DAY 28. Summary of Primary Topics Covered. Damage to Living Things

Transcription

1 DY 28 Summary of Primary Topics Covered Damage o Living Things The,, paricles emied in radioacive decay carry energy and ac like lile bulles ha can do damage o he cells of living hings. Because hey are mos massive and carry he mos charge, paricles do he mos damage if hey hi living issue. On he oher hand, because hey are so large hey are leas peneraing, and can be sopped by heavy cardboard in some cases. The relaive danger posed by he differen ypes of radiaion is quanified by is Relaive Biological Effeciveness (RBE). The higher he RBE, he more damaging i is. hp:// Damage RBE facor Peneraion Leas damaging. o damage o cells. 0 Mos peneraing. Canno be shielded agains. Can pass hrough he whole Earh unaffeced. Dangerous o living cells. o mass, no charge pure energy. 1.0 Highly peneraing. Canno be sopped by a ypical meal plae. Requires heavy lead shielding o block. More dangerous o living cells. paricles have some mass (very lile, bu some) and hey have charge. These hings make paricles more dangerous han - rays Peneraing. May pass hrough meal foil bu ypically will be sopped by a meal shee or plae. Mos damaging o cells. Per joule of energy deposied in a given amoun of issue, hese are 10x - 20x more damaging han - rays Leas peneraing can be sopped by hin foil, heavy paper, or a few inches of air.

2 Measuring Radiaion Exposure When a person is exposed o a source of radiaion ha person receives energy ha has been given off by he decaying nuclei as discussed las class. common means of measuring exposure o radiaion is he radiaion absorbed dose or RD. RD is 0.01 kg of energy from he source per kilogram of issue. 1 RD = 0.01 J/kg The RD uni does no disinguish beween energy from,, or sources. s we jus learned, differen ypes of radiaion do differing amoun of damage, measured by he Relaive Biological Effeciveness (RBE). measuremen of exposure ha incorporaes he RBE facor is he Radiaion Equivalen in Mammals or REM. 1 REM = 1 RD x RBE X-rays can also be added o he RBE lis (RBE X-rays = 1.0) because exposure o energy from X-rays has similar effecs on living issue as exposure o energy from radioacive sources (energy eners a cell; elecrons are sripped from aoms in cells, creaing ions and oherwise damaging he cell), and X-ray exposure can also be From hp://hyperphysics.phy-asr.gsu.edu/hbase/nucene/radexp.hml#c2: measured in REMS. Exposure o Radiaion Radiaion is par of he environmen. Radiaion comes from boh ouer space and from radioisoopes in he Earh. The average merican receives a couple of millirem of exposure per week due o naural sources. I

3 is unavoidable. However, increased exposure can occur due o he use of radiaion in medicine or he workplace. Effecs of Low Dose Radiaion Exposure (Risk Levels and Risk Comparisons) Relaively low-level exposure like wha is lised here does no cause immediaely noiceable effecs. Like smoking cigarees, exposure o low levels of radiaion exposure has a cumulaive effec and is linked o cancer and oher healh problems. However, small, frequen doses of radiaion creae very limied risks. ccording he Georgia Sae Universiy s HyperPhysics web sie (hp://hyperphysics.phy-asr.gsu.edu/hbase/hph.hml), he risk posed by being exposed o one millirem of radiaion dose is a 1 in 8 million risk of dying of cancer or a loss in life expecancy (LLE) of abou 1.2 minues. This is a risk equivalen o crossing he sree hree imes (where you risk geing hi by a car), hree puffs on a cigaree (where you risk obacco-relaed healh effecs), or 10 exra Calories for an overweigh person (where you risk obesiy-relaed healh effecs). This all assumes ha large dose effecs exrapolae linearly hrough small doses o zero dose and ha assumpion is no known for cerain. Wha is Loss of Life Expecancy? LLE is a way of quanifying levels of risk. If exposure o Z amoun of radiaion has an LLE of 1 monh, for example, ha does no mean ha if you are exposed o Z hen you will die one monh earlier han you would have oherwise. I means ha people exposed o Z will, on average, die one monh earlier. For example, suppose ha he hip new exreme spor is ramping super-charged ll Terrain Vehicles over pis filled wih spikes and landing in shark infesed waers while wearing a bloody piece of mea ied o one s back. This spor is performed by healhy 20-year-olds who oherwise could expec o live o be 80. Suppose ha of every 10 people who ry an exreme ramp, 1 dies, bu he oher 9 emerge basically unhur. So, if 100 people ry exreme ramping, we expec 10 o die. Each dead person represens a loss of life of 60 years by dying a 20 insead of 80. So he oal loss of life is 10 x 60 = 600 years among a oal of 100 people rying an exreme ramp. Thus he LLE for any person doing an exreme ramp is 600/100 = 6 years.

4 oe ha an LLE of 6 years doesn mean ha if you ry an exreme ramp you will live o be 74 insead of 80. Raher, eiher you die a 20, or you live hrough i and vow never o be ha supid again. Bu he risk measuremen is an LLE of 6 years. Some risks, such as radiaion exposure or cigaree smoking, may no be as eiher/or as his. Some people may be exposed o radiaion and sill live a long life. Some people may smoke a pack a day and sill live a long life. Bu on average boh radiaion exposure and cigaree smoking will cause an earlier deah someimes much earlier and LLE is a way of measuring ha risk. Oher risks (such as moor vehicle accidens) are very much eiher/or proposiions. LLE is a way of comparing he risks of all differen kinds of aciviies. When discussing radiaion risks we also need o keep in mind ha mericans end o be very worried abou some kinds of risk, bu no abou ohers. One example of his would be eens and risk. People worry abou eens and crime, and end o associae ciies wih being dangerous places. However, if you look a Kenucky counies in erms of how dangerous hey are for eens, you find ha he more urban counies are among he safes counies for eens in Kenucky, whereas he mos dangerous counies end o be rural. Why? The reasons are complex, bu a Teen Violen Deah Rae (per 100,000 eens aged 15-19) Includes homicide, suicide, accidens, ec. Teen Violen Deah Rae & Circles mark Kenucky s larges mero areas (Louisville, Lexingon,. Ky, Owensboro, Bowling Green) Daa from he Kenucky Sae Daa cener Kids Coun pages: hp://ksdc.louisville.edu/1kidscoun.hm quick explanaion is ha eens are far more likely o be killed by moor vehicles han by criminals, and rural areas require a lo more driving a high speed. The ciy kid may pass a corner frequened by drug dealers when he walks o school, bu he

5 counry kid has o pass a dangerous curve when he s driving o school. noher example would be smoking and marriage. We all hear ha we shouldn smoke because of healh reasons, and ha is rue. Smoking has a very high LLE. Marriage vs. Smoking ccording o Marial Saus and Moraliy: The Role of Healh (Demography, ugus 1996) by Lee. Lillard, Consanijn W.. Panis, he healh benefis of being married have been known since a leas he 1850 s. From Before I's Too Lae: Scienis's Case For uclear Energy, Bernard L. Cohen 1983: LLE of Smoking (1 pack/day): 4.4 years LLE of Being Single: 5.5 years However, wha has an even higher LLE is being single, especially for men. man who is boh single and a smoker could well expec more healh benefis from geing and saying married han he would from quiing smoking permanenly bu saying single. Why? gain, he reasons are complex, bu a quick explanaion is ha married people are, on average, less likely o do supid hings ha ge hem killed, and hey have someone else waching ou for hem and heir overall healh, alking hem ino going o a docor when hey need o, and so forh. mericans spend much ime and effor debaing he healh effecs of smoking, and how o ge people no o smoke, bu less ime and effor on he healh effecs of marriage. The boom line is ha risks due o low-level radiaion doses do exis, bu need o be kep in perspecive. Effecs of High Dose Radiaion Exposure In conras o low-level radiaion doses, large doses of radiaion (over 25,000 millirem) do creae immediae effecs. The effecs in he able below are no long-erm effecs, hey show up righ afer a person has received an all-a-once dose of he amoun of radiaion shown: cue Radiaion Exposure -- Effecs of Large, Whole-Body Radiaion Doses DOSE (REM) DOSE (millirem) EFFECT ,000 o observable effec Sligh blood changes Significan reducion in blood plaeles and whie blood cells (emporary) Severe blood damage, nausea, hair loss, hemorrhage, deah in many cases >600 > 600,000 Deah in less han wo monhs for over 80% hp://hyperphysics.phy-asr.gsu.edu/hbase/nucene/radexp.hml#cc1

6 noher uni ofen used insead of a REM is a Siever, which is equal o 100 rems. Thus any dose above 6 Sievers is generally faal. civiy, Power, Time, Disance, Shielding In summary, he danger from radioacive sources depends on a number of facors. Firs, he amoun of unsable nuclei presen in a source and he half-life of hose nuclei deermine he aciviy level of he source (usually measured in Curies Ci). The energy released in each decay (which involved he mass defec and E=mc 2 ) deermines he rae a which he source pus ou energy. For a source of a cerain aciviy level, increasing disance from he source means ha he paricle flux rae he inensiy of radiaion is decreased. Shielding also decreases inensiy of radiaion. nd limiing he ime which one is exposed o a source decreases he amoun of millirems absorbed. Decay Series Ofen he daugher nucleus formed by he decay of an unsable nucleus is iself unsable. This nucleus will in urn decay and if is daugher is unsable he daugher will decay and so on unil a sable nucleus resuls. There are four naurally occurring decay series ha are responsible for mos naurally occurring radioaciviy. Manmade radioisoopes can also sar a decay series.

7 Shown here are he four naural radioacive decay series from hp://hyperphysics.phy-asr.gsu.edu/hbase/nuclear/radser.hml Example Problem #1: 170 lb man is exposed o an source. He receives energy a a rae of 10 J/min. If he man is exposed o he source for 10 seconds, deermine approximaely how much exposure he received. Will his produce immediae healh effecs? Soluion: Calculae power: P = 10 J/min = J/s Calculae energy received: P E E = 1.67 J E J/s 10 s Calculae mass of man: 1kg 170 lb kg lb The absorbed dose is he energy per kilogram:

8 1.67 J = J/kg kg 1RD J/kg RD.01 J/kg The exposure is found using REM = RD x RBE ccording o he able RBE for is so REM = x 10 = REM (lower esimae) REM = x 20 = REM (upper esimae) So he man received beween 22 and 43 REM. Tha s no good. I will probably do damage o his blood. Example Problem #2: person who has mass of 100 kg sicks his hand ino a box, no knowing ha i conains a sample of Cobal-60. There are 500 mg of he Co-60 in he box. The person s hand is 20 cm from he Co- 60. Someone yells a warning, and he person pulls he hand ou afer i has been in he box for 2 seconds. The person s hand measures roughly 20 cm long by 9 cm wide (including fingers). Esimae he exposure his person received (in millirem). Soluion: Jus go a i one sep a a ime. Find ou he power oupu of 500 mg of Co-60, figure he inensiy a he person s hand, and he amoun of energy absorbed. Firs I go o he periodic able and look up Co-60. The able says i is a - decay, and has a half-life of 5.27 years. I ll work ou he decay and find ou wha he daugher is: Co β 0 ν i ow I look up he mass of Co-60 and i-60 and an elecron ( - ):

9 Co-60 mass is u, according o able. Bu his includes he 27 elecrons in a Cobal aom. The nucleus iself is u 27( u) = u Toal mass before decay is u i-60 mass is u according o able. Bu his includes he 28 elecrons in a ickel aom. The nucleus iself is u - 28( u) = u elecron mass is u neurino mass is 0 Toal mass afer decay is u u u ow find he mass defec he amoun of mass convered o energy in he decay. I subrac o find how much mass disappeared: Mass defec = u u = u los in he decay. Conver ha o kg: x kg u = x kg 1 u OK, now le s find he energy released in one decay: E = m c 2 = x kg (3 x 10 8 m/s) 2 E = x J ow o find he power oupu of 500 mg of Co-60 I need o find ou he aciviy rae (decays per second). R =.693(/T 1/2 ) OK, le s find he (number of Co-60 nuclei): There are 500 mg of Co-60. Tha s.5 grams of Co-60 or kg of Co-60. Le me ge ha ino u unis: 1 u kg = x u x kg ow I know he mass of 1 Co-60 nucleus from he informaion I looked up earlier:

10 1 Co-60 nucleus x u = x Co-60 nuclei u So = x ow I ll find he T 1/2 -- have o look ha up T 1/2 = 5.27 years 5.27 yr x (3.156 x 10 7 sec/1 yr) = x 10 8 sec So T 1/2 = x 10 8 sec R =.693( x nuclei/ x 10 8 sec) = x nuclei/sec So Co-60 is decaying a a rae of x nuclei/sec. Each decay releases x J of energy. So he power oupu is P = ( x J of energy released each ime a nucleus decays) X ( x nuclei decaying each second) P = ( x J/nucleus)( x nuclei/sec) P = J/sec = W The inensiy a a disance of 20 cm from he Co-60 will be I = P/ = 4 r 2 = 4(3.1416)(20 cm) 2 = cm 2 I = W / cm 2 I = W/cm 2 The power received by he hand will be he W/cm 2 imes he area of he hand: P on hand = W/cm 2 (20 cm x 9 cm) = W The hand was in he box for 2 seconds, so E = W (2 sec) E = J/s (2 s) = J

11 Tha s J in a 100 kg person, so he radiaion dose is J/100 kg = J/kg 1 RD J/kg = RD 0.01 J/kg The RBE for b is 1.7 so he exposure is REM = RBE x RD REM = 1.7 x = REM Or 1160 millirem. Tha s more han hree imes he average annual dose received by a hospial radiologis. Example Problem #3: Radon-222 ( Radon Gas ) does no decay ino a sable nucleus. Raher, he decay of Rn-222 is followed by a series of decays. Deermine all he decays of he daughers of Rn-222 and deermine wha sable daugher finally resuls from his series of decays. Soluion: I used he Periodic Table wih Isoope informaion from he class web page o look up Rn-222 and is daughers. Tha old me wha ype of decay each daugher underwen. I worked ou each reacion equaion as I wen along. s seen in from he work on he nex page, he sable produc is Lead-206.

12 Here is a sample of how I did his. Taking he case of Lead-214 (3 rd line), I wen o he Period Table wih Isoope Informaion and clicked on Lead (Pb). Tha ook me o a page full of informaion on Lead isoopes.

13 I scrolled down unil I found Pb- 214, hen I clicked on ha. ow I have los of informaion on Pb-214. nd I see ha Pb-214 undergoes - decay 100% of he ime. Once I know how i decays I work ou he reacion equaion. I did his for each decay.

14 Example Problem #4 (PHY 232 only): In a decay series, paren nucleus decays ino daugher nucleus B, which decays ino granddaugher nucleus C. has half-life T ½ and decay consan, B has half-life T ½B and decay consan B, and C is sable. We sar wih 0 nuclei (all ). The number of s as a funcion of ime is simply he usual exponenial 0 e because whaever happens afer he s decay has no effec on hem. Bu he number of B s and C s is much more complex. The number of B s is given by B 0 e B e B Do he following: a. Come up wih an equaion for he rae of change of B s. b. Show ha he above equaion solves he rae equaion. c. Derive an equaion for he number of C s as a funcion of ime. Soluion: I ll do par (a) firs: The decay rae of s is R = -. Every ime an decays i produces a B, so he rae B s are produced is. However, B s also decay a rae - B B. So he rae of change of B s should be R B = rae of producion minus rae of decay R B = - B B d B /d = - B B ha s my answer for par (a) ow for par (b): Firs I ll wrie down my equaion for and B Then I ll find d B /d

15 ow I ll sub hose ino my rae equaion d B /d = - B B and see if i works ou

16 Tha akes car of par (b). Par c should be prey easy -- he number of C s is jus 0 minus he s and B s. B C B C B C B B e e e e e e Tha akes car of par (c). Example Problem #5 (PHY 232 only): In he above problem, make a graph of he number of s, B s, and C s vs. ime if 0 = 100 Trillion nuclei and a. T ½ = 10 years and T ½B = 2 years. b. T ½ = 2 years and T ½B = 10 years. c. Commen on your resuls. Soluion: = 0.693/T ½ =.693/10 years = /years. B = 0.693/T ½B =.693/2 years = /years.

17 0 = 100 rillion I ll plug in poins and plo he equaions for, B, and C : nd now here s par (b), following he same mehod: My commens -- i appears ha he C s numbers were he same in boh cases -- or prey darn close. In he second case you go a lo more B s.