Nuclear fission and fusion Types of decay process Types of decay process Rates of decay Rates of decay Nuclear stability Nuclear stability Energy changes Energy changes Fission and fusion Fission and fusion

Forces at work in the nucleus Electrostatic repulsion: pushes protons apart Electrostatic repulsion: pushes protons apart Strong nuclear force: pulls protons together Strong nuclear force: pulls protons together Nuclear force is much shorter range: protons must be close together Nuclear force is much shorter range: protons must be close together 

Neutrons only experience the strong nuclear force Proton pair experiences both forces Proton pair experiences both forces Neutrons experience only the strong nuclear force Neutrons experience only the strong nuclear force But: neutrons alone are unstable But: neutrons alone are unstable 

Neutrons act like nuclear glue Helium nucleus contains 2 protons and 2 neutrons – increase attractive forces Helium nucleus contains 2 protons and 2 neutrons – increase attractive forces Overall nucleus is stable Overall nucleus is stable   

As nuclear size increases, electrostatic repulsion builds up There are electrostatic repulsions between protons that don’t have attractive forces There are electrostatic repulsions between protons that don’t have attractive forces More neutrons required More neutrons required      Long range repulsive force with no compensation from attraction 

Neutron to proton ratio increases with atomic number Upper limit of stability

Upper limit to nuclear stability Beyond atomic number 83, all nuclei are unstable and decay via radioactivity Beyond atomic number 83, all nuclei are unstable and decay via radioactivity Radioactive decay (Transmutation) – formation of new element Radioactive decay (Transmutation) – formation of new element Atomic number decreases Alpha particle emitted Mass number Atomic number

Odds and sods All elements have a radioactive isotope All elements have a radioactive isotope Only H has fewer neutrons than protons Only H has fewer neutrons than protons The neutron:proton ratio increases with Z The neutron:proton ratio increases with Z All isotopes heavier than bismuth-209 are radioactive All isotopes heavier than bismuth-209 are radioactive Most nonradioactive isotopes contain an even number of neutrons (207 out of 264). 156 have even protons and neutrons; 51 have even protons and odd neutrons; 4 have odd protons and neutrons Most nonradioactive isotopes contain an even number of neutrons (207 out of 264). 156 have even protons and neutrons; 51 have even protons and odd neutrons; 4 have odd protons and neutrons

Nuclear processes relieve instability Chemical reactions involve electrons; nuclear reactions involve the nucleus Chemical reactions involve electrons; nuclear reactions involve the nucleus Isotopes behave the same in chemical reactions but differently in nuclear ones Isotopes behave the same in chemical reactions but differently in nuclear ones Rate of nuclear process independent of T,P, catalyst Rate of nuclear process independent of T,P, catalyst Nuclear process independent of state of the atom – element, compound Nuclear process independent of state of the atom – element, compound Energy changes are massive Energy changes are massive

Types of radiation

Alpha particle emission 92 protons 146 neutrons 238 nucleons 2 protons 2 neutrons 4 nucleons 90 protons 144 neutrons 234 nucleons

Beta particle emission 53 protons 78 neutrons 131 nucleons 54 protons 77 neutrons 131 nucleons 0 nucleons -1 charge

Other decay processes Positron emission: the conversion of a proton into a neutron plus positive electron Positron emission: the conversion of a proton into a neutron plus positive electron Decrease in z with no decrease in m Decrease in z with no decrease in m Electron capture: the capture of an electron by a proton to create a neutron Electron capture: the capture of an electron by a proton to create a neutron Decrease in z with no decrease in m Decrease in z with no decrease in m 19 protons 21 neutrons 40 nucleons 18 protons 22 neutrons 40 nucleons 0 nucleons +1 charge 80 protons 117 neutrons 197 nucleons 79 protons 118 neutrons 197 nucleons 0 nucleons -1 charge

ProcessSymbol Change in atomic number Change in mass number Change in neutron number Alphaα Beta β-β-β-β-+10 Gammaγ000 Positron β+β+β+β+0+1 Electron capture E.C.0+1 Summary of processes and notation

Measuring decay Rates of radioactive decay vary enormously – from fractions of a second to billions of years Rates of radioactive decay vary enormously – from fractions of a second to billions of years The rate equation is the same first order process The rate equation is the same first order process Rate = k x N

Half-life measures rate of decay Concentration of nuclide is halved after the same time interval regardless of the initial amount – Half-life Concentration of nuclide is halved after the same time interval regardless of the initial amount – Half-life Can range from fractions of a second to millions of years Can range from fractions of a second to millions of years

Mathematical jiggery pokery Calculating half life from decay rate Calculating half life from decay rate t = 0, N = N o ; t = t 1/2, N = N o /2 Calculating residual amounts from half life Calculating residual amounts from half life

Magic numbers Certain numbers of protons and/or neutrons convey unusual stability on the nucleus Certain numbers of protons and/or neutrons convey unusual stability on the nucleus 2, 8, 20, 28, 50, 82, 126 There are ten isotopes of Sn (Z=50); but only two of In (Z=49) and Sb (Z=51) There are ten isotopes of Sn (Z=50); but only two of In (Z=49) and Sb (Z=51) Magic numbers are associated with the nuclear structure, which is analogous to the electronic structure of atoms Magic numbers are associated with the nuclear structure, which is analogous to the electronic structure of atoms

Correlation of neutron:proton ratio and decay process

Stability is not achieved in one step: products also decay Here atomic number actually increases, but serves to reduce the neutron:proton ratio Here atomic number actually increases, but serves to reduce the neutron:proton ratio Beta particle emission occurs with neutron-excess nuclei Beta particle emission occurs with neutron-excess nuclei Alpha particle emission occurs with proton-heavy nuclei Alpha particle emission occurs with proton-heavy nuclei

Radioactive 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 decay In principle there will be an energy associated with the binding of nuclear particles to form a nucleus In principle there will be an energy associated with the binding of nuclear particles to form a nucleus Experimentally demanding! Experimentally demanding!

Use Einstein’s relationship E = mc 2 Consider the He nucleus: Consider the He nucleus: Mass of individual particles = amu Mass of He nucleus = amu Mass loss = amu The “lost” mass is converted into energy – the binding energy, which is released during the nuclear process The “lost” mass is converted into energy – the binding energy, which is released during the nuclear process For the example above, the energy is 2.73 x 10 9 kJ/mol For the example above, the energy is 2.73 x 10 9 kJ/mol

Inter-changeability of mass and energy Loss in mass equals energy given out Loss in mass equals energy given out E = mc 2 Tiny amount of matter produces masses of energy: Tiny amount of matter produces masses of energy: 1 gram  J Energy and mass are conserved, but can be inter- changed Energy and mass are conserved, but can be inter- changed Binding energy per nucleon presents the total binding energy as calculated previously per nuclear particle Binding energy per nucleon presents the total binding energy as calculated previously per nuclear particle Usually cited in eV, where 1 eV = 1.6x J Usually cited in eV, where 1 eV = 1.6x J

Average mass per nucleon varies with atomic number H He Fe U Nucleon 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? Conservation of mass and energy means that energy changes in chemical processes involve concomitant changes in mass Conservation of mass and energy means that energy changes in chemical processes involve concomitant changes in mass Magnitude is so small as to be undetectable Magnitude is so small as to be undetectable A ΔH of -436 kJ/mol corresponds to a weight loss of 4.84 ng/mol A ΔH of -436 kJ/mol corresponds to a weight loss of 4.84 ng/mol

Fission and fusion: ways to harness nuclear energy Attempts to grow larger nuclei by bombardment with neutrons yielded smaller atoms instead. Attempts to grow larger nuclei by bombardment with neutrons yielded smaller atoms instead. Distorting the nucleus causes the repulsive forces to overwhelm the attractive Distorting the nucleus causes the repulsive forces to overwhelm the attractive The foundation of nuclear energy and the atomic bomb The foundation of nuclear energy and the atomic bomb

Nuclear fission Nuclear fission produces nuclei with lower nucleon mass Nuclear fission produces nuclei with lower nucleon mass One neutron produces three: the basis for a chain reaction – explosive potential One neutron produces three: the basis for a chain reaction – explosive potential Many fission pathways – 800 fission products from U-235 Many fission pathways – 800 fission products from U-235

Chain reactions require rapid multiplication of species

Nuclear fusion: opposite of fission Small nuclei fuse to yield larger ones Small nuclei fuse to yield larger ones Nuclear mass is lost Nuclear mass is lost Example is the deuterium – tritium reaction Example is the deuterium – tritium reactiondeuterium – tritiumdeuterium – tritium About 0.7 % of the mass is converted into energy About 0.7 % of the mass is converted into energy + E+ E

The sun is a helium factory The sun’s energy derives from the fusion of hydrogen atoms to give helium The sun’s energy derives from the fusion of hydrogen atoms to give helium

Fusion would be the holy grail if... The benefits : The 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 metals Clean products – no long-lived radioactive waste or toxic heavy metals The challenge: The challenge: Providing enough energy to start the process – positive charges repel Providing enough energy to start the process – positive charges repel Reproduce the center of the sun in the lab Reproduce the center of the sun in the lab Fusion is demonstrated but currently consumes rather than produces energy Fusion is demonstrated but currently consumes rather than produces energy

Useful radioisotopes and half-lives RadioisotopeSymbol Radiation Half- life Use Tritium β-β-β-β y Biochemical tracer Carbon-14 β-β-β-β y Archeologocial dating Phosphorus-32 β-β-β-β d Leukemia therapy Potassium-40 β-β-β-β x 10 9 y Geological dating Cobalt-60 β-,γβ-,γβ-,γβ-,γ 5.27 y Cancer therapy Technecium- 99m γ 6.01 h Brain scans Iodine-123γ h Thyroid therapy Uranium-238α 7.04 x 10 8 y Power generation

Radioisotopes have wide range of uses H-3 Triggering nuclear weapons, luminous paints and gauges, biochemical tracer H-3 Triggering nuclear weapons, luminous paints and gauges, biochemical tracer I-131 Thyroid treatment and medical imaging I-131 Thyroid treatment and medical imaging Co-60 Food irradiation, industrial applications, radiotherapy Co-60 Food irradiation, industrial applications, radiotherapy Sr-90 Tracer in medical and agricultural studies Sr-90 Tracer in medical and agricultural studies U-235/238 Nuclear power generation, depleted U used in weapons and shielding U-235/238 Nuclear power generation, depleted U used in weapons and shielding Am-241 Thickness and distance gauges, smoke detectors Am-241 Thickness and distance gauges, smoke detectors

Nuclear power prevalent in Europe

Different units for measuring radiation Unit Quantity measured Description Becquerel (Bq) Decay events Amount of sample that undergoes 1 disintegration/s Curie (Ci) Decay events Amount of sample that undergoes 3.7 x disintegrations/s Gray (Gy) Energy absorbed per kg tissue 1 Gy = 1J/kg tissue Rad Energy absorbed per kg tissue 1 rad = 0.01 Gy Sievert (Sv) Tissue damage 1 Sv = 1 J/kg Rem Tissue damage 1 rem = 0.01 Sv

Radiation is nasty Dose (rem) Biological effects 0 – 25 No detectable effects 25 – 100 Temporary decrease in white blood cell count 100 – 200 Nausea, vomiting, longer-term decrease in white blood cell count 200 – 300 Vomiting, diarrhea, loss of appetite 300 – 600 Vomiting, diarrhea, hemorrhaging, eventual death in some cases > 600 Death in nearly all cases