SUMMER REV: Half-Life DUE DATE: JULY 2 nd

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1 NAME: DUE DATE: JULY 2 nd AP Chemistry SUMMER REV: Half-Life Why? Every radiistpe has a characteristic rate f decay measured by its half-life. Half-lives can be as shrt as a fractin f a secnd r as lng as billins f years. Many radiistpes are used by scientists t determine the age f ancient artifacts and rcks. Thse istpes with very shrt half-lives are als used in nuclear medicine since they d nt pse a lng-term radiatin hazard t patients. Since half-lives are cnstants fr radiistpes never altering r changing time they can be used t date artifacts, fssils, and rck samples. Success Criteria Calculate the amunt f time that has passed fr a sample with a knwn half-life. Calculate the half-life f a sample with a knwn decay amunt ver a set time perid. Calculate the amunt f a sample that will remain after a set time perid with a knwn half-life. Identify parent and daughter elements during a decay series. Infrmatin A half-life (t ½ ) is the time required fr ne-half f the nuclei f a radiistpe sample t decay t prducts. After each half-life, half f the existing radiactive atms (parent element) have decayed int atms f a new element (daughter element). Equatin ln [ A ] = ( ) t A 0 t ½ ln = natural lg (anti- ln = e x ) A t = amunt f radiactive istpe at time sample is taken A 0 = amunt f radiactive istpe at time = 0 (start) t = time t ½ = half-life Intrductry PhET: Radiactive Dating Game Prcedure: PhET Chemistry Radiactive Dating Game 1. Hw many prtns des Carbn-14 have? 2. Hw many neutrns des Carbn-14 have? 3. Add a Carbn-14 atm t the play area. What happens t that Carbn-14 atm? 4. Click the buttn at the bttm f the windw. 5. Click the buttn belw the Bucket Atms repeatedly, until there are n mre atms left in the bucket. 6. There are nw 100 carbn-14 atms n the screen. The half-life f carbn-14 is abut 5700 years. If yu left thse 100 carbn-14 atms t sit arund fr 5700 years, hw many wuld yu expect t decay during that time? 7. Click the Play buttn at the bttm f the windw. Watch the graph at the tp f the windw carefully. Was yur predictin frm #6 crrect? Was it clse?

2 S U M M E R R E V : H a l f - L i f e 2 8. Click and then repeat steps #4-7. Was yur predictin frm #6 crrect this time? Was it clse? 9. Is radiactive decay an exactly predictable prcess r a statistical prcess? 10. D all Carbn-14 s decay at the same time? 11. Add 50 Carbn-14s. What happens? 12. and Using 20 Carbn-14s, draw the pie graph at the fllwing time perids: 5000 Years years years Red the abve with 100 Carbn-14 atms and fill in the three bxes belw Years years years Hw d the pie graphs f 20 atms cmpare t thse f 100 atms? Generally, des the size f a radiactive sample affect half-life? Why/Why nt? Cnsider Uranium Carbn-14 s half-life was measured in thusands (5700) f years. Abut hw lng is Uranian- 238 s half-life? Hw many prtns des U-238 have? Hw many neutrns? Int what atm des Uranium-238 decay? Des the size f the sample f Uranium-238 affect its half-life? Abut that Unknwn Element. Hw wuld yu determine the half-life f this unknwn element? Write up a little plan here: Estimate the half-life f this element. secnds. 1. Click the Decay Rates tab at the tp f the screen. 2. On the right side f the screen, click the buttn next t Uraniam-238. This time we will watch the decay f this atm. Uranium-238 has a half-life f abut 4.5 billin years.

3 S U M M E R R E V : H a l f - L i f e 3 3. On the bucket f atms, there is a slider. Drag the slider all the way t the right and watch the graph at the bttm f the screen. 4. Fill in the answers in this table: After ne half-life (4.5 billin years), what percent f the riginal uranium remains? After tw half-lives (9 billin years), what percent f the riginal uranium remains? After three half-lives (13.5 billin years), what percent f the riginal uranium remains? After fur half-lives (18 billin years), what percent f the riginal uranium wuld remain? 5. Suppse yu fund a rck, and thrugh testing fund ut that it had just as much lead-206 as uranium-238 in it. Hw ld wuld yu cnclude the rck t be? Observe the decay curves ( % remaining vs time) fr Carbn-14 and Uranium-238. Sketch the decay curve fr thse istpes here: Carbn-14 Uranium-238 Mdel 1: Sample Decay Refer t the series f pictures belw t answer yur key questins. Dark pixels are radiactive atms, light pixels are stable atms. Each picture represents the passage f a half-life. 1. Wuld yu describe the pattern f radiactive decay f the nuclides t be in a specific rder r randm? Explain. 2. Des the rate f decay remain the same as yu prgress thrugh the pictures? Explain any changes yu see. 3. In Mdel 1, which atms are cnsidered t be the parent element and the daughter element?

4 Mdel 2: Parent and Daughter Atms S U M M E R R E V : H a l f - L i f e 4 4. What is the relatinship between a parent atm and a daughter atm? 5. After tw half-lives, hw many parent atms remain radiactive? Hw many daughter atms were frmed? 6. What is the mathematical relatinship between the decay f the parent atm and the frmatin f the daughter element? Mdel 3: Half-Lives f Radiactive Elements Sdium-24 has a half-life f 15 hurs. The fllwing shws the decay rate if we start with 64 grams f 24 Na. # Of Half-Lives Time (+ 15h) 0h 15h 30h 45h 60h 75h 90h 105h Mass f 24 Na 64g 32g 16g 8g 4g 2g 1g 0.5g 7. Why is the number f half-lives and time recrded as zer fr the starting amunt f 24 Na? 8. Hw much time is added t each half-life? Why? 9. Hw much des the mass f radiactive sdium-24 decrease fr each half-life? Why? 10. What happens t the 24 Na atms that decay? (Where d they g?)

5 S U M M E R R E V : H a l f - L i f e 5 Practice 11. Manganese-56 is a beta emitter with a half-life f 2.6 hurs. What is the mass f manganese-56 in a 1.0 mg sample remaining at the end f 13.0 hurs? Cmplete the table belw fr yur answer. # Of Half-Lives Time (+ 2.6h) 0h 2.6h 5.2h 7.8h 10.4h 13.0h Mass 56 Mn 1.0mg 12. The mass f a cbalt-60 sample is fund t have decreased frm g t g in a perid f 10.5 years. Frm this infrmatin, calculate the half-life f cbalt-60. (Hint: Cmplete the Mass rw first, then fill in the rest.) # Of Half-Lives 0 Time (+?) 0y Mass 60 C 0.800g 13. Carbn-14 has a half-life f 5730 years. After an rganism dies, it stps taking in radiactive carbn-14 frm the envirnment. If the carbn-14:carbn-12 rati in a piece f petrified wd is ne sixteenth (1/16) f the rati in living matter, hw ld is the rck? (Hint: Start ff with a sample size f 1 and use fractins fr yur amunts.) # Of Half-Lives 0 Time 0y Amunt f 14 C 1

6 S U M M E R R E V : H a l f - L i f e 6 MODEL 4: The Half-life Equatin Nt all f yur half-life prblems will be in whle half-lives. Fr thse that d nt, yu will need t calculate them using the natural lg (ln). [A] = Amunt f A r the amunt f yur radiactive istpe remaining 14. Can yu write the slpe intercept (y = mx + b) equatin fr the half-life graph n the LEFT? Explain yur answer. 15. Which f the fllwing is the prper slpe intercept equatin fr the equatin n the RIGHT? Explain yur answer. a. ln[a] = kt + ln[a 0 ] b. ln[a] = kt - ln[a 0 ] c. ln[a] = -kt + ln[a 0 ] The equatin in #2 can be slved we can shw yu the math if yu want fr half-life (t ½ ) and rewritten as: ln [ A ] = ( ) t A 0 t ½ Practice Prblems 16. The half-life f 161 Tb is 6.9 days. Hw many grams f an riginal 5.70-g sample will remain after 27 days? 17. If yu start with a 325-g sample f 188 Au, hw lng will it take t decay t 247 g? (t 1/2 = 8.8 min)