Presentation on theme: "Lecture 6 Radioactive Isotopes"— Presentation transcript:
1 Lecture 6 Radioactive Isotopes Definitions and types of decayDerivation of decay equationsHalf lives and mean livesSecular EquilibriumUseful radiotracers in oceanographyE & H Chpt 5
2 The chart of the nuclides - decay Q. 230Th90 How many protons / neutrons?
3 Full Chart of the Nuclides Valley of Stability1:1 lineFor 230Th N/P = 1.55
4 Radioisotopes and decay Definitions and UnitsParent – Original radioactive atomDaughter – The product of decayDecay Chain – A series of sequential decaysfrom one initial parentDecay is independent of chemistry and Temp and Pressure.Decay is only a property of the nucleus (see Chart of Nuclides)Types of DecayDP DN DAtomic Wt.Alpha a HeBeta b e(n → P+ + e-)Gamma g “packets of excess energy”Measurements
5 The chart of the nuclides – decay pathways b decayXXa decay
6 Mathematical Formulation of Decay Decay Activity (A) = decays per time(e.g. minutes (dpm) or second (dps))A = l N l = decay constant (t-1)N = # of atoms or concentration (atoms l-1)Remember 1 mol = 6.02 x 1023 atomsUnits:Becquerel (Bq) = 1 dps (the official SI unit)Curie (Ci) = 3.7 x 1010 Bq = Activity of 1 gram of 226RaNamed after Pierre CurieSee this link for the history:
7 Decay Equations (essential math lessons) Decay is proportional to the # of atoms present (first order)dN/dt = - N = ANwhereN = the number of atoms of the radioactive substance present at time t = the first order decay constant (time-1)The 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 tooror
9 Half LifeThe half life is defined as the time required for half of theatoms initially present to decay.After one half life:From the decay equation= t1/2ln (2) = t1/2= t1/2soMath note:-ln(1/2) = - (ln 1 – ln 2)= - ( 0 – ln 2)= + ln2 = 0.693
10 Mean Life = Average Life of an Atom = 1 / l = (1/0.693) t1/2t = 1.44 t1/2Q. Why is the mean life longer than the half life?
11 Isotopes used in Oceanography steady state transient U-Th series are shown on the nextpage. These tracers have a rangeof chemistries and half lives.Very useful for applications inoceanography.
12 Two forms of Helium 3He2 from beta decay of 3H1 (called tritium) and primordial from the mantle4He2 the product of alpha decay frommany elementsHow would you expect their distributionsto vary in the ocean?
14 Q. Why is the inside of the earth hot? Q. What is the age of the earth? 5000 years or 5.5 x 109 years
15 238U decay products in the ocean U – conservativeTh – particle reactiveRa – intermediate (like Ca)Rn = conservativePb – particle reactiveQ. What controls the concentration of 238U in SW?
16 Radon is a health hazzard! Radon source strength from rocksWhy are some zones high (red)?
17 Parent-Daughter Relationships Radioactive Parent (A)Stable Daughter (B)A → B e.g. 14C → 15N (stable)Production of Daughter = Decay of Parent2-box modell AABExample: 14C → 15N (stable)t1/2 = 5730 years
18 Radioactive Parent (A) Radioactive Daughter (B) A → B →2-box modellAlBAl ABl Bsourcesinkmass balance for Bsolution:solution after assuming NB = 0 at t = 0
19 Three Limiting Cases1) t1/2(A) > t1/2(B) or lA < lB one important example:2) t1/2(A) = t1/2(B) or lA = lB e.g. 226Ra → 222Rn3) t1/2(A) < t1/2(B) or lA > lB yrs daysCase #1: long half life of parent = small decay constant of parentSECULAR EQUILIBRIUMActivity of daughterequals activity ofparent!Are concentrations also equal???
20 Q. Are concentrations also equal??? Example: 226Ra and 222Rn
21 Secular equilibrium (hypothetical) t1/2 daughter = 0.8 hrt1/2 parent = Total Activity(parent+daughter)Parentdoesn’t changeActivity of parentand daughter atsecular equilibriumdaughterActivity(log scale)! Daughter growsin with half life ofthe daughter!t1/2time (hr)
22 Example: Grow in of 222Rn from 226Ra After 5 half lives Another way to plotAfter 5 half livesactivity of daughter =95% of activity of parent
23 Example: Rate of grow in Assume we have a really big wind storm over the ocean so that all the inert gas222Rn is stripped out of the surface ocean by gas exchange. The activity of the parentof 222Rn, 226Ra, is not affected by the wind.Then the wind stops and 222Rn starts to increase (grows in) due to decay.Q. 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 to calculate the activity A at time t
24 There is considerable exposure due to artificially produced sources! Possibly largest contributor is tobacco which contains radioactive 210Po which emits 5.3 MeV a particles with an half life of T1/2=138.4days.
25 Was Litvinenko (a former Russian spy) killed by 210Po 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 thanhydrogen 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 verydifficult 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, requiringspecialized equipment and strict handling procedures. Alpha particles emitted bypolonium 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 poloniumis outside the body). Acute effects The 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 210Pois 0.51 µSv/Bq if ingested, and 2.5 µSv/Bq if inhaled. Since 210Po has an activity of166 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 millionwould die (LD50).
26 Body burden limit The 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 isabout 10 Bq/m3 (2.7 × µCi/cm3). The biological half-life of polonium inhumans is 30 to 50 days. The target organs for polonium in humans are the spleenand liver. As the spleen (150 g) and the liver (1.3 to 3 kg) are much smaller than therest of the body, if the polonium is concentrated in these vital organs, it is a greaterthreat to life than the dose which would be suffered (on average) by the whole bodyif it were spread evenly throughout the body, in the same way as cesium or tritium. Notably, the murder of Alexander Litvinenko in 2006 was announced as due to210Po poisoning. Generally, 210Po is most lethal when it is ingested. Litvinenko wasprobably the first person ever to die of the acute α-radiation effects of 210Po , althoughIrene Joliot-Curie was actually the first person ever to die from the radiation effects ofpolonium (due to a single intake) in the late 1950s. It is reasonable to assume thatmany people have died as a result of lung cancer caused by the alpha emission ofpolonium present in their lungs, either as a radon daughter or from tobacco smoke.