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![Page 1: Radioactivity Types of particles: Alpha particles Two protons + two neutrons Same as helium-4 nucleus + 2 charge; deflected by a magnetic field, and attracted.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649f4a5503460f94c6c3d0/html5/thumbnails/1.jpg)
Radioactivity
Types of particles:Alpha particles
• Two protons + two neutrons
• Same as helium-4 nucleus
• + 2 charge; deflected by a magnetic field, and attracted to negative charges
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Alpha particles
• Largest particle of radioactivity
• Short range• Stopped by sheet of
paper• Most damaging due
to large mass
Alpha tracks in a cloud chamber
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Nuclear equations
• Mass must be conserved• Mass numbers and atomic numbers must have same
sum on each side of equation• Result of alpha emission: mass number decreases by 4,
atomic number decreases by 2• Note symbol for alpha particle – sometimes
writtenor just
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Beta Particles
• Consist of free electrons
• Low mass, -1 charge• Medium range,
medium penetrating power
• Stopped by thick wood, thin sheet of lead
• Symbol is the Greek
letter beta or 0-1e
• Produced by a neutron, which turns into a proton
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Nuclear equations
• In beta decay a neutron turns into a proton and ejects an electron
• Mass number does not change, and atomic number increases by 1
• Example of transmutation
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Gamma Radiation
• Consists of high-energy photons
• No rest mass, no charge
• Not deflected by magnetic field
• Long range, very penetrating
• Accompanies many other types of decay
• Symbol is Greek letter
gamma• Only product of IT –
internal transition• Produces no change
of mass or atomic numbers
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Other types of decay
Positron Emission• Positrons are the
electron’s antiparticle• Same characteristics
as electron, except for positive charge
• Symbol: + or 01e
Positron Emission Tomography(PET scan)
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Positron emission
• In positron emission a proton ejects a positron and becomes a neutron
• Mass number does not change• Atomic number decreases by one
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Electron Capture
• If there are too many protons in a nucleus, it may capture an electron
• A proton becomes a neutron
Symbol for an electron
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Electron capture
• Mass number stays the same• Atomic number decreases by one• Same result as positron emission
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Nuclear Stability
• Nuclear particles (protons and neutrons) are called nucleons
• Nucleons are held together by nuclear strong force (short range, very strong)
• Neutrons are “glue” – necessary to hold the nucleus together
• Without neutrons the nucleus would fly apart due to electrostatic repulsion
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Nuclear Band of Stability
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Stability and Decay
• Above the stability band: Too many neutrons
• Beta decay reduces the neutron/proton ratio
• Very large nuclei (Z>83) undergo alpha decay, which reduces the size of the nucleus
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Stability and decay
• Below the band of stability: too many protons
• Positron emission or electron capture
• Protons are reduced, neutrons increased1
1p 10n + 0
1
11p + 0
-1e 10n
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Nuclear Magic Numbers
• Nuclei with certain numbers of protons or neutrons are especially stable
• “Magic numbers” are 2, 8, 20, 28, 50, 82, and 126
• When both neutrons and protons are magic numbers, the nucleus is specially stable: 208
82Pb
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Nuclear Magic Numbers
• Most stable nuclei have the same “magic number” of protons and neutrons: 4
2He, 16
8O, and 4020Ca
• “Even-odd” rule: Nuclei with even numbers of protons and neutrons are more stable than odds:
• Stable isotopes: 264
• Both even: 157 Both odd: 5
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Decay series
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Induced Transmutation
• Transmutation can be induced by allowing high-energy particles to strike atomic nuclei
42He + 14
7N 178O + 1
1p238
92U + 10n 239
92U 23993Np + 0
-1e239
93Np 23994Pu + 0
-1e
10n + 14
7N 146C + 1
1H
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Radioactive Decay
• Radioactive isotopes decay at predictable rates
• Half Life: the time it takes for 1/2 of a sample to decay
• Half of the remaining sample decays every half life period
Radioactive decayRadioactive decay
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Half Life Graph
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Half Life
• Follows exponential decay
• Moment of decay of any one particle is unpredictable
• Example: Radon-222 decays with a half life of 3.8 days. Approximately how long will it take for 9.5 grams of a 10 gram sample to decay?
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Half Life Problems
• Solution: Divide sample mass in half until 0.5 grams or less is reached.
10/2 = 5 (one half life)
5/2 = 2.5 (two half lives)
2.5/2 = 1.25 (three half lives)
1.25/2 = 0.625 (four half lives)
0.625/2 = 0.3125 (five half lives)
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Half life Problems
• Four half lives = 4 HL x 3.8 days/HL = 15.2 days
• Five half lives = 5 HL x 3.8 days/HL = 19 days
• Therefore, 9.5 grams of a 10 gram sample will decay in somewhere between 15.2 and 19 days.
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Half Life Problems
• Example #2: Sally has a 15.0 g sample of phosphorus-32 (half life 14.28 days). About how much will be left two months later (60 days)?
• Find time in half-lives: 60 days/14.28 days/HL = 4.20 half lives.
• Multiply the sample mass by (1/2)y, where y = number of half-lives (use xy key on calculator)
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Half Life Problems
• 15.0g(1/2)4.20 = 15.0g(0.0544) = 0.816 g remaining
• Half life equation: Nt = N0(1/2)t/t1/2 or
Nt = N0e-t where is the decay constant
t = (t1/2/0.693)ln(N0/Nt)
Nuclear Reactions and Energy• Mass is not strictly conserved in nuclear
reactions• Some mass is lost as energy
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Nuclear Reactions and Energy
• Mass to energy conversion is governed by E = mc2, where c = the speed of light in a vacuum (3.0x108m/s)
• Nuclear binding energy is the energy lost when the nucleus is formed.
• Mass equivalent of the nuclear binding energy is the mass defect.
• Protons and neutrons in the nucleus have less mass than separate nucleons
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Calculating Binding Energy
• Example:
• Mass of 1 proton = 1.00735 amu
• Mass of 1 neutron = 1.00875 amu
• Mass of 1 electron = 0.0005485 amu
• If 1 amu = 1.66 x 10-24g, calculate the binding energy of an atom of helium-4 (mass 4.00260325415 amu)
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Binding energy of helium-4
• Mass of constituents Protons: 1.00735 amu/p(2p) = 2.01470 amuNeutrons: 1.00875 amu/n(2n) = 2.01750 amuElectrons: 0.0005485 amu/e(2e) = 0.001097 amuTotal: 4.03330 amu4.03330 amu(1.66x10-24g/amu) = 6.70x10-24gHelium atom: 4.0026amu(1.66x10-24g/amu) = 6.64x10-24g)
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Binding energy of helium-4
• Mass deficit = 6.70x10-24g - 6.64x10-24g = 0.06x10-24g = 6x10-26g = 6x10-29kg
• Binding energy: E = mc2
• E = 6x10-29kg(3.00x108m/s)2 = 5x10-12J
• Energy per gram: one gram of helium-4 would have 1g/(6.64x10-24) = 1.51x1023 atoms
• 1.51x1023 a/g(5 x 10-12J/a) = 8 x 1011J/g
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Binding energy of helium-4
• 8 x 1011J/g(1 kW-hr/3600 J) = 2 x 108 kW-hr• Average household uses 10,656 kW-hr/yr• 2 x 108 kW-hr/10,656 kW-hr/(house-yr) = 20,000• Binding energy in one gram of helium-4 could
power 20,000 average households for one year• Alternatively, it could power one house for
20,000 years, or Al Gore’s mansion for 904 years.
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Nuclear Fission
• Some larger nuclei will split into two parts when struck by a neutron
• The two smaller nuclei are more stable, so energy is released
• The two smaller nuclei will have a higher binding energy per nucleon
• Neutrons are also released, producing a chain reaction
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Nuclear Fission
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Nuclear chain reactions
• Occur if the product of the reaction is necessary to start new reactions
10n + 235
92U --> 23692U --> 92
36Kr + 14156Ba + 31
0n
• Critical mass - minimum mass necessary to sustain a chain reaction
• Large enough critical mass will explode
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Nuclear Power Plants
• Nuclear fuel is usually a supercritical mass of U-235 enriched uranium
• Reaction is promoted by a moderator - a material that slows neutrons down so they will cause fission - usually carbon or D2O
Nuclear reactor at Chernobyl
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Nuclear Power Plants
• Reaction is controlled by control rods (cadmium or boron), which absorb neutrons
• Reaction generates heat, which makes steam to run a turbine
CROCUS, a small research nuclear reactor
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Geiger Counter
• Counts individual particles of radioactivity
• Ionizing radiation enters the tube through a mica window
• Ionization of gas in tube allows current to flow for an instant between high voltage cathode and anode