Transcript Nuclear forces and Radioactivity

Nuclear fission and
fusion
Types of decay process
Rates of decay
Nuclear stability
Energy changes
Fission and fusion
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Forces at work in the nucleus
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Electrostatic repulsion: pushes protons apart
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Strong nuclear force: pulls protons together
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Nuclear force is much shorter range: protons must be close together
Neutrons only experience the strong
nuclear force
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Proton pair experiences both forces
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Neutrons experience only the strong nuclear force
But: neutrons alone are unstable
Neutrons act like nuclear glue
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Helium nucleus contains 2 protons and 2
neutrons – increase attractive forces
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Overall nucleus is stable
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As nuclear size increases,
electrostatic repulsion builds up
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There are electrostatic repulsions between
protons that don’t have attractive forces
Long range
repulsive force
with no
compensation
from attraction
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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
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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
Alpha
particle
emitted
Odds and sods
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All elements have a
radioactive isotope
Only H has fewer neutrons
than protons
The neutron:proton ratio
increases with Z
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
Nuclear processes relieve instability
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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
U  He 
238
92
92 protons
146 neutrons
238 nucleons
4
2
2 protons
2 neutrons
4 nucleons
234
90
90 protons
144 neutrons
234 nucleons
Th
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
Other decay processes
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Positron emission: the
40
conversion of a proton into a
19
neutron plus positive
electron
19 protons
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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
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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
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
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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
Half-life measures rate of decay
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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
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Calculating half life from decay rate
t = 0, N = No; t = t1/2, N = No/2
t1/ 2
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ln 2

k
Calculating residual amounts from half life
 N 
 t 
   ln 2

ln
 No 
 t1/ 2 
Magic numbers
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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
Correlation of neutron:proton ratio
and decay process
Stability is not achieved in one step:
products also decay
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Here atomic number actually increases, but
serves to reduce the neutron:proton ratio
Th Pa e  
234
90
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234
91
0
1
Beta particle emission occurs with neutron-excess 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
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In principle there will be an energy associated
with the binding of nuclear particles to form a
nucleus
2 H 2 n He
1
1
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1
0
4
2
Experimentally demanding!
Use Einstein’s relationship
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E = mc2
Consider the He nucleus:
Mass of individual particles = 4.03188 amu
Mass of He nucleus
= 4.00150 amu
Mass loss
= 0.03038 amu
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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
Inter-changeability of mass and
energy
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Loss in mass equals energy given out
E = mc2
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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
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Usually cited in eV, where 1 eV = 1.6x10-19J
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.
Mass changes in chemical reactions?
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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
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Attempts to grow larger
nuclei by bombardment
with neutrons yielded
smaller atoms instead.
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Distorting the nucleus causes the
repulsive forces to overwhelm the
attractive
The foundation of
nuclear energy and the
atomic bomb
Nuclear fission
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Nuclear fission produces nuclei with lower
nucleon mass
1
0
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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: opposite of fission
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Small nuclei fuse to yield larger ones
Nuclear mass is lost
+E
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Example is the deuterium – tritium
reaction
About 0.7 % of the mass is converted into
energy
The sun is a helium factory
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The sun’s energy derives from the fusion of hydrogen
atoms to give helium
4 H  He 2 e 2 e
0
0
1 e 1 e  2
1
1
4
2
0
1
0
1
Fusion would be the holy grail if...
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The benefits:
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The challenge:
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High energy output (10 x more output than fission)
Clean products – no long-lived radioactive waste or toxic heavy metals
Providing enough energy to start the process – positive
charges repel
Reproduce the center of the sun in the lab
Fusion is demonstrated but currently consumes
rather than produces energy
Useful radioisotopes and half-lives
Radioisotope Symbol
Tritium
Carbon-14
Phosphorus-32
Potassium-40
Cobalt-60
Technecium99m
Iodine-123
Uranium-238
Radiation
3
1
14
6
32
15
40
19
60
27
βC βP βK βCo β-,γ
99
γ
43Tc
H
123
53
238
92
I
U
γ
α
Halflife
Use
12.33 y
Biochemical tracer
5730 y
Archeologocial dating
14.25 d
Leukemia therapy
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
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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