Plan for Today (AP Physics Plan for Today (AP Physics 2)2)

• Notes on Alpha, Beta, and Gamma Notes on Alpha, Beta, and Gamma DecayDecay

• HW: Finish half-life lab for MondayHW: Finish half-life lab for Monday

RadioactivityRadioactivity

As the heavier atoms become more unstable, particles and photons are emitted from the nucleus and it is said to be radioactive. All elements with A > 82 are radioactive.

As the heavier atoms become more unstable, particles and photons are emitted from the nucleus and it is said to be radioactive. All elements with A > 82 are radioactive. Examples Examples

are:are:Alpha particles Alpha particles particles particles

(electrons)(electrons) particles particles (positrons)(positrons)

Gamma rays Gamma rays

Decay – General RulesDecay – General Rules

• When one element changes into another When one element changes into another element, the process is called element, the process is called spontaneous spontaneous decaydecay or or transmutationtransmutation

• The sum of the mass numbers, A, must be The sum of the mass numbers, A, must be the same on both sides of the equationthe same on both sides of the equation

• The sum of the atomic numbers, Z, must The sum of the atomic numbers, Z, must be the same on both sides of the equationbe the same on both sides of the equation

• Conservation of mass-energy and Conservation of mass-energy and conservation of momentum must holdconservation of momentum must hold

The Alpha ParticleThe Alpha Particle

An An alpha particlealpha particle is the nucleus of a is the nucleus of a helium atom consisting of two protons helium atom consisting of two protons and two neutrons tightly bound.and two neutrons tightly bound.

Charge = +2Charge = +2ee- - = = 3.2 x 103.2 x 10--

1919 C C Mass = 4.001506 uMass = 4.001506 u

Relatively low speeds (Relatively low speeds ( 0.1c )0.1c ) Not very penetratingNot very penetrating

Radioactive DecayRadioactive DecayAs discussed, when the ratio of N/Z gets As discussed, when the ratio of N/Z gets very large, the nucleus becomes unstable very large, the nucleus becomes unstable and often particles and/or photons are and often particles and/or photons are emitted.emitted.Alpha decayAlpha decay results in the loss of results in the loss of two protons and two neutrons from the two protons and two neutrons from the nucleus. nucleus.

42

4 42 2

A AZ ZX Y energy

4 42 2

A AZ ZX Y energy

X X is is parent parent atom and atom and YY isis daughter daughter atomatomThe energy is carried away The energy is carried away

primarily by the K.E. of the alpha primarily by the K.E. of the alpha particle.particle.

Alpha DecayAlpha Decay

• When a nucleus emits an alpha particle it When a nucleus emits an alpha particle it loses two protons and two neutronsloses two protons 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

Alpha Decay – ExampleAlpha Decay – Example

• Decay of Decay of 226226 Ra Ra

• Half life for this decay is Half life for this decay is 1600 years1600 years

• Excess mass is Excess mass is converted into kinetic converted into kinetic energyenergy

• Momentum of the two Momentum of the two particles is equal and particles is equal and oppositeopposite

HeRnRa 42

22286

22688

Example 5:Example 5: Write the reaction that Write the reaction that occurs when radium-226 decays by occurs when radium-226 decays by alpha emission.alpha emission.

4 42 2

A AZ ZX Y energy

4 42 2

A AZ ZX Y energy

226 226 4 488 88 2 2Ra Y energy

From tables, we find Z and A for From tables, we find Z and A for nuclides. The daughter atom: Z = 86, nuclides. The daughter atom: Z = 86, A = 222A = 222

226 222 488 86 2Ra Rn energy 226 222 4

88 86 2Ra Rn energy

Radium-226 decays into radon-222.Radium-226 decays into radon-222.

The Beta-minus ParticleThe Beta-minus Particle

A A beta-minus particlebeta-minus particle is simply an is simply an electron that has been expelled from the electron that has been expelled from the nucleus. nucleus.

Charge = Charge = ee- - = -= -1.6 x 101.6 x 10-19-19 C C-

High speeds (near High speeds (near cc))-

Mass = 0.00055 uMass = 0.00055 u-

Very penetratingVery penetrating-

The PositronThe Positron

A A beta positive particlebeta positive particle is essentially is essentially an electron with positive charge. The an electron with positive charge. The mass and speeds are similar.mass and speeds are similar.

Charge = +Charge = +ee- - = = 1.6 x 101.6 x 10-19-19 CC

+

High speeds (near High speeds (near cc))+

Mass = 0.00055 uMass = 0.00055 u+

Very penetratingVery penetrating+

Beta-minus DecayBeta-minus Decay

Beta-minus Beta-minus decay decay results when a results when a neutron decays into a proton and an neutron decays into a proton and an electron. Thus, the Z-number electron. Thus, the Z-number increasesincreases by one.by one.

01 1

A AZ ZX Y energy 0

1 1A AZ ZX Y energy

X X is is parent parent atom and atom and YY isis daughter daughter atomatom

The energy is carried away The energy is carried away primarily by the K.E. of the primarily by the K.E. of the electron.electron.

-

Beta-plus DecayBeta-plus Decay

Beta-plus Beta-plus decay decay results when a results when a proton decays into a neutron and a proton decays into a neutron and a positron. Thus, the Z-number positron. Thus, the Z-number decreasesdecreases by one. by one.

01 1

A AZ ZX Y energy 0

1 1A AZ ZX Y energy

X X is is parent parent atom and atom and YY isis daughter daughter atomatom

The energy is carried away The energy is carried away primarily by the K.E. of the primarily by the K.E. of the positron.positron.

+

Beta DecayBeta Decay

• During beta decay, the daughter During beta decay, the daughter nucleus has the same number of nucleus has the same number of nucleons as the parent, but the nucleons as the parent, but the atomic number is changed by oneatomic number is changed by one

• Symbolically Symbolically

eYX

eYXA1Z

AZ

A1Z

AZ

Beta Decay, contBeta Decay, cont

• The emission of the electron is from The emission of the electron is from the nucleusthe nucleus– The nucleus contains protons and The nucleus contains protons and

neutronsneutrons

– The process occurs when a neutron is The process occurs when a neutron is transformed into a proton and an transformed into a proton and an electronelectron

– Energy must be conservedEnergy must be conserved

Beta Decay – Electron Beta Decay – Electron EnergyEnergy• The energy released The energy released

in the decay process in the decay process should almost all go should almost all go to kinetic energy of to kinetic energy of the electron (KEthe electron (KEmaxmax))

• Experiments showed Experiments showed that few electrons that few electrons had this amount of had this amount of kinetic energykinetic energy

NeutrinoNeutrino• To account for this “missing” energy, in 1930 To account for this “missing” energy, in 1930

Pauli proposed the existence of another particlePauli proposed the existence of another particle

• Enrico Fermi later named this particle the Enrico Fermi later named this particle the neutrinoneutrino

• Properties of the neutrinoProperties of the neutrino– Zero electrical chargeZero electrical charge

– Mass much smaller than the electron, probably not zeroMass much smaller than the electron, probably not zero

– Spin of ½Spin of ½

– Very weak interaction with matterVery weak interaction with matter

Beta Decay – Completed Beta Decay – Completed • 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 To summarize, in beta decay, the following pairs of particles are following pairs of particles are emittedemitted

– An electron and an An electron and an antineutrinoantineutrino

– A positron and a neutrinoA positron and a neutrino

eYX

eYXA1Z

AZ

A1Z

AZ

Pure Pure -- (Negatron) (Negatron) EmissionEmission

Beta (Negatron) Beta (Negatron) EmissionEmission

Positron Positron ++ Emission Emission

Fate of the PositronFate of the Positron

The Gamma PhotonThe Gamma Photon

A A gamma raygamma ray has very high has very high electromagnetic radiation carrying electromagnetic radiation carrying energy away from the nucleus.energy away from the nucleus.

Charge = Zero Charge = Zero (0)(0)

Mass = zero (0)Mass = zero (0)

Speed = c (3 x 10Speed = c (3 x 1088 m/s) m/s)

Most penetrating Most penetrating radiationradiation

Gamma DecayGamma Decay

• Gamma rays are given off when an excited Gamma rays are given off when an excited nucleus “falls” to a lower energy statenucleus “falls” to a lower energy state– Similar to the process of electron “jumps” to Similar to the process of electron “jumps” to

lower energy states and giving off photonslower energy states and giving off photons

– The photons are called gamma rays, very high The photons are called gamma rays, very high energy relative to lightenergy relative to light

• The excited nuclear states result from The excited nuclear states result from “jumps” made by a proton or neutron“jumps” made by a proton or neutron

• The excited nuclear states may be the The excited nuclear states may be the result of violent collision or more likely of an result of violent collision or more likely of an alpha or beta emissionalpha or beta emission

Gamma DecayGamma Decay

• Nuclear transition from an excited state to a Nuclear transition from an excited state to a lower energy statelower energy state

• Nuclear excited state can be created by particle Nuclear excited state can be created by particle collision or as a result of nuclear decay.collision or as a result of nuclear decay.

XX AZ

AZ

*

The Gamma PhotonThe Gamma Photon

A A gamma raygamma ray has very high has very high electromagnetic radiation carrying electromagnetic radiation carrying energy away from the nucleus.energy away from the nucleus.

Charge = Zero Charge = Zero (0)(0)

Mass = zero (0)Mass = zero (0)

Speed = c (3 x 10Speed = c (3 x 1088 m/s) m/s)

Most penetrating Most penetrating radiationradiation

Gamma Decay – ExampleGamma Decay – Example

• Example 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 The C* indicates the Carbon nucleus is in an excited stateexcited 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

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 Ionization type smoke detectors use a radioactive

source to ionize the air in a chambersource to ionize the air in a chamber

– A voltage and current are maintained A voltage and current are maintained

– When smoke enters the chamber, the current is When smoke enters the chamber, the current is decreased and the alarm soundsdecreased and the alarm sounds

More Uses of RadioactivityMore Uses of Radioactivity

• Radon pollutionRadon pollution– Radon is an inert, gaseous element Radon is an inert, gaseous element

associated with the decay of radiumassociated with the decay of radium

– It is present in uranium mines and in It is present in uranium mines and in certain types of rocks, bricks, etc that certain types of rocks, bricks, etc that may be used in home buildingmay be used in home building

– May also come from the ground itselfMay also come from the ground itself

Natural RadioactivityNatural 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 Nuclei produced in the laboratory through nuclear reactionsreactions• Exhibit Exhibit artificial radioactivityartificial radioactivity

• Three series of natural radioactivity existThree series of natural radioactivity exist– UraniumUranium

– ActiniumActinium

– ThoriumThorium

Nuclear ReactionsNuclear ReactionsIt is possible to alter the structure of a It is possible to alter the structure of a nucleus by bombarding it with small nucleus by bombarding it with small particles. Such events are called nuclear particles. Such events are called nuclear reactions:reactions:

General Reaction:

x + X Y + y

For example, if an alpha particle For example, if an alpha particle bombards a nitrogen-14 nucleus it bombards a nitrogen-14 nucleus it produces a hydrogen atom and produces a hydrogen atom and oxygen-17:oxygen-17:

4 14 1 172 7 1 8N H O 4 14 1 17

2 7 1 8N H O

Conservation LawsConservation Laws

For any nuclear reaction, there are three conservation laws which must be obeyed:For any nuclear reaction, there are three conservation laws which must be obeyed:

Conservation of Charge:Conservation of Charge: The total charge The total charge of a system can neither be increased nor of a system can neither be increased nor decreased.decreased.Conservation of Nucleons:Conservation of Nucleons: The total The total number of nucleons in a reaction must be number of nucleons in a reaction must be unchanged.unchanged.Conservation of Mass Energy:Conservation of Mass Energy: The total The total mass-energy of a system must not mass-energy of a system must not change in a nuclear reaction.change in a nuclear reaction.

Example 7:Example 7: Use conservation criteria to Use conservation criteria to determine the unknown element in the determine the unknown element in the following nuclear reaction:following nuclear reaction:

1 7 41 3 2

AZH Li He X energy

Charge before = +1 + 3 = +4Charge before = +1 + 3 = +4

Charge after = +2 + Z = +4Charge after = +2 + Z = +4

Z = 4 – 2 = 2Z = 4 – 2 = 2

Nucleons before = 1 + 7 = Nucleons before = 1 + 7 = 88Nucleons after = 4 + A = 8Nucleons after = 4 + A = 8

(Helium has (Helium has Z = Z = 22))

(Thus, (Thus, A =A = 44))

1 7 4 41 3 2 2H Li He He energy

1 7 4 41 3 2 2H Li He He energy

Conservation of Mass-Conservation of Mass-EnergyEnergy

There is always mass-energy associated There is always mass-energy associated with any nuclear reaction. The energy with any nuclear reaction. The energy released or absorbed is called the Q-value released or absorbed is called the Q-value and can be found if the atomic masses are and can be found if the atomic masses are known before and after.known before and after.

1 7 4 41 3 2 2H Li He He Q

1 7 4 41 3 2 2H Li He He Q

1 7 4 41 3 2 2Q H Li He He

QQ is the energy is the energy released released in the reaction. in the reaction. If If QQ is is positivepositive, it is , it is exothermicexothermic. If . If QQ is is negativenegative, it is , it is endothermicendothermic..

Example 8:Example 8: Calculate the energy released Calculate the energy released in the bombardment of lithium-7 with in the bombardment of lithium-7 with hydrogen-1.hydrogen-1.

1 7 4 41 3 2 2H Li He He Q

1 7 4 41 3 2 2H Li He He Q

1 7 4 41 3 2 2Q H Li He He

73 7.016003 uLi

42 4.002603 uHe1

1 1.007825 uH

Substitution of these masses gives:Substitution of these masses gives:

QQ = 0.018622 u(931.5 = 0.018622 u(931.5 MeV/u)MeV/u)

Q =17.3 MeV

Q =17.3 MeV

42 4.002603 uHe

The positive Q means the reaction is The positive Q means the reaction is exothermic.exothermic.

Summary (Decay Summary (Decay Particles)Particles)

An An alpha particlealpha particle is the nucleus of a is the nucleus of a helium atom consisting of two protons helium atom consisting of two protons and two tightly bound neutrons.and two tightly bound neutrons.

A A beta-minus particlebeta-minus particle is simply an is simply an electron that has been expelled from the electron that has been expelled from the nucleus. nucleus. A A beta positive particlebeta positive particle is essentially is essentially an electron with positive charge. The an electron with positive charge. The mass and speeds are similar.mass and speeds are similar.

A A gamma raygamma ray has very high has very high electromagnetic radiation carrying electromagnetic radiation carrying energy away from the nucleus.energy away from the nucleus.

Summary (Cont.)Summary (Cont.)

4 42 2

A AZ ZX Y energy

4 42 2

A AZ ZX Y energy

Alpha Decay:Alpha Decay:

01 1

A AZ ZX Y energy 0

1 1A AZ ZX Y energy

Beta-minus Decay:Beta-minus Decay:

01 1

A AZ ZX Y energy 0

1 1A AZ ZX Y energy

Beta-plus Decay:Beta-plus Decay:

Summary (Cont.)Summary (Cont.)

Conservation of Charge:Conservation of Charge: The total charge The total charge of a system can neither be increased nor of a system can neither be increased nor decreased.decreased.Conservation of Nucleons:Conservation of Nucleons: The total The total number of nucleons in a reaction must be number of nucleons in a reaction must be unchanged.unchanged.Conservation of Mass Energy:Conservation of Mass Energy: The total The total mass-energy of a system must not mass-energy of a system must not change in a nuclear reaction. (Q-value = change in a nuclear reaction. (Q-value = energy released)energy released)

Nuclear Reaction:x + X Y + y + Q