Nuclear fission and fusionNuclear fission and fusion

Types of decay processTypes of decay processRates of decayRates of decayNuclear stabilityNuclear stabilityEnergy changesEnergy changesFission and fusionFission and fusion

Forces at work in the nucleusForces at work in the nucleus

Electrostatic repulsion: pushes protons apartElectrostatic repulsion: pushes protons apart

Strong nuclear force: pulls protons togetherStrong nuclear force: pulls protons together

Nuclear force is much shorter range: protons must be close togetherNuclear force is much shorter range: protons must be close together

Neutrons only experience the strong Neutrons only experience the strong nuclear forcenuclear force

Proton pair experiences both forcesProton pair experiences both forces

Neutrons experience only the strong nuclear forceNeutrons experience only the strong nuclear force

But: neutrons But: neutrons alonealone are unstable are unstable

Neutrons act like nuclear glueNeutrons act like nuclear glue

Helium nucleus contains 2 protons and 2 Helium nucleus contains 2 protons and 2 neutrons – increase attractive forcesneutrons – increase attractive forces Overall nucleus is stableOverall nucleus is stable

As nuclear size increases, As nuclear size increases, electrostatic repulsion builds upelectrostatic repulsion builds up

There are electrostatic repulsions between There are electrostatic repulsions between protons that don’t have attractive forcesprotons that don’t have attractive forces

More neutrons requiredMore neutrons required

Long range repulsive force

with no compensation from attraction

Neutron to proton ratio increases Neutron to proton ratio increases with atomic numberwith atomic number

Upper limit of stability

Upper limit to nuclear stabilityUpper limit to nuclear stability

Beyond atomic number 83, all nuclei are Beyond atomic number 83, all nuclei are unstable and decay via radioactivityunstable and decay via radioactivity

Radioactive decay (Radioactive decay (TransmutationTransmutation) – ) – formation of new elementformation of new element

HeThU 42

23490

23892

HeThU 42

23490

23892

Atomic number

decreases

Alpha particle emitted

Mass number

Atomic number

Odds and sodsOdds and sods All elements have a All elements have a

radioactive isotoperadioactive isotope Only H has fewer neutrons Only H has fewer neutrons

than protonsthan protons The neutron:proton ratio The neutron:proton ratio

increases with Zincreases with Z All isotopes heavier than All isotopes heavier than

bismuth-209 are radioactivebismuth-209 are radioactive Most nonradioactive isotopes Most nonradioactive isotopes

contain an even number of contain an even number of neutrons (207 out of 264). 156 neutrons (207 out of 264). 156 have even protons and neutrons; have even protons and neutrons; 51 have even protons and odd 51 have even protons and odd neutrons; 4 have odd protons and neutrons; 4 have odd protons and neutronsneutrons

Nuclear processes relieve instabilityNuclear processes relieve instability

Chemical reactions involve electrons; nuclear Chemical reactions involve electrons; nuclear reactions involve the nucleusreactions involve the nucleus

Isotopes behave the same in chemical Isotopes behave the same in chemical reactions but differently in nuclear onesreactions but differently in nuclear ones

Rate of nuclear process independent of T,P, Rate of nuclear process independent of T,P, catalystcatalyst

Nuclear process independent of state of the Nuclear process independent of state of the atom – element, compoundatom – element, compound

Energy changes are massiveEnergy changes are massive

Types of radiationTypes of radiation

Alpha particle emissionAlpha particle emission

238 4 23492 2 90U He Th

92 protons146 neutrons238 nucleons

2 protons2 neutrons4 nucleons

90 protons144 neutrons234 nucleons

Beta particle emissionBeta particle emission

131 0 13153 1 54I e Xe

53 protons78 neutrons

131 nucleons

54 protons77 neutrons

131 nucleons

0 nucleons-1 charge

Other decay processesOther decay processes

Positron emission: the Positron emission: the conversion of a proton into conversion of a proton into a neutron plus positive a neutron plus positive electronelectron Decrease in z with no Decrease in z with no

decrease in mdecrease in m

Electron capture: the Electron capture: the capture of an electron by a capture of an electron by a proton to create a neutronproton to create a neutron Decrease in z with no Decrease in z with no

decrease in mdecrease in m

40 40 019 18 1K Ar e

19 protons21 neutrons40 nucleons

18 protons22 neutrons40 nucleons

0 nucleons+1 charge

197 0 19780 1 79Hg e Au

80 protons117 neutrons197 nucleons

79 protons118 neutrons197 nucleons

0 nucleons-1 charge

ProcessProcess SymbolSymbol Change Change in atomic in atomic numbernumber

Change Change in mass in mass numbernumber

Change Change in in neutron neutron numbernumber

Alpha Alpha αα -2-2 -4-4 -2-2

BetaBeta ββ-- +1+1 00 -1-1

GammaGamma γγ 00 00 00

PositronPositron ββ++ -1-1 00 +1+1

Electron Electron capturecapture

E.C.E.C. -1-1 00 +1+1

42 He

01e

01e

00

Summary of processes and notationSummary of processes and notation

Measuring decayMeasuring decay

Rates of radioactive decay vary enormously – Rates of radioactive decay vary enormously – from fractions of a second to billions of yearsfrom fractions of a second to billions of years

The rate equation is the same first order The rate equation is the same first order process process

Rate = k x NRate = k x N

ktN

N

o

ln

Half-life measures rate of decayHalf-life measures rate of decay

Concentration of Concentration of nuclide is halved after nuclide is halved after the same time interval the same time interval regardless of the initial regardless of the initial amount – Half-lifeamount – Half-life

Can range from Can range from fractions of a second to fractions of a second to millions of yearsmillions of years

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25 30 35 40

Mathematical jiggery pokeryMathematical jiggery pokery

Calculating half life from decay rateCalculating half life from decay rate

t = 0, N = Nt = 0, N = Noo; t = t; t = t1/21/2, N = N, N = Noo/2/2

Calculating residual amounts from half lifeCalculating residual amounts from half life

kt

2ln2/1

2/1

2lnlnt

t

N

N

o

Magic numbersMagic numbers

Certain numbers of protons and/or neutrons Certain numbers of protons and/or neutrons convey unusual stability on the nucleusconvey unusual stability on the nucleus

2, 8, 20, 28, 50, 82, 1262, 8, 20, 28, 50, 82, 126 There are ten isotopes of Sn (Z=50); but only There are ten isotopes of Sn (Z=50); but only

two of In (Z=49) and Sb (Z=51)two of In (Z=49) and Sb (Z=51) Magic numbers are associated with the nuclear Magic numbers are associated with the nuclear

structure, which is analogous to the electronic structure, which is analogous to the electronic structure of atomsstructure of atoms

Correlation of neutron:proton ratio Correlation of neutron:proton ratio and decay processand decay process

Stability is not achieved in one step: Stability is not achieved in one step: products also decayproducts also decay

Here atomic number actually increases, but Here atomic number actually increases, but serves to reduce the neutron:proton ratioserves to reduce the neutron:proton ratio

Beta Beta particle emission occurs with particle emission occurs with neutronneutron-excess nuclei-excess nuclei Alpha Alpha particle emission occurs with particle emission occurs with protonproton-heavy nuclei-heavy nuclei

ePaTh 01

23491

23490

Radioactive series are complexRadioactive series are complex

The decay series from uranium-238 to lead-206. Each nuclide except for the last is radioactive and undergoes nuclear decay. The left-pointing, longer arrows (red) represent alpha emissions, and the right-pointing, shorter arrows (blue) represent beta emissions.

Energy changes and nuclear decayEnergy changes and nuclear decay

In principle there will be an energy associated In principle there will be an energy associated with the binding of nuclear particles to form a with the binding of nuclear particles to form a nucleusnucleus

Experimentally demanding!Experimentally demanding!

HenH 42

10

11 22

Use Einstein’s relationshipUse Einstein’s relationship

E = mcE = mc22

Consider the He nucleus:Consider the He nucleus:Mass of individual particles = 4.03188 amuMass of individual particles = 4.03188 amuMass of He nucleus = 4.00150 amuMass of He nucleus = 4.00150 amuMass loss = 0.03038 amuMass loss = 0.03038 amu The “lost” mass is converted into energy – the The “lost” mass is converted into energy – the

bindingbinding energy, which is released during the nuclear energy, which is released during the nuclear processprocess

For the example above, the energy is 2.73 x 10For the example above, the energy is 2.73 x 1099 kJ/mol kJ/mol

Inter-changeability of mass and Inter-changeability of mass and energyenergy

Loss in mass equals energy given outLoss in mass equals energy given out

E = mcE = mc22

Tiny amount of matter produces masses of energy:Tiny amount of matter produces masses of energy:

1 gram 1 gram 10 101414 J J Energy Energy and and mass are conserved, but can be inter-mass are conserved, but can be inter-

changedchanged Binding energy per nucleon presents the total binding Binding energy per nucleon presents the total binding

energy as calculated previously per nuclear particleenergy as calculated previously per nuclear particle Usually cited in eV, where 1 eV = 1.6x10Usually cited in eV, where 1 eV = 1.6x10-19-19JJ

Average mass per nucleon varies with atomic number Average mass per nucleon varies with atomic number Average Nuclear

Binding En/Nucleon

0

1

2

3

4

5

6

7

8

9

10

0 50 100 150 200 250

Mass Number (A)

MeV

H

HeFe

UNucleon mass

The binding energy per nucleon for the most stable isotope of each naturally occurring element. Binding energy reaches a maximum of 8.79 MeV/nucleon at 56Fe. As a result, there is an increase in

stability when much lighter elements fuse together to yield heavier elements up to 56Fe and when much heavier elements split apart to yield lighter elements down to 56Fe, as indicated by the arrows.

Mass changes in chemical reactions?Mass changes in chemical reactions?

Conservation of mass and energy means that Conservation of mass and energy means that energy changes in chemical processes involve energy changes in chemical processes involve concomitant changes in massconcomitant changes in mass

Magnitude is so small as to be undetectableMagnitude is so small as to be undetectable A A ΔΔH of -436 kJ/mol corresponds to a weight H of -436 kJ/mol corresponds to a weight

loss of 4.84 ng/molloss of 4.84 ng/mol

Fission and fusion: ways to harness Fission and fusion: ways to harness nuclear energynuclear energy

Attempts to grow larger Attempts to grow larger nuclei by bombardment nuclei by bombardment with neutrons yielded with neutrons yielded smaller atoms instead.smaller atoms instead. Distorting the nucleus causes the Distorting the nucleus causes the

repulsive forces to overwhelm repulsive forces to overwhelm the attractivethe attractive

The foundation of The foundation of nuclear energy and the nuclear energy and the atomic bombatomic bomb

Nuclear fissionNuclear fission

Nuclear fission produces nuclei with lower Nuclear fission produces nuclei with lower nucleon massnucleon mass

One neutron produces three: the basis for a One neutron produces three: the basis for a chain reaction – explosive potentialchain reaction – explosive potential

Many fission pathways – 800 fission products Many fission pathways – 800 fission products from U-235from U-235

nBaKrUn 10

14256

9136

23592

10 3

Chain reactions require rapid multiplication Chain reactions require rapid multiplication of speciesof species

Nuclear fusion: opposite of fissionNuclear fusion: opposite of fission

Small nuclei fuse to yield larger onesSmall nuclei fuse to yield larger ones Nuclear mass is lostNuclear mass is lost

Example is the Example is the deuterium – tritiumdeuterium – tritium reactionreaction

About 0.7 % of the mass is converted into About 0.7 % of the mass is converted into energyenergy

+ E

The sun is a helium factoryThe sun is a helium factory

The sun’s energy derives from the fusion of hydrogen The sun’s energy derives from the fusion of hydrogen atoms to give heliumatoms to give helium

eeHeH 01

01

42

11 224

201

01 ee

Fusion would be the holy grail if...Fusion would be the holy grail if...

The benefitsThe benefits:: High energy output (10 x more output than fission)High energy output (10 x more output than fission) Clean products – no long-lived radioactive waste or toxic heavy metalsClean products – no long-lived radioactive waste or toxic heavy metals

The challenge:The challenge: Providing enough energy to start the process – positive Providing enough energy to start the process – positive

charges repelcharges repel Reproduce the center of the sun in the labReproduce the center of the sun in the lab

Fusion is demonstrated but currently consumes Fusion is demonstrated but currently consumes rather than produces energyrather than produces energy

Useful radioisotopes and half-livesUseful radioisotopes and half-livesRadioisotopeRadioisotope SymbolSymbol

RadiationRadiationHalf-Half-lifelife

UseUse

TritiumTritium ββ-- 12.33 y12.33 y Biochemical tracerBiochemical tracer

Carbon-14Carbon-14 ββ-- 5730 y5730 y Archeologocial datingArcheologocial dating

Phosphorus-32Phosphorus-32 ββ-- 14.25 d14.25 d Leukemia therapyLeukemia therapy

Potassium-40Potassium-40 ββ-- 1.28 x 101.28 x 1099 y y Geological datingGeological dating

Cobalt-60Cobalt-60 ββ--,,γγ 5.27 y5.27 y Cancer therapyCancer therapy

Technecium-Technecium-9999mm

γγ 6.01 h6.01 h Brain scansBrain scans

Iodine-123Iodine-123 γγ 13.27 h13.27 h Thyroid therapyThyroid therapy

Uranium-238Uranium-238 αα 7.04 x 107.04 x 1088 y y Power generationPower generation

31 H146C3215 P4019 K6027Co9943Tc

12353 I

23892U

Radioisotopes have wide range of usesRadioisotopes have wide range of uses

H-3 Triggering nuclear weapons, luminous paints and H-3 Triggering nuclear weapons, luminous paints and gauges, biochemical tracergauges, biochemical tracer

I-131 Thyroid treatment and medical imagingI-131 Thyroid treatment and medical imaging Co-60Co-60 Food irradiation, industrial applications, Food irradiation, industrial applications,

radiotherapyradiotherapy Sr-90 Tracer in medical and agricultural studiesSr-90 Tracer in medical and agricultural studies U-235/238 Nuclear power generation, depleted U U-235/238 Nuclear power generation, depleted U

used in weapons and shieldingused in weapons and shielding Am-241 Thickness and distance gauges, smoke Am-241 Thickness and distance gauges, smoke

detectorsdetectors

Nuclear power prevalent in EuropeNuclear power prevalent in Europe

Different units for measuring Different units for measuring radiationradiation

UnitUnit Quantity measuredQuantity measured DescriptionDescription

Becquerel (Bq)Becquerel (Bq) Decay eventsDecay events Amount of sample that Amount of sample that undergoes 1 undergoes 1 disintegration/sdisintegration/s

Curie (Ci)Curie (Ci) Decay eventsDecay events Amount of sample that Amount of sample that undergoes 3.7 x 10undergoes 3.7 x 101010 disintegrations/sdisintegrations/s

Gray (Gy)Gray (Gy) Energy absorbed per Energy absorbed per kg tissuekg tissue

1 Gy = 1J/kg tissue1 Gy = 1J/kg tissue

RadRad Energy absorbed per Energy absorbed per kg tissuekg tissue

1 rad = 0.01 Gy1 rad = 0.01 Gy

Sievert (Sv)Sievert (Sv) Tissue damageTissue damage 1 Sv = 1 J/kg1 Sv = 1 J/kg

RemRem Tissue damageTissue damage 1 rem = 0.01 Sv1 rem = 0.01 Sv

Radiation is nastyRadiation is nasty

Dose (rem)Dose (rem) Biological effectsBiological effects

0 – 250 – 25 No detectable effectsNo detectable effects

25 – 10025 – 100 Temporary decrease in white Temporary decrease in white blood cell countblood cell count

100 – 200100 – 200 Nausea, vomiting, longer-term Nausea, vomiting, longer-term decrease in white blood cell countdecrease in white blood cell count

200 – 300200 – 300 Vomiting, diarrhea, loss of Vomiting, diarrhea, loss of appetiteappetite

300 – 600300 – 600 Vomiting, diarrhea, hemorrhaging, Vomiting, diarrhea, hemorrhaging, eventual death in some caseseventual death in some cases

> 600> 600 Death in nearly all casesDeath in nearly all cases