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

b 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

g 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 g Symbol is Greek letter gamma Only product of IT – internal transition Produces no change of mass or atomic numbers

Positron Emission Tomography 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

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, 168O, 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

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 11p 10n + 01b 11p + 0-1e 10n

Decay series

Induced Transmutation Transmutation can be induced by allowing high-energy particles to strike atomic nuclei 42He + 147N  178O + 11p 23892U + 10n  23992U  23993Np + 0-1e 23993Np  23994Pu + 0-1e 10n + 147N  146C + 11H

Radioactive Decay 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

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)

Nuclear Reactions and Energy 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 10n + 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