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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 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 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 written 42a or just a Beta Particles • Consist of free electrons • Low mass, -1 charge • Medium range, medium penetrating power • Stopped by thick wood, thin sheet of lead b • Symbol is the Greek letter beta or 0-1e • Produced by a neutron, which turns into a proton 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 Gamma Radiation • Consists of highenergy photons • No rest mass, no charge • Not deflected by magnetic field • Long range, very penetrating • Accompanies many other types of decay g • Symbol is Greek letter gamma • Only product of IT – internal transition • Produces no change of mass or atomic numbers Other types of decay Positron Emission • Positrons are the electron’s antiparticle • Same characteristics as electron, except for positive charge • Symbol: b+ or 01e Positron Emission Tomography (PET scan) Positron emission • In positron emission a proton ejects a positron and becomes a neutron • Mass number does not change • Atomic number decreases by one 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 Electron capture • Mass number stays the same • Atomic number decreases by one • Same result as positron emission 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 Nuclear Band of Stability 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 Stability and decay • Below the band of stability: too many protons • Positron emission or electron capture • Protons are reduced, neutrons increased 1 p 1 n + 0 b 1 0 1 1 1p + 0 -1e 1 0n 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: 20882Pb Nuclear Magic Numbers • Most stable nuclei have the same “magic number” of protons and neutrons: 42He, 16 O, and 40 Ca 8 20 • “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 Decay series Induced Transmutation • Transmutation can be induced by allowing high-energy particles to strike atomic nuclei 4 He + 14 N 17 O + 1 p 2 7 8 1 238 U + 1 n 239 U 239 Np + 0 e 92 0 92 93 -1 239 Np 239 Pu + 0 e 93 94 -1 1 n 0 + 147N 146C + 11H Radioactive Decay decay Radioactive • 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 Half Life Graph 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? 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) 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. 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) 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-lt where l 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 Nuclear Reactions and Energy • Mass to energy conversion is governed by DE = Dmc2, 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 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) Binding energy of helium-4 • Mass of constituents Protons: 1.00735 amu/p(2p) = 2.01470 amu Neutrons: 1.00875 amu/n(2n) = 2.01750 amu Electrons: 0.0005485 amu/e(2e) = 0.001097 amu Total: 4.03330 amu 4.03330 amu(1.66x10-24g/amu) = 6.70x10-24g Helium atom: 4.0026amu(1.66x10-24g/amu) = 6.64x10-24g) Binding energy of helium-4 • Mass deficit = 6.70x10-24g - 6.64x10-24g = 0.06x10-24g = 6x10-26g = 6x10-29kg • Binding energy: DE = Dmc2 • DE = 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 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. 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 Nuclear Fission Nuclear chain reactions • Occur if the product of the reaction is necessary to start new reactions 1 0n + 23592U --> 23692U --> 9236Kr + 14156Ba + 310n • Critical mass - minimum mass necessary to sustain a chain reaction • Large enough critical mass will explode 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 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 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