov/PHY2140/

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Lightning ReviewLightning Review

Last lecture:

1.1. Nuclear physicsNuclear physics Properties of nucleiProperties of nuclei Binding energy, types of radiationBinding energy, types of radiation

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

1/30r r A

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29.3 Radioactivity29.3 Radioactivity

RadioactivityRadioactivity is the spontaneous emission of radiation is the spontaneous emission of radiation

Experiments suggested that radioactivity was the result Experiments suggested that radioactivity was the result of the decay, or disintegration, of unstable nucleiof the decay, or disintegration, of unstable nuclei

Three types of radiation can be emittedThree types of radiation can be emitted AlphaAlpha particles particles

The particles are The particles are 44He nucleiHe nuclei BetaBeta particles particles

The particles are either electrons or positronsThe particles are either electrons or positrons A positron is the A positron is the antiparticleantiparticle of the electron of the electron It is similar to the electron except its charge is +eIt is similar to the electron except its charge is +e

GammaGamma rays raysThe “rays” are high energy photonsThe “rays” are high energy photons

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The Decay ConstantThe Decay Constant

The number of particles that decay in a given time is proportional to The number of particles that decay in a given time is proportional to the total number of particles in a radioactive samplethe total number of particles in a radioactive sample

λλ is called the is called the decay constantdecay constant and and determines the rate at which the determines the rate at which the material will decaymaterial will decay

The The decay decay raterate or or activityactivity, R, of a sample is defined as the number , R, of a sample is defined as the number of decays per secondof decays per second

NR N

t

N N t

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Decay CurveDecay Curve

The decay curve follows the The decay curve follows the equationequation

The The half-lifehalf-life is also a useful is also a useful parameterparameter

The half-life is defined as the The half-life is defined as the time it takes for half of any time it takes for half of any given number of radioactive given number of radioactive nuclei to decaynuclei to decay

693.02lnT 21

0tN N e

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UnitsUnits

The unit of activity, R, is the The unit of activity, R, is the Curie, CiCurie, Ci 1 Ci = 3.7 x 101 Ci = 3.7 x 101010 decays/second decays/second

The SI unit of activity is the The SI unit of activity is the Becquerel, BqBecquerel, Bq 1 Bq = 1 decay / second1 Bq = 1 decay / second

Therefore, 1 Ci = 3.7 x 10Therefore, 1 Ci = 3.7 x 101010 Bq Bq

The most commonly used units of activity are the mCi The most commonly used units of activity are the mCi and the µCiand the µCi

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QUICK QUIZ

What fraction of a radioactive sample has decayed after two half-lives have elapsed?

(a) 1/4 (b) 1/2 (c) 3/4 (d) not enough information to say

(c). At the end of the first half-life interval, half of the original sample has decayed and half remains. During the second half-life interval, half of the remaining portion of the sample decays. The total fraction of the sample that has decayed during the two half-lives is: 1 1 1 3

2 2 2 4

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29.4 The Decay Processes – General Rules29.4 The Decay Processes – General Rules

When one element changes into another element, the process When one element changes into another element, the process is called is called spontaneous decayspontaneous decay or or transmutationtransmutation

The The sum of the mass numberssum of the mass numbers, , AA, must be , must be the samethe same on both on both sides of the equationsides of the equation

The The sum of the atomic numberssum of the atomic numbers, , ZZ, must be , must be the samethe same on both on both sides of the equationsides of the equation

Conservation of mass-energy and conservation of momentum Conservation of mass-energy and conservation of momentum must holdmust hold

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Alpha DecayAlpha Decay

When a nucleus emits an When a nucleus emits an alpha particlealpha particle it loses two it loses two protons and two neutronsprotons and two neutrons

N decreases by 2N decreases by 2 Z decreases by 2Z decreases by 2 A decreases by 4A decreases by 4

SymbolicallySymbolically

X is called the X is called the parent nucleusparent nucleus Y is called the Y is called the daughter nucleusdaughter nucleus

HeYX 42

4A2Z

AZ

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Alpha Decay -- ExampleAlpha Decay -- Example

Decay of Decay of 226226RaRa

Half life for this decay is 1600 Half life for this decay is 1600 yearsyearsExcess mass is converted into Excess mass is converted into kinetic energykinetic energyMomentum of the two particles Momentum of the two particles is equal and oppositeis equal and opposite

HeRnRa 42

22286

22688

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QUICK QUIZ

If a nucleus such as 226Ra that is initially at rest undergoes alpha decay, which of the following statements is true? (a) The alpha particle has more kinetic energy than the daughter nucleus. (b) The daughter nucleus has more kinetic energy than the alpha particle. (c) The daughter nucleus and the alpha particle have the same kinetic energy.

(a). Conservation of momentum requires the momenta of the two fragments be equal in magnitude and oppositely directed. Thus, from KE = p2/2m, the lighter alpha particle has more kinetic energy that the more massive daughter nucleus.

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Beta DecayBeta Decay

During beta decay, During beta decay, the daughter nucleus has the same the daughter nucleus has the same number of nucleons as the parent, but the atomic number of nucleons as the parent, but the atomic number is one lessnumber is one less

In addition, an electron (positron) was observed In addition, an electron (positron) was observed

The emission of the electron is The emission of the electron is from the nucleusfrom the nucleus The nucleus contains protons and neutronsThe nucleus contains protons and neutrons The process occurs when a neutron is transformed into a proton The process occurs when a neutron is transformed into a proton

and an electronand an electron Energy must be conservedEnergy must be conserved

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Beta Decay – Electron EnergyBeta Decay – Electron EnergyThe energy released in the decay The energy released in the decay process should process should almost allalmost all go to go to kinetic energy of the electronkinetic energy of the electronExperiments showed that Experiments showed that fewfew electrons had this amount of electrons had this amount of kinetic energykinetic energyTo account for this “missing” To account for this “missing” energy, in 1930 Pauli proposed the energy, in 1930 Pauli proposed the existence of another particleexistence of another particleEnrico Fermi later named this Enrico Fermi later named this particle the particle the neutrinoneutrinoProperties of the neutrinoProperties of the neutrino

Zero electrical chargeZero electrical charge Mass much smaller than the Mass much smaller than the

electron, probably not zeroelectron, probably not zero Spin of Spin of ½½ Very weak interaction with matterVery weak interaction with matter

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Beta Decay Beta Decay

SymbolicallySymbolically

is the symbol for the is the symbol for the neutrinoneutrino is the symbol for the is the symbol for the antineutrinoantineutrino

To summarize, in beta decay, the following pairs of To summarize, in beta decay, the following pairs of particles are emittedparticles are emitted

An electron and an antineutrinoAn electron and an antineutrino A positron and a neutrinoA positron and a neutrino

eYX

eYXA1Z

AZ

A1Z

AZ

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Gamma DecayGamma Decay

Gamma rays are given off when an excited nucleus “falls” to a lower Gamma rays are given off when an excited nucleus “falls” to a lower energy stateenergy state

Similar to the process of electron “jumps” to lower energy states and giving off Similar to the process of electron “jumps” to lower energy states and giving off photonsphotons

The excited nuclear states result from “jumps” made by a proton or neutronThe excited nuclear states result from “jumps” made by a proton or neutronThe excited nuclear states may be the result of violent collision or more The excited nuclear states may be the result of violent collision or more likely of an alpha or beta emissionlikely of an alpha or beta emissionExample of a decay sequenceExample of a decay sequence

The first decay is a beta emissionThe first decay is a beta emission The second step is a gamma emissionThe second step is a gamma emission

The C* indicates the Carbon nucleus is in an excited stateThe C* indicates the Carbon nucleus is in an excited state Gamma emission doesn’t change either A or ZGamma emission doesn’t change either A or Z

C*C

e*CB126

126

126

125

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Uses of RadioactivityUses of Radioactivity

Carbon DatingCarbon Dating Beta decay of Beta decay of 1414C is used to date organic samplesC is used to date organic samples The ratio of The ratio of 1414C to C to 1212C is usedC is used

Smoke detectorsSmoke detectors Ionization type smoke detectors use a radioactive source to ionize the Ionization type smoke detectors use a radioactive source to ionize the

air in a chamberair in a chamber A voltage and current are maintained A voltage and current are maintained When smoke enters the chamber, the current is decreased and the When smoke enters the chamber, the current is decreased and the

alarm soundsalarm sounds

Radon pollutionRadon pollution Radon is an inert, gaseous element associated with the decay of radiumRadon is an inert, gaseous element associated with the decay of radium It is present in uranium mines and in certain types of rocks, bricks, etc It is present in uranium mines and in certain types of rocks, bricks, etc

that may be used in home buildingthat may be used in home building May also come from the ground itselfMay also come from the ground itself

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29.5 Natural Radioactivity29.5 Natural Radioactivity

Classification of nucleiClassification of nuclei Unstable nuclei found in natureUnstable nuclei found in nature

Give rise to Give rise to natural radioactivitynatural radioactivity Nuclei produced in the laboratory through nuclear reactionsNuclei produced in the laboratory through nuclear reactions

Exhibit Exhibit artificial radioactivityartificial radioactivity

Three series of natural radioactivity existThree series of natural radioactivity exist UraniumUranium ActiniumActinium ThoriumThorium

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Decay SeriesDecay Series of of 232232ThTh

Series starts with Series starts with 232232ThTh

Processes through Processes through a series of alpha a series of alpha and beta decaysand beta decays

Ends with a stable Ends with a stable isotope of lead, isotope of lead, 208208PbPb

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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

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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.

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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 called The energy required to balance a nuclear reaction is called the the Q valueQ value of the reaction of the reaction

An An exothermicexothermic reaction reactionThere is a mass “loss” in the reactionThere is a mass “loss” in the reactionThere is a release of energyThere is a release of energyQ is positiveQ is positive

An An endothermicendothermic reaction reactionThere is a “gain” of mass in the reactionThere is a “gain” of 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

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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

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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 10

2 2 2.79nLi He BQ m c m m m m c MeV

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 ?XYLi He n

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Threshold EnergyThreshold Energy

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 particle M is the mass of the target particleM is the mass of the target particle

If the energy is less than this amount, the reaction cannot occurIf the energy is less than this amount, the reaction cannot occur

QM

m1KEmin

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QUICK QUIZ

If the Q value of an endothermic reaction is -2.17 MeV, the minimum kinetic energy needed in the reactant nuclei if the reaction is to occur must be (a) equal to 2.17 MeV, (b) greater than 2.17 MeV, (c) less than 2.17 MeV, or (d) precisely half of 2.17 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.