HALF-LIFE PROBLEMS

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HALF-LIFE PROBLEMSNameBlockI. An isotope of cesium (cesium-137) lias a half-life of 30 years. If 1.0 g of cesium-137disintegrates over a period of 90 years, how many g of cesium-137 would remain? ?P . * '2'/X" 42. Actinium-226 has a half-life of 29 hours. If 100 mg of actinium-226 disintegrates over aperiod of 58 hours, how many mg of actinium-226 will remain?isr' "I 3, Sodium-25 was to be used in an experiment, but it took 3.0 minutes to get the sodiumfrom the reactor to the laboratory. If 5.0 mg of sodium-25 was removed from the reactor,how many mg of sodium-25 were placed in the reaction vessel 3 0 minutes later if the halflife of sodium-25 is 60 seconds?,ma?.4. The half-life of isotope X is 2.0 years. How many years would it take for a 4.0 mg sampleof X to decay and have only 0.50 mg of it remain? /1 n3K 2 0 H ' ' VVf5. Selenium-83 has a half-life of 25.0 minutes. How many minutes would it take for a 10.0mg sample to decay and have only 1.25 mg of it remain?5 x. 2 i r 7 C : k:L6. The half-life of Po-218 is three minutes. How much of a 2.0 gram sample remains after '' 15 minutes?/Suppose you wanted to buy some of this isotope, and it required half ah hourfor it reach yoti. How much should you order if you need to use 0.10 gram of thismaterial?&f: UPi ,;5"

HALF-LIFE WORKSHEETNameUse Reference Table on side to assist you in answering the following questions.Yt lifes:Equations:As-81 33 secondsAu-198 2.69 daysC-14 5730 years1 How long does it take a lOO.OOg sampJe of As-81 to decay to 6.25g?J2. How long does it take a 180g sample of Au-198 to decay to 1/8 its original mass? . sJ /3. What percent of a sample of As-81 remains un-decayed after 43.2 seconds?2 //i4. What is the half-life of a radioactive isotope if a 500.0g sample decays to 62.5g in 24.3 hours?5. How old is a bone if it presently contains 0.3125g of C-14, but it was estimated to have originallycontained SO.QOOg of C-14?

NameHALF-LIFE CALCULATIONSHalf-life is th time required for one-half of a radioactive nuclide to decay (change toanother element), it Is possible to'calculate the amount of a radioactive element that willbe left If we know its half-life. ''fVExample: The half-fife of Po-214 is 0.001 second. How muchof a 10 g sample will be left after 0.003 seconds?Answer: Calculate the number of haif-lfves;0.003 seconds x 1 half-ilfe 3 half-iives0,001 secondAfter 0 half-lives, 10 g are left.After 1 half-fife, 5 gare left.After 2 half-lives, 2.5 g are left.After 3 half-lives, 1.25 g are left.Solve the following problems.The half-life of radon-222 Is 3.8 days, How much of a 100 g sample is left after1.15.2 days? I( r ,' s,-/A/rf' oi2.\ f \Carbon-14 has a half-ilfe of 5,730 years. If a sample contains 70 mg originally, how *much is left after 17,190 years? "2.3 h 1 -h /7.5" (f-? V3,uHow much of a 500 g sample of potasslum-42 is left after 62 hours? The half-life ofK 42 is 12,4 hours? 1 i '51 2 vf 4.1 The half-life of cobalt-60 Is 5,26 years. If 50 g are left after 15.8 years, how manygrams were In the original sample? "43KI *S o5. The half-life of 1-131 is 8.07 days. ifc2g g are left after 40.35 days, how many gramswere in the original sample? ;'1?6.}—If 100 g of Au-198 decays to 6,25 g in 10.8 days, what is the half-life of Au-198?Physical Science IF8767100 Instructional Fair, inc.

Half-life WorksheetNameHalf-life Worksheet1. What is radioactivity?* . What is nuclear radiation?.'Vhat is half-life?.-we start with 400 atoms of a radioactive substance, how many would remain after one half-life?/ after two half-lives? I flu after three half-lives? after four half-lives? 5. If we start with 48 atoms of a radioactive substance, how many would remain after one half-life?after four half-lives?after three half-lives?After two half-lives?6. If we start with 16 grams of a radioactive substance, how much will remain after three half-lives?-7/ 6 - V V —) J-7. If we start with 120 atoms of a radioactive substance, how many will remain after three half-lives?8. Which type of radiation (beta particles, gamma rays, or alpha particles) can be blocked by.a) apiece of paper,Radioactive Decay of C rbon-14c) a piece of lead100%d) a large block of leadUse the following graph to answer questions9-12,.t'75%.Amountofcarbon-14 50%25% 412.5%575010,740 16,1Time {years)9. How long is a half-life forcarbon-14? * w10. If only 25% of the carbon-14remains, how old \i the material containing the carbon-14? /c 11. If a sample originally had120 atoms of carbon-14, how many atoms will remain after 16,110years? 12. If a sample known to be about 10,740 years old has 400 carbon-14 atoms, how many atoms were in thesample when the organism died? J;8 uVL '* fH ocUse the following chart to answer questions 13-16.Approximate half-lifeRadioactive SubstanceRadon'-2224 days8 daysIodine-131Radium"2261600 yearsCarbon-145 J30 yearsPIutcmimn-23924,120 years4,470,000,000Ui:anium-23813. If we start with 8000 atoms of radium-226, how much would remain after 3,200years? 2—%14. If we start with 20 atoms of piutonium-239, how many would remain after 48,240 years? v* If we start with 60 atoms of uranium-238, how many remain after 4,470,000,000 years? /,/ 'Va* If we start with 24 atoms of iodine-131, how many remain after 32 days?k ! y kj -) / I ") 'i

ChetfAeinq: Form WS12.6.1ANameNUCLEAR CHEMISTRYDatePeriodWhen radioactive materials decay they release high speed particlesthat bang into other unstable radioactive atoms, hastening theirdecay. As the process proceeds, the amount of radioactive materialdecreases. This causes the number of high speed emissions todecrease. The fewer emissions there are, the slower the decayprocess becomes. As a result, large samples of radioactive materialdecay at a faster rate than small samples. In fact, as the sample sizedecreases, the rate of decay slows in such a way that the amount oftime it takes for half the sample to decay is constant regardless of thesample size. In other words, it takes 500 g of uranium the sameamount of time to decay into 250 g of uranium as it does for 2 g ofuranium to decay into 1 g of uranium. The amount of time it takesfor a radioactive sample to decay to half its original mass is calledthe half-life.The easiest way to solve half life problems is to set up a table.Answer the questions below using data fromTable N, the table of Selected Radioisotopes.Sample ProblemHow much '"K will be left in a 320 g sample after 62 h?Step 1: Look up the half life In Table N, the table of Selected Radioisotopes12.4 hStep 2: Set up a table showing the mass, time elapsed, the fraction1. How long will it take for 30 g of todecay to 7.5 g?remaining, and number of half [Ives starting with the initial conditionsand ending when the full time has elapsed. For each half life elapsed,cut the mass in half, increase the time by an amount equaf to the halflife, cut the fraction in half, and add one to the number of half lives.MassTimeFractionHalf %i«(S7' ' /' 0 x. X? c2. Howmany grams ofI6N will be left from a16 g sample after 21.6 s?-7 Sc rFollowing this procedure It is possible to determine the final mass, the timeelapsed, the fraction of the original sample, orthe number of half lives elapsed.Continue cSf6's)

Working with Half-LifeC/iyMhistogf: Form WS12.6.1APage 2NUCLEAR CHEMISTRY3. How many half lives will it take for 50 g of "Tc to decay to 6.25 g?4. What fraction of a sample of 32P will be left after 42,9 d? 5. How long will it take for a 28 g sample of Ra to decay to 3.5 g?/v:,-",/ //5 Cr/ -6. How long will it take for 50% of a sample of l31I to decay?/ ;5 r/7. After 9.8 x 10!0 y, how many grams will be left from a 256 g sample of Th?//'-''/, V,/'-/'Y /')\"I ';/? L i '; '8. How long will it take for 500 g of MSr to decay to 125 g? r — 1 J A // 9. What fraction of a sample of 3H will be leftafter 36,78 y?i j Evan P. Silberstein, 2003x/X

Radioactive Decay and Half-LifePage 4 of 5Table NSelected 0SAu2.69 drgolcI-198UQ5730 yrcarbon-14175 msP*calciiiin-375.26 yp-cobttlt-60isrcs30.23 yrcevsium-137u'aq-5-3 Co Fe8.51 minp 220Pj.27.5 saah12.26 yhydrogen-3fyanchuTi-2208.07 drrsrK1.23 sP potassiinn-3742K12.4 lirpatas.sii i ra-42wKr10.76 yrr131j16n7.2 s10Ne17.2 s32.p14.3 diodine-131kiyptv n-S5nitrogen-16neou-19rphosplioriis-32p Lutoiiiu u 1-239aaopn2.44 x I0-4 ya23RRfl1600 ya.222rtt3.82 aaradon-22290 Sr28.1 yrstrontium-OO"Tc2.13 x 105yrtecIinetliim-99joarh1.4 x 1010 yatliDrittm-232233U1.62 x 105yaurummu-233235u7.1 x 108yatu'aiihim-23523SU4.51 x 10 yauranio rn-23Sms - rnillisecomlx; s seconds,' rriin minutes;h hours; cl days; y ry/stevens03.h1ml11/8/2010

and ending when the full time has elapsed. For each half life elapsed, cut the mass in half, increase the time by an amount equaf to the half life, cut the fraction in half, and add one to the number of half lives. Mass Time Fraction Half lives 320 0 i 0 160 12.4 Vz 1 80 24.8 % 2 40 37.2 v, 3 20 49.6 X 4 10 62 %i « Answer the questions below .

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