Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Lecture 12 Radioactive IsotopesDecay EquationsHalf LivesUseful Radiotracers in OceanographySecular EquilibriumE & H Chpt 5Radioisotopes and decayDefinitions and UnitsParent – Original Radioactive AtomDaughter – The Product of DecayDecay Chain – A Series of DecaysTypes of Decay P N Atomic Wt.Alpha  He2+ -2 -2 -4Beta  e-+ 1 -1 0(n → P+ + e-)Gamma  “excess energy”Decay is independent of chemistry and T and P.Decay is only a property of the nucleus (see Chart of Nuclides)The chart of the nuclides - decayX decayX decayMathematical Formulation of Decay Decay Activity (A) = decays per time (dpm or dps)A =  N  = decay constant (t-1) N = # of atoms or concentration (atoms l-1)Units:Becquerel (Bq) = 1 dps Curie = 3.7 x 1010 Bq = Activity of 1 gram of 226RaDecay EquationsDecay is proportional to the # of atoms present (first order)= ANwhereN = the number of atoms of the radioactive substance present at time t = the first order decay constant (time-1)dNdt – NThe number of parent atoms at any time t can be calculated as follows. The decay equation can be rearranged and integrated over a time interval.where No is the number of parent atoms present at time zero. Integration leads toor 0 – oN tNdNdtNl=� �ln –oNtNl=toN N el-=tA A el-�=orDecay CurveBoth N and A decrease exponentiallyHalf LifeThe half life is defined as the time required for half of the atoms initially present to decay. After one half life:Thus =  t1/2 ln (2) =  t1/2 0.693 =  t1/2so 12o oN AN A= =1– ln 2� �� �� �1/ 20.693tl=Math note:-ln(1/2) = - (ln 1 – ln 2) = - ( 0 – ln 2) = + ln2 = 0.69301 oNotdNN=�Mean Life = Average Life of an Atom= 1 /  = 1.44 t1/2Q. Why is the mean life longer than the half life?Isotopes used in Oceanographysteady state transientU-Th series are shown on the nextpage. These tracers have a range of chemistries and half lives.Very useful for applications inoceanography.238U decay products in the oceanParent-Daughter RelationshipsRadioactive Parent (A)Stable Daughter (B)A → B e.g. 14C → 15N (stable)Production of Daughter = Decay of Parent, AtBA A A A odNN N edtll l-= =A BA2-box modelExample: 14C → 15N (stable) t1/2 = 5730 yearsRadioactive Parent (A)Radioactive Daughter (B)A → B → ABsource sinkBA A B BdNN Ndtl l= -( ),0( ) A BB At tBB ANN e el lll l- -= --( ),0( ) – A BB At tBB AAA e el lll l- -=-A B ABsolution after assuming NB = 0 at t = 02-box modelmass balance for Bsolution:Three Limiting Cases1) 1/2(A) > 1/2(B) or A < B one important case2) 1/2(A) = 1/2(B) or A = B e.g. 226Ra → 222Rn3) 1/2(A) < 1/2(B) or A > B 1600yrs 3.8 daysCase #1: long half life of parent = small decay constant of parent( ),0( ) AB AtBB AB A B AAA e Allll l l l-= =- -/( )BB B AAAAl l l= -1ABAA=SECULAR EQUILIBRIUMActivity of daughterequals activity ofparent!Are concentrations also equal???Secular equilibrium1/2 daughter = 0.8 hr1/2 parent = time (hr)Activity(log scale)daughter1/2parent! Daughter growsin with half life of the daughter!Grow in of 222Rnfrom 226RaExample:After 5 half livesactivity of daughter = 95% of activity of parentExample: Rate of grow inAssume we have a really big wind storm over the ocean so that all the inert gas 222Rn is stripped out of the surface ocean by gas exchange. The activity of the parent of 222Rn, 226Ra, is not affected by the wind. Then the wind stops and 222Rn starts to increase (grows in) due to decay.How many half lives will it take for the activity of 222Rn to equal 50% (and then 95%)of the 226Ra present?Answer: Use the following equation:( )1/ 20.693 /,01t tB AA A e-= -There is considerable exposure due to artificially produced sources!Possibly largest contributor is tobacco which Possibly largest contributor is tobacco which contains radioactive contains radioactive 210210Po which emits 5.3 MeV Po which emits 5.3 MeV  particles particles with an half life of Twith an half life of T1/21/2=138.4days.=138.4days.Was Litvinenko (a former Russian spy) killed by 210Po?? A case study of 210PoToxicity of Polonium 210Weight-for-weight, polonium's toxicity is around 106 times greater than hydrogen cyanide (50 ng for Po-210 vs 50 mg for hydrogen cyanide). The main hazard is its intense radioactivity (as an alpha emitter), which makes it very difficult to handle safely - one gram of Po will self-heat to a temperature of around 500°C. It is also chemically toxic (with poisoning effects analogous with tellurium). Even in microgram amounts, handling 210Po is extremely dangerous, requiring specialized equipment and strict handling procedures. Alpha particles emitted by polonium will damage organic tissue easily if polonium is ingested, inhaled, or absorbed (though they do not penetrate the epidermis and hence are not hazardous if the polonium is outside the body).Acute effectsThe lethal dose (LD50) for acute radiation exposure is generally about 4.5 Sv. (Sv = Sievertwhich is a unit of dose equivalent). The committed effective dose equivalent 210Po is 0.51 µSv/Bq if ingested, and 2.5 µSv/Bq if inhaled. Since 210Po has an activity of 166 TBq per gram (1 gram produces 166×1012 decays per second), a fatal 4-Sv dose can be caused by ingesting 8.8 MBq (238 microcurie), about 50 nanograms (ng), or inhaling 1.8 MBq (48 microcurie), about 10 ng. One gram of 210Po could thus in theory poison 100 million people of which 50 million would die (LD50).Body burden limitThe maximum allowable body burden for ingested polonium is only 1,100 Bq (0.03 microcurie), which is equivalent to a particle weighing only 6.8 picograms. The maximum permissible concentration for airborne soluble polonium compounds is about 10 Bq/m3 (2.7 × 10-10 µCi/cm3). The biological half-life of polonium in humans is 30 to 50 days. The target organs for polonium in humans are the spleen and liver. As the spleen (150 g) and the liver (1.3 to 3 kg) are much smaller than the rest of the body, if the polonium is concentrated in these vital organs, it is a greater threat to life than the dose which would be suffered (on average) by