atomic structure and radioactivity

Atomic Structure/Atomic Structure/Radioactivity Radioactivity

Excitation/IonizationExcitation/Ionization

Takes a specific/exact amount of E to Takes a specific/exact amount of E to excite an eexcite an e-- from one state to the next from one state to the next

E in addition to this can ionizeE in addition to this can ionize Result = ion pairResult = ion pair

This a key concept in HP as it is the This a key concept in HP as it is the method by which E is transferred to method by which E is transferred to living materialliving material

Some Key PointsSome Key Points

All matter composed All matter composed of combinations of of combinations of elementselements

Smallest piece of Smallest piece of element that retains element that retains characteristics is an characteristics is an atomatom

Known elements Known elements arranged on periodic arranged on periodic table according to table according to their chemical their chemical characteristicscharacteristics

118, or so, elements 118, or so, elements discovered, only 92 discovered, only 92 occur naturallyoccur naturally

Atomic ModelsAtomic Models

Solar systemSolar system Problems…Problems…

Planetary – BohrPlanetary – Bohr Maybe classical EM theory doesn’t apply Maybe classical EM theory doesn’t apply

to atomic electronsto atomic electrons Used Planck’s Quantum Theory – atomic Used Planck’s Quantum Theory – atomic

model we use todaymodel we use today

Planetary Model of the Atom

1)Protons (nucleus)

1)Positive charge

2)Large mass

2)Neutrons (nucleus)

1)No charge

2)Large mass

3)Electrons

1)Negative charge

2)Small mass

• Charge on an electron is equal but opposite the charge on a proton.

• An ion is an atom that has either lost or gained electrons and therefore has a net charge

• Electrons “orbit” nucleus

• Force of attraction between e- and nucleus balanced by centrifugal force of revolution

• A neutral atom has equal numbers of protons and electrons (zero net charge)

Fundamental PostulatesFundamental Postulates

Electron can only revolve around Electron can only revolve around nucleus in fixed radii – stationary statenucleus in fixed radii – stationary state

Photon is emitted ONLY when e- falls Photon is emitted ONLY when e- falls from orbit of higher energy to one of from orbit of higher energy to one of lowerlower

When this happens we get what?When this happens we get what?

Characteristic X-rayCharacteristic X-ray

What is What is happening?happening?

Application?Application?

Nuclear StructureNuclear Structure

What do we find in the nucleus?What do we find in the nucleus?

Neutrons (n) and protons (p)Neutrons (n) and protons (p)- Most of the mass of an atom is in - Most of the mass of an atom is in the nucleusthe nucleus

- Mass of a proton is 1836 times - Mass of a proton is 1836 times greater than the mass of the electrongreater than the mass of the electron

P and N about equalP and N about equal

What are nucleons comprised of?

Useful DefinitionsUseful Definitions

Atomic number (Z):Atomic number (Z): No. of protons No. of protons (electrons) in a given neutral atom (electrons) in a given neutral atom determines the elementdetermines the element

Atomic mass (A):Atomic mass (A): No. of neutrons No. of neutrons plusplus the number of protons in an the number of protons in an atomatom

Neutron Number (N):Neutron Number (N): Number of Number of neutrons in an atomneutrons in an atom

Useful DefinitionsUseful Definitions

Isotope:Isotope: Atoms with the same Z but Atoms with the same Z but different Adifferent A

Isotone:Isotone: Same N Same N

Isobar:Isobar: Same A Same A

• Light stable isotopes (Z<20) have N approximately equal to Z

• Heavy stable isotopes (Z>20) have N greater than Z

• Neutrons act as “spacers” to reduce electric repulsion between the protons in nucleus

Proton Mass = 1.007277 u

Neutron Mass = 1.008665 u

Neutron Mass

+ Proton Mass = 2.015942 u

Deuteron Mass = 2.013553 u

Missing Mass

(N + P – D) = 0.002389 u

What happened to the mass?????

Answer: It is converted into binding energy according to Einstein’s mass energy relation

E=mc2

For the deuteron example, this is

2.22 MeV of energy. If we want to break the deuteron apart we must give this energy back.

Units of energy : 1 calorie = 4.186 Joule

1 Btu = 252 calorie

1 MeV = 1.6 10 -13 Joule

akamass decrementmass defect

What is actually more important is the binding energy per nucleon

For Deuterium: BE/A = 2.22 MeV/2 = 1.11 MeV

Atomic Mass No (A)

Note that iron (Fe) has the highest binding energy per nucleon. This is the most stable element in nature in that it requires more energy per particle to break it apart than anything else.

Fusion energy comes from combining light elements to make heavier ones (increase binding energy per nucleon for elements lighter than iron).

Fission energy comes from breaking heavy elements into lighter ones (increase binding energy per nucleon for elements heavier than iron).

Nuclear TransformationNuclear Transformation

When the atomic nucleus undergoes When the atomic nucleus undergoes spontaneous transformation, called spontaneous transformation, called radioactive decayradioactive decay, radiation is emitted, radiation is emitted If the daughter nucleus is stable, this If the daughter nucleus is stable, this

spontaneous transformation endsspontaneous transformation ends If the daughter is unstable, the process If the daughter is unstable, the process

continues until a stable nuclide is reachedcontinues until a stable nuclide is reached

Nuclear TransformationNuclear Transformation

Radionuclides decay in one or more Radionuclides decay in one or more of the following ways: (a) alpha of the following ways: (a) alpha decay, (b) beta-minus emission, (c) decay, (b) beta-minus emission, (c) beta-plus (positron) emission, (d) beta-plus (positron) emission, (d) electron capture, (e) internal electron capture, (e) internal conversion, or (f) spontaneous conversion, or (f) spontaneous fission.fission.

Alpha Decay

An alpha () particle is composed of two protons and two neutrons, thus its atomic mass is 4 and its atomic number is 2. (Note: this is a He-4 nucleus)

XZ

A

Example

YZ-2

A-4

2

4

Th90

232

Ra88

228

2

4

Occurs with heavy nuclides (Z > 82)

Beta-Minus (Negatron) Beta-Minus (Negatron) DecayDecay

Beta-minus (Beta-minus (--) decay: occurs with ) decay: occurs with radionuclides that have high n:p ratioradionuclides that have high n:p ratio

A A 0Z Z 1 -1X Y β

Beta-Plus Decay (Positron Beta-Plus Decay (Positron Emission)Emission)

Beta-plus (Beta-plus (++) decay occurs with ) decay occurs with radionuclides that have low n:p ratio radionuclides that have low n:p ratio

Eventual fate of positron is to annihilate Eventual fate of positron is to annihilate with its antiparticle (an electron), yielding with its antiparticle (an electron), yielding two 0.511 MeV photons emitted in two 0.511 MeV photons emitted in opposite directionsopposite directions

A A 0Z Z-1 1X Y β

Ra88

228

Ac89

228

-1

0

Examples of Beta Decay

C6

11

B5

11

1

0

Beta Plus Decay

Beta Minus Decay

Electron Capture Electron Capture

Alternative to positron decay Alternative to positron decay Nucleus captures an orbital (usually K- or L-Nucleus captures an orbital (usually K- or L-

shell) electronshell) electron

Electron capture radionuclides used in Electron capture radionuclides used in medical imaging decay to atoms in excited medical imaging decay to atoms in excited states that subsequently emit detectable states that subsequently emit detectable gamma raysgamma rays

A 0 AZ -1 Z-1X e Y

Alternative emission:Alternative emission:Isomeric TransitionIsomeric Transition

During radioactive decay, a daughter may During radioactive decay, a daughter may be formed in an excited statebe formed in an excited state

Gamma rays emitted as the daughter Gamma rays emitted as the daughter nucleus transitions from the excited state to nucleus transitions from the excited state to a lower-energy statea lower-energy state

No mass/charge therefore, no change in No mass/charge therefore, no change in elementelement

Am AZ ZX X

In spontaneous fission, an atom splits instead of emitting an alpha or beta particle. Very common for heavy elements. Usually also results in neutron emissions

Example:

Spontaneous Fission

Fm100

256

Xe54

140

Pd46

112

n0

1

4

Line of StabilityLine of Stability

N=P

Proton

Neu

tron

β-

ec, β+, α

Decay SchemesDecay Schemes

Each decay process is unique to that Each decay process is unique to that radionuclideradionuclide

Majority of pertinent information about the Majority of pertinent information about the decay process and its associated radiation decay process and its associated radiation can be summarized in a line diagram can be summarized in a line diagram called a called a decay schemedecay scheme

Decay schemes identify the parent, Decay schemes identify the parent, daughter, mode of decay, intermediate daughter, mode of decay, intermediate excited states, energy levels, radiation excited states, energy levels, radiation emissions, and sometimes physical half-lifeemissions, and sometimes physical half-life

Radioactive decay seriesOften times the products of a radioactive decay are themselves radioactive. These products will continue to decaying until we reach a stable isotope.

222222RnRn

decaydecay

3.8 day3.8 day218218PoPo

decaydecay

3.1 min3.1 min214214PbPb

214214BiBi 214214PoPo

- - decaydecay

26.8 26.8 minmin

- - decaydecay

19.9 19.9 minmin

decaydecay

164164sesecc

210210PbPb

General Format for Decay General Format for Decay SchemesSchemes

β-(E, %)β+

Radionuclide

Final productγ

ecDecay Mechanism

Determining Dtr Product in Determining Dtr Product in Chart of NuclidesChart of Nuclides

OriginalNucleus

p in

n out

p out

n in

β- out

β+, ec out

out

in

Decay ConstantDecay Constant

Number of atoms decaying per unit Number of atoms decaying per unit time is proportional to the number of time is proportional to the number of unstable atomsunstable atoms

Constant of proportionality is the Constant of proportionality is the decay constantdecay constant ( ())

dN/dt = -dN/dt = - N N

A = A = N NUnits = time -1

Physical Half-LifePhysical Half-Life

= ln 2/t1/2 = 0.693/t1/2

Physical half-life and decay constant Physical half-life and decay constant are inversely related and unique for are inversely related and unique for each radionuclideeach radionuclide

The half-life of various isotopes can range from billions of years to small fractions of a second.

IsotopeIsotope Half-LifeHalf-Life

TritiumTritium 12.26 years (beta 12.26 years (beta minus)minus)

Strontium 90Strontium 90 28.8 years (beta minus)28.8 years (beta minus)

Cesium 137Cesium 137 30.2 years (beta minus)30.2 years (beta minus)

Carbon 14Carbon 14 5730 years (beta minus)5730 years (beta minus)

Radon 222Radon 222 3.8 days (alpha)3.8 days (alpha)

Polonium 218Polonium 218 3.1 minutes (alpha)3.1 minutes (alpha)

Polonium 214Polonium 214 164 microseconds (beta 164 microseconds (beta minus)minus)

Uranium 238 Uranium 238 4.5 billion years (alpha)4.5 billion years (alpha)

Uranium 235Uranium 235 710 million years (alpha)710 million years (alpha)

Plutonium 238Plutonium 238 86 years (alpha)86 years (alpha)



Plutonium 241Plutonium 241 13.2 years (beta minus)13.2 years (beta minus)

Fundamental Decay Fundamental Decay EquationEquation

Nt = N0e-t or At = A0e-t

where:Nt = number of radioactive atoms at time t

At = activity at time t

N0 = initial number of radioactive atoms

A0 = initial activitye = base of natural logarithm = 2.71828… = decay constant = ln 2/Tp1/2 = 0.693/Tp1/2

t = time

ActivityActivity

The The quantityquantity of radioactive material, of radioactive material, expressed as the number of radioactive expressed as the number of radioactive atoms undergoing nuclear transformation atoms undergoing nuclear transformation per unit time, is called per unit time, is called activityactivity (A) (A)

Traditionally expressed in units of curies Traditionally expressed in units of curies (Ci), where 1 Ci = 3.70E10 disintegrations (Ci), where 1 Ci = 3.70E10 disintegrations per second (dps)per second (dps)

The SI unit is the becquerel (Bq)The SI unit is the becquerel (Bq) 1 mCi = 37 MBq1 mCi = 37 MBq

1 g of Ra-226 = 3.7E10 dis/sec

Specific ActivitySpecific Activity

Defn of activity tells us nothing about Defn of activity tells us nothing about mass/volumemass/volume

SA = concentration of radioactivitySA = concentration of radioactivity

Ra Ra( / )i i

A TSA Ci gm N

A T

g/moleHalf-life

6.023E23 at/mole A g/mole

0.693 T1/2

Naturally Occurring SeriesNaturally Occurring Series

Thorium Series (4Thorium Series (4nn)) Neptunium Series (4Neptunium Series (4nn+1)+1) Uranium Series (4Uranium Series (4nn+2)+2) Actinium Series (4Actinium Series (4nn+3)+3)

AUNT

44nn

Divide mass numbers in a series by 4Divide mass numbers in a series by 4 The +1, +2, +3 is the remainder after The +1, +2, +3 is the remainder after

dividing by 4dividing by 4 Due to emission of either alpha (4 mass Due to emission of either alpha (4 mass

units) or beta (0 mass units)units) or beta (0 mass units) End point for three series is lead End point for three series is lead

Np series end is Bi-209Np series end is Bi-209 Each series named for long lived isotopeEach series named for long lived isotope

Serial TransformationSerial Transformation

rate of change = rate of formation - rate of change = rate of formation - rate of transformationrate of transformation

Equilibrium - special cases of serial Equilibrium - special cases of serial transformationtransformation Secular EquilibriumSecular Equilibrium Transient EquilibriumTransient Equilibrium No EquilibriumNo Equilibrium

CBA BA

Secular EquilibriumSecular Equilibrium

Half life of parent very much greater than Half life of parent very much greater than that of daughterthat of daughter occurs about 5-6 half-lives of dtroccurs about 5-6 half-lives of dtr

TT½ parent½ parent >> T>> T½ daughter½ daughter

AA << << BB

Activity of parent and dtr are equal if Activity of parent and dtr are equal if parent atoms decay only to dtrparent atoms decay only to dtr

Ex.Ex. 9090Sr is in secular equilibrium with Sr is in secular equilibrium with 9090YY

Secular EquilibriumSecular Equilibrium

BBNNBB = = AANNAA ( 1 - e ( 1 - e--t t ))

After 7 half lives: After 7 half lives: AANNAA = = BBNNBB

Activity of daughter = activity of parentActivity of daughter = activity of parent

Transient EquilibriumTransient Equilibrium

Half life of parent slightly greater Half life of parent slightly greater than that of daughterthan that of daughter

TT½ parent ½ parent > T> T½ daughter½ daughter

AA < < BB

Tc-99m = TransientTc-99m = Transient 9999Mo and Mo and 99m99mTcTc


Equations 4.55 and 4.56Equations 4.55 and 4.56

AAB

BB

AB

AABBB

QQ

NN


Total activity reaches a maximum Total activity reaches a maximum Equation 4.57Equation 4.57

After maximum, daughter seems to After maximum, daughter seems to decay with same half life as parentdecay with same half life as parent

AB

ABt

)/ln(

md

General Equation for Serial General Equation for Serial TransformationTransformation

0 ( )A BA A t tB

B A

N e e

SummarySummary

Decay = spontaneous nuclear Decay = spontaneous nuclear transformation which results in transformation which results in formation of new elementsformation of new elements Chemical properties do not affect decayChemical properties do not affect decay

Decay mechanisms…Decay mechanisms… Decay kinetics…Decay kinetics… Activity…Activity…

Radionuclide GeneratorsRadionuclide Generators

Technetium-99m has been the most Technetium-99m has been the most important radionuclide used in nuclear important radionuclide used in nuclear medicinemedicine

Short half-life (6 hours) makes it impractical Short half-life (6 hours) makes it impractical to store even a weekly supplyto store even a weekly supply

Supply problem overcome by obtaining Supply problem overcome by obtaining parent Mo-99, which has a longer half-life (67 parent Mo-99, which has a longer half-life (67 hours) and continually produces Tc-99mhours) and continually produces Tc-99m

A system for holding the parent in such a A system for holding the parent in such a way that the daughter can be easily way that the daughter can be easily separated for clinical use is called a separated for clinical use is called a radionuclide generatorradionuclide generator

Radionuclide ProductionRadionuclide Production

All radionuclides commonly All radionuclides commonly administered to patients in nuclear administered to patients in nuclear medicine are artificially producedmedicine are artificially produced

Most are produced by cyclotrons, Most are produced by cyclotrons, nuclear reactors, or radionuclide nuclear reactors, or radionuclide generatorsgenerators

CyclotronsCyclotrons

Cyclotrons produce radionuclides by Cyclotrons produce radionuclides by bombarding stable nuclei with high-energy bombarding stable nuclei with high-energy charged particlescharged particles

Most cyclotron-produced radionuclides are Most cyclotron-produced radionuclides are neutron poor and therefore decay by positron neutron poor and therefore decay by positron emission or electron captureemission or electron capture

Specialized hospital-based cyclotrons have Specialized hospital-based cyclotrons have been developed to produce positron-emitting been developed to produce positron-emitting radionuclides for positron emission tomography radionuclides for positron emission tomography (PET)(PET) Usually located near the PET imager because of Usually located near the PET imager because of

short half-lives of the radionuclides producedshort half-lives of the radionuclides produced

Nuclear ReactorsNuclear Reactors

Specialized nuclear reactors used to Specialized nuclear reactors used to produce clinically useful radionuclides from produce clinically useful radionuclides from fission products or neutron activation of fission products or neutron activation of stable target materialstable target material

Uranium-235 fission products can be Uranium-235 fission products can be chemically separated from other fission chemically separated from other fission products with essentially no stable isotopes products with essentially no stable isotopes (carrier) of the radionuclide present(carrier) of the radionuclide present

Concentration of these “carrier-free” Concentration of these “carrier-free” fission-produced radionuclides is very highfission-produced radionuclides is very high

Neutron ActivationNeutron Activation

Neutrons produced by the fission of Neutrons produced by the fission of uranium in a nuclear reactor can be used uranium in a nuclear reactor can be used to create radionuclides by bombarding to create radionuclides by bombarding stable target material placed in the reactorstable target material placed in the reactor

Process involves capture of neutrons by Process involves capture of neutrons by stable nucleistable nuclei

Almost all radionuclides produced by Almost all radionuclides produced by neutron activation decay by beta-minus neutron activation decay by beta-minus particle emissionparticle emission

Ideal RadiopharmaceuticalsIdeal Radiopharmaceuticals

Low radiation doseLow radiation dose High target/nontarget activityHigh target/nontarget activity SafetySafety ConvenienceConvenience Cost-effectivenessCost-effectiveness