Nuclear fission and fusion Types of decay process Rates of decay Nuclear stability Energy changes Fission and fusion
Learning objectives
Identify and name types of radiation Balance nuclear equations for natural decay or artificial nuclear reactions Apply half-life (first order kinetics) to determination of age of samples
Forces at work in the nucleus
Electrostatic repulsion: pushes protons apart
Strong nuclear force: pulls protons together
Nuclear force is much shorter range: protons must be close together
Neutrons only experience the strong nuclear force
Proton pair experiences both forces
Neutrons experience only the strong nuclear force
But: neutrons alone are unstable
Neutrons act like nuclear glue
Helium nucleus contains 2 protons and 2 neutrons – increase attractive forces
Overall nucleus is stable
As nuclear size increases, electrostatic repulsion builds up
There are electrostatic repulsions between protons that don’t have attractive forces Long range repulsive force with no compensation from attraction
More neutrons required
Neutron to proton ratio increases with atomic number Upper limit of stability
4 U 234 90Th 2 He
238 92
Upper limit to nuclear stability
Beyond atomic number 83, all nuclei are unstable and decay via radioactivity Radioactive decay (Transmutation) – formation of new element
Mass number
Atomic number
U Th He
238 92
Atomic number decreases
234 90
4 2
0 0
Alpha particle emitted
Odds and sods
All elements have radioactive isotope(s) Only H has fewer neutrons than protons in stable 1H 1 isotope The neutron:proton ratio increases with Z All isotopes heavier than 209 83 Bi are radioactive Most nonradioactive isotopes contain even # neutrons (207 out of 264). 156 have even # protons & neutrons; 51 have even protons & odd neutrons; 4 have odd protons & neutrons
Nuclear processes vs chemical
Chemical reactions involve electrons; nuclear reactions involve the nucleus Isotopes behave the same in chemical reactions but differently in nuclear ones Rate of nuclear process independent of T,P, catalyst Nuclear process independent of state of the atom – element, compound Energy changes are massive
Types of radiation
Alpha particle emission: nuclear equations balance mass and charge
U He
238 92 92 protons 146 neutrons 238 nucleons
4 2
2 protons 2 neutrons 4 nucleons
Th
234 90
90 protons 144 neutrons 234 nucleons
0 0
0 protons 0 neutrons 0 nucleons
Beta particle emission
Neutron is converted into a proton + electron
Proton stays in nucleus Electron is emitted (beta particle)
0 1
e
Beta particle emission
I e
131 53 53 protons 78 neutrons 131 nucleons
0 1
0 nucleons -1 charge
131 54
54 protons 77 neutrons 131 nucleons
Xe 0 0
Conversion of neutron to proton + electron
It is incorrect to say that a neutron consists of a proton + electron altho’ beta decay suggests it Neutrons and protons are made from quarks A down-quark is converted to an up-quark In β− decay, the weak interaction converts a neutron (n0) into a proton (p+) while emitting an electron (e−) and an antineutrino (νe):
n0 → p+ + e− + νe
Other decay processes
Positron emission: the 40 conversion of a proton into a 19 neutron plus positive electron 19 protons
Decrease in z with no decrease in m
21 neutrons 40 nucleons
Electron capture: the capture of an electron by a proton to 197 create a neutron
Decrease in z with no decrease in m
80 protons 117 neutrons 197 nucleons
80
K Ar e 40 18
18 protons 22 neutrons 40 nucleons
0 nucleons +1 charge
Hg e 0 1
0 nucleons -1 charge
0 1
197 79
79 protons 118 neutrons 197 nucleons
Au
Positrons and antimatter
Protons are converted to nucleus and positively 0 charged electron (positron) e
Neutron stays in nucleus Positron emitted
1
Positron is antimatter and is annihilated by 0 0 electron: 1 e 1 e
Summary of processes and notation Process
Symbol
Alpha
α
Change in mass number
Change in neutron number
He -2
-4
-2
Beta
β-
0 1
0
-1
Gamma
γ
0 0
0
0
0
Positron
β+
0 1
e -1
0
+1
Electron capture
E.C.
-1
0
+1
4 2
Change in atomic number
e +1
Measuring decay
Rates of radioactive decay vary enormously – from fractions of a second to billions of years The rate equation is the same first order process Rate = k x N
N kt ln N o
The first order rate equation
Half-life measures rate of decay
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
1.2 1 0.8 0.6 0.4 0.2 0 0
5
10
15
20
25
30
35
40
Mathematical jiggery pokery
Calculating half life from decay rate t = 0, N = No; t = t1/2, N = No/2
t1/ 2
ln 2 k
Calculating residual amounts from half life N t ln 2 ln No t1/ 2
Variations on a theme
Magic numbers
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) Magic numbers are associated with the nuclear structure, which is analogous to the electronic structure of atoms
Stability is not achieved in one step: products also decay
Here atomic number actually increases, but serves to reduce the neutron:proton ratio
Th Pa e
234 90
234 91
0 1
Beta particle emission occurs with neutron-excess nuclei Alpha particle emission occurs with proton-heavy nuclei
Correlation of neutron:proton ratio and decay process
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 is energy involved with binding nuclear particles to form a nucleus
2 H 2 n He 1 1
1 0
4 2
Experimentally demanding to measure!
Use Einstein’s relationship
E = mc2 Consider He nucleus (without electrons):
Mass of individual particles = 4.03188 amu Mass of He nucleus = 4.00150 amu Mass loss = 0.03038 amu
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 109 kJ/mol
Masses of masses
Mass of proton = 1.0072765 amu (1.67262158 x 10-24 g) Mass of neutron = 1.0086649 amu (1.67492716 x 10-24 g) Mass of electron = 5.485799 x 10-4 amu (9.10938188 x 10-28 g)
Sample calculation
Inter-changeability of mass and energy
Loss in mass equals energy given out
E = mc2
Tiny amount of matter produces masses of energy: 1 gram 1014 J Energy and mass are conserved, but can be interchanged Binding energy per nucleon presents the total binding energy as calculated previously per nuclear particle
Usually cited in eV, where 1 eV = 1.6x10-19J
Inter-changeability of mass and energy
Energy and mass are conserved, but can be interchanged In the fission process, the combined mass of the smaller nuclei is less than the original nucleus
AB+C
MA > MB + MC
Loss in mass equals energy given out
E = mc2 (Einstein’s relation)
In the fission of U-235, about 0.08 % of its mass is converted into energy
Nuclear energy: a vast reservoir
Comparison of nuclear and chemical energy sources Chemical process:
1 gram fuel produces 103 J
Nuclear process:
1 gram uranium at 0.08 % produces 1011 J
Average mass per nucleon varies with atomic number Average Nuclear Binding En/Nucleon 10 9 8
Fe
7
He
MeV
6 5
Nucleon mass
4
U
3
H
2 1 0 0
50
100
150
200
250
Mass Number (A)
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.
Much binding in the marsh
The binding energy is the energy required to separate the nucleus into individual nucleons Equal to the gain in mass Binding energy increases with atomic number
4.53 x
10-12
4 2
J He 7.90 x 10-11 J
56 26
Fe
Binding energy per nucleon is maximum for Fe
1.13 x 10-12 J
4 2
He 1.41 x 10-12 J 2656 Fe 1.21 x 10-12 J
238 92
U
Binding energy calculation: mass defect in He = 0.03038 amu 4 2
Mass changes in chemical reactions?
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 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.
Distorting the nucleus causes the repulsive forces to overwhelm the attractive
The foundation of nuclear energy and the atomic bomb
Nuclear fission
Nuclear fission produces nuclei with lower nucleon mass 1 0
n U Kr Ba 3 n 235 92
91 36
142 56
1 0
One neutron produces three: the basis for a chain reaction – explosive potential Many fission pathways – 800 fission products from U-235
Chain reactions require rapid multiplication of species
Nuclear fusion
Small nuclei fuse to yield larger ones – losing nucleon mass +E Example is the deuterium – tritium reaction
High energy output Clean products – no long-lived radioactive waste or toxic heavy metals
Problem is providing enough energy to initiate the process
Useful radioisotopes and half-lives Radioisotope Symbol
Radiation
3 1 14 6 32 15 40 19 60 27
Halflife
Use
βC βP βK βCo β-,γ 99 γ 43Tc
12.33 y
Biochemical tracer
5730 y
Archeological dating
14.25 d
Leukemia therapy
Iodine-123
123 53
Uranium-235
235 92
Tritium Carbon-14 Phosphorus-32
Potassium-40 Cobalt-60 Technecium99m
H
I
U
γ α
1.28 x 109 y Geological dating 5.27 y
Cancer therapy
6.01 h
Brain scans
13.27 h
Thyroid therapy
7.04 x 108 y Power generation
Radioisotopes have wide range of uses
H-3 Triggering nuclear weapons, luminous paints and gauges, biochemical tracer I-131 Thyroid treatment and medical imaging Co-60 Food irradiation, industrial applications, radiotherapy Sr-90 Tracer in medical and agricultural studies U-235/238 Nuclear power generation, depleted U used in weapons and shielding 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 1010 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
So what is my exposure?
Worksheet for calculating annual exposure
Is nuclear power so dangerous?
Calculate Your Radiation Dose
