Problem du Jour
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Problem du Jour A 65-kg person is exposed for 240 s to a 15-mCi source of beta radiation from a sample of ππ πππΊπ. What is the activity of the source in disintegrations/sec? in Bq? Each beta particle has an energy of 8.75 x 10-14 J, and 7.5% of the radiation is absorbed by the person. Calculate the absorbed dose in rads and greys. If the RBE of the beta particles is 1.0, what is the effective dose in mrem and sieverts? 247 Rates of Radioactive Decay Why are some radioisotopes found in nature, while others are not and must be made synthetically? nuclei undergo radioactive decay at different rates radioactive decay follows first-order kinetics: Rate = kN N is the number of radioactive nuclei k is the decay constant The rate at which a sample decays is called its activity Activity is expressed as the number of disintegrations per time Units: Bequerel (bq) = 1 disintegration/sec Curie (Ci): 1 Ci = 3.7x1010 disintegrations/sec 248 For any system which follows first-order kinetics, we have π΅ ππ π΅ π = −ππ π what are Nt, k, and N0? A first-order process has a characteristic half-life Half-life = time required for half of any substance to react 9 e.g., πππ πππΌhas a half-life of 4.5x10 years and decays by ο‘emission e.g. πππ πππ·π has a half-life of 24000 years 249 e.g., Suppose that we start with a 1.00 g sample of and we find that 0.953 g remains after 2.00 years. What is the half-life of ππ πππΊπ? How much ππ πππΊπ will remain after 5.00 years? What is the initial activity of the sample in Bq and Ci? 250 ππ πππΊπ, Detection of radiation Geiger counter based on ionization of matter caused by radiation phosphors/ Energy changes in nuclear reactions what are the magnitudes of the energies associated with nuclear reactions? given by E = mc2 note that the mass and energy of an object are proportional because the proportionality constant (c2) is so large, even small changes in mass are accompanied by large changes in energy note that mass changes in chemical reactions are too small to detect easily; we therefore speak of conservation of mass in chemical processes 251 however, mass changes and the associated energy changes in nuclear processes are much larger than those in chemical reactions e.g., mass change accompanying the ο‘-decay of 1 mol of 238U is 50,000 x greater than the mass change for combustion of 1 mol of CH4 e.g., πππ πππΌ → πππ πππ»π + πππ―π The energy change per mol can be calculated from the Einstein relation. 252 Nuclear fission and fusion Fission: fragmentation of heavy nuclei into two mid-sized nuclei Used to: generate energy in nuclear power plants nuclear weapons Fusion: combination of lighter nuclei to give more massive nuclei Reaction which powers the sun Both fission and fusion are VERY exothermic processes 253 Nuclear power plants and most forms of nuclear weaponry depend on the fission reaction T he three most important fissionable nuclei are 235U, 233U, and 239Pu These nuclei undergo fission when struck by a slow-moving neutron: e.g., for 235U: one possible way to split is… π ππ + πππ πππΌ → πππ πππ©π π + ππ πππ²π + π ππ >200 isotopes of more than 35 elements have been found among the fission products of πππ πππΌ - most are radioactive!!!! On average: 2.4 neutrons are produced by each fission of 235U these neutrons can cause 2 fissions, and then 4 fissions, and so on The number of fissions and the energy released quickly increase, and the result is an explosion 254 In order for a fission chain reaction to occur, the sample must have a certain minimum mass otherwise, neutrons escape the sample before they can cause additional fission the amount of material large enough to maintain a chain reaction with a constant rate is known as the critical mass the critical mass of 235U is about 1 kg supercritical mass: more than a critical mass; very few neutrons escape, resulting in a nuclear explosion Nuclear reactors: how do they function? 255 Nuclear fusion Massive amounts of energy are produced when light nuclei fuse to form heavier ones fusion reactions are responsible for the energy produced by the sun, e.g. π ππ― + πππ― → πππ― + πππ π ππ― π ππ―π + πππ― → πππ―π + πππ―π → πππ―π + π πππ― π ππ―π + πππ― → πππ―π + πππ incredibly high temperatures are needed to overcome the repulsions between the nuclei and initiate fusion reactions e.g., the reaction π ππ― + πππ― → πππ―π + πππ requires a temperature of about 40,000,000 K this is the basis of thermonuclear reactions and weapons 256 Radiation and living systems Ionizing vs nonionizing radiation Nonionizing: low-energy radiation, e.g. radiofrequency EMR Ionizing: defined as radiation which can cause the ionization of water ( E at least 1216 kJ/mol) ο‘ο¬ο ο’ο¬ο ο§ radiation (and X-rays and higher-energy UV): all posess energy > 1216 kJ/mol and are considered to be ionizing in nature Ionizing radiation removes electrons from water, forming H2O+… H2O+ reacts with H2O… H2O+ + H2O ο H3O+ + OH OH is a free radical – has a single unpaired eOH can attack surrounding biomolecules to produce other radicals, which can in turn attack other compounds 257 Damage produced by radiation depends on: Activity and energy of radiation Length of exposure Location of source (inside or outside body) ο§ rays (and X rays) penetrate tissue very readily damage not limited to skin ο‘ rays stopped by skin ο’ rays penetrate to ~ 1 cm ο§ rays more dangerous than ο‘ or ο’ rays unless the ο‘source enters the body ο‘-rays transfer energy very efficiently to surrounding tissue – cause major tissue damage Fastest-growing tissues (bone marrow, blood-forming tissues, lymph nodes) show the greatest damage from radiation 258 How are radiation doses measured? Gray (gy) SI unit of absorbed dose Absorption of 1 J energy/kg tissue Rad (radiation absorbed dose) Absorption of 1x10-2 J/kg tissue Notice that 1 gy = 100 rad Not all forms of radiation harm biological tissue with the same efficiency e.g. a rad of ο‘ radiation can cause more damage than a rad of ο’ radiation introduce a multiplicative factor to reflect this: RBE, relative biological effectiveness RBE ~ 1 for ο§ο¬ο ο’ radiation RBE ~ 10 for ο‘ο radiation Product of the dose in rads x RBE = rem 259 SI unit for effective dose: sievert (sv) = RBE x gy Sv is the unit of radiation damage commonly used in medicine Radon Radon-222 is a product of the nuclear disintegration series of uranium-238 Continually generated as uranium in rocks and soils decays Half-life of 222Rn is 3.82 days; Rn is a stable noble gas, which does not react chemically… However: 222 Rn decays by alpha emission… πππ πππΉπ → πππ πππ·π + πππ―π The half-life of polonium-218 is only 3.11 min, but… πππ ππππ → πππ πππ·π + πππ―π Polonium-218 atoms are trapped in the lungs – alpha emission causes severe tissue damage May contribute to ~ 10% of all lung cancer deaths in the US 260 261
