TEACHER NOTES HIGH SCHOOL SCIENCE NSPIRED

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1 Radioacive Daing Science Objecives Sudens will discover ha radioacive isoopes decay exponenially. Sudens will discover ha each radioacive isoope has a specific half-life. Sudens will develop mahemaical model for he radioacive decay of C-14 and U-238. Sudens will esimae he age of various objecs using radioacive daing wih common radioacive isoopes, such as C-14 in daing living organisms and U-238 in daing geological formaions and fossils. Vocabulary radioacive decay radioacive isoope half-life radioacive daing exponenial Abou he Lesson Sudens will use he simulaion o measure he percen of remaining isoopes for Carbon-14 and Uranium-238 during radioacive decay process. Sudens will develop mahemaical models for he radioacive decay and use hese o esimae he age of organic and inorganic maerials. TI-Nspire Navigaor Send ou he Radioacive Daing Game.ns file. Monior suden progress using Class Capure. Use Quick Poll o assess sudens undersanding. Use Live Presener for sudens o share heir work and presen resuls of exploraions. Aciviy Maerials Compaible TI Technologies: TI-Nspire CX Handhelds, TI-Nspire Apps for ipad, TI-Nspire Sofware Tech Tips: This aciviy includes screen Nspire CX handheld. I is also appropriae for use wih he TI-Nspire family of producs including TI-Nspire sofware and TI-Nspire App. Sligh variaions o hese direcions may be required if using oher echnologies besides he handheld. Wach for addiional Tech Tips hroughou he aciviy for he specific echnology you are using. Access free uorials a hp://educaion.i.com/calcul capures aken from he TI- aors/pd/us/online- Learning/Tuorials Lesson Files: Suden Aciviy Radioacive_Daing_Suden _HS.doc Radioacive_Daing_Suden _HS.pdf Radioacive Daing Game.ns 2013 Texas Insrumens Incorporaed 1 educaion.i.com

2 Radioacive Daing Discussion Poins and Possible Answers Par 1. Exploring Radioacive Decay Move o page In his par of he aciviy sudens will observe changes in he remaining percen of an isoope in wo radioacive decay processes: C N and U Pb. Based on simulaed experimen, sudens will measure percen of remaining elemen afer given periods of ime. Once on he screen, suden can sar, pause, and rese he simulaion. The percen of elemen remaining will be shown on a graph as a funcion of ime. Sudens can also coun he number of remaining isoopes on he op of he page. Q1. Wha is a half-life of a radioacive elemen? Answer: he ime i akes for he elemen o decay o 50% of is iniial amoun Q2. Wha is he half-life of Carbon-14? Answer: he half-life is abou 5700 years 2. Sudens should selec he play buon a he boom of he page and observe he changes in he percen of carbon remaining in he sample. They could use pause buon afer each half-life o ge beer esimaion by couning he number of remaining carbon isoopes shown on he op of he page. They should repea experimen a leas 3 imes and record percen of carbon remaining in he able below. Percen of Carbon-14 Remaining Half-lives Trial 1 Trial 2 Trial 3 Average 1 s nd rd Texas Insrumens Incorporaed 2 educaion.i.com

3 Radioacive Daing Q3. Wha percen of Carbon-14 is remaining afer 1 half-life? Two half-lives? Three half-lives? Answer: abou 50% of iniial amoun; abou 25% of iniial amoun; abou 12.5% of iniial amoun (sudens answers will vary slighly) TI-Nspire Navigaor Opporuniies Use Quick Poll o collec suden responses o quesions 3-5. Discuss he reasons for sligh differences in suden answers, such as probabilisic naure of he half-life. The half-life is he ime when he expeced value of he number of isoopes ha have decayed is equal o half he original number. Q4. Wha do you hink he similariies and differences will be in he decay of Uranium-238? Answer: The half-life of Uranium-238 will be differen. The decay will follow he same paern over ime, e.g abou half of elemen remaining afer each half-life. Q5. Wha is he half-life of Uranium-238? Answer: abou 4.5 billion years 3. In order o explore decay of Uranium-238 suden should selec in he boom lef corner of he page o swich he elemen. 4. Sudens should selec he play buon a he boom of he page and observe he changes in he percen of uranium remaining in he sample. They could use he pause buon afer each half-life o ge a beer esimaion by couning he number of remaining uranium isoopes shown on he op of he page. They should repea experimen a leas 3 imes and record percen of uranium remaining in he able below Texas Insrumens Incorporaed 3 educaion.i.com

4 Radioacive Daing Percen of Uranium-238 Remaining Half-lives Trial 1 Trial 2 Trial 3 Average 1 s nd rd Q6. Wha percen of Uranium-238 is remaining afer 1 half-life? Two half-lives? Three half-lives? Answer: abou 50% of iniial amoun; abou 25% of iniial amoun; abou 12.5% of iniial amoun (sudens answers will vary slighly) TI-Nspire Navigaor Opporuniies Use Quick Poll o collec suden responses o quesions Discuss differences and similariies in wo radioacive decays observed. Q7. Wha funcion ype bes describes he radioacive decay curve? Why? Answer: he exponenial funcion, since amoun of remaining isoope is halved afer equal inerval of ime (half-life). Par 2: Mahemaical Model of Radioacive Decay Move o page In his par of he aciviy sudens will examine he decay curves of Carbon-14 and Uranium-238 and will develop mahemaical model for each curve. 6. Sudens should grab and drag an examinaion line o display he ime and percen of remaining elemen for he poins on he curve in order o collec necessary informaion. They should use hese daa o develop and/or verify he mahemaical model for he curve Texas Insrumens Incorporaed 4 educaion.i.com

5 Radioacive Daing Teacher Tip: Sudens can collec daa from he page 1.3 Graph ab and use exponenial regression in order o find he mahemaical model. Alernaively, sudens can develop mahemaical model based on heir earlier observaion ha percen of remaining isoopes is halved afer each half-life, creaing geomeric sequence wih raio ½. Then, hey can subsiue he daa from he simulaion o verify heir model. A his par of he lesson provide sudens wih acual half-lives of he wo isoopes, 5,730 years for C-14 and billion years for U-238. Q8. Wha is he mahemaical model for he exponenial decay of Carbon-14? Explain how you developed his model. Verify your model using daa colleced on page 1.3. Answer: NC 1, so NC , where is ime in years and N C is percen of remaining carbon. Given poin on he curve (8,610 years, 35.29%). Subsiue, 8610, N C %. Sudens can subsiue several poins from he curve. Tech Tip: Sudens can selec» o perform quick calculaions. Tech Tip: Sudens can selec > Calculaor o add a new page o perform calculaions. Q9. Wha is he mahemaical model for he exponenial decay of Uranium-238? Verify your model using daa on page 1.3. Answer: 100 2, where is ime in billion years and N U N U is percen of remaining uranium. The formula is similar o he one for he carbon. Selec poin (3.38 BY, 59.2%). N U % Par 3: Radioacive Daing Move o page 1.3 Objec ab. 8. Sudens will selec differen objecs ha can be found on he earh s surface and a differen geological layers and use radioacive daing o esimae he age of he objec. Sudens should selec o swich beween carbon daing and uranium daing according o he ype of he objec Texas Insrumens Incorporaed 5 educaion.i.com

6 Radioacive Daing Q10. For wha ype of objecs should you use carbon daing? Why? Answer: Carbon daing should be used o deermine he age of living maerials. Plans and animals naurally incorporae radiocarbon isoope ino heir issues. When a creaure dies, i ceases o consume more radiocarbon while he C-14 already in is body coninues o decay back ino nirogen. Q11. For wha ype of objecs should you use uranium daing? Why? Answer: Uranium daing could be used o deermine he age of geological formaions. The geologis finds minerals ha were formed in igneous rock as i cooled. The mineral raps he uranium bu no lead as i cools. Once cooled, he uranium slowly urns o lead, bu he lead is rapped. The raio of he uranium o he lead ells how long i has been since he mineral was formed. Uranium daing could also be used o deermine he age of pre-hisoric animals. 9. Sudens should selec he blue arrow on eiher side of he objec o swich he objec o dae. For each objec sudens should record ype of daing used (carbon or uranium) and percen of radioacive elemen remaining. Sudens should calculae an esimaed age of each objec based on heir mahemaical model of radioacive decay. Sudens should selec he Graph ab, ener he age, and hen selec. If he answer is correc, he smiley green face will appear on he page. If he answer is incorrec, he frown red face will appear. The esimaed age could be given wihin abou 20% margin error. Objec Type of % Elemen Daing Remaining Tree Carbon House Carbon Bone Carbon Calculaed Age (show your calculaions) (2 ), 220 years (2 ), 75 years (2 ), 1,450 years 2013 Texas Insrumens Incorporaed 6 educaion.i.com

7 Radioacive Daing Wooden cup Carbon Human skull Carbon Fish bones Carbon Rock 1 Uranium Dinosaur skull Uranium Rock 2 Uranium Trilobie Uranium Rock 3 Uranium Rock 4 Uranium (2 ), 1,035 years (2 ), 2,200 years (2 ), 15,997 years (2 ), BY (2 ), BY (2 ), BY (2 ), BY (2 ), BY (2 ), BY TI-Nspire Navigaor Opporuniies Use Quick Poll o collec calculaed ages of differen objecs given in he simulaion. Q12. Is here a relaionship beween he age of he objec and he geological layer where i is found? If so, wha? Answer: Suden answers will vary. The older objecs lay in he layers ha were formed earlier, and hey are deeper under he surface of he earh. Wrap Up When sudens are finished wih he aciviy, collec sudens workshees. Assessmen Formaive assessmen will consis of quesions embedded in he suden workshee. Analyze quesions in he suden workshee wih he sudens. Teacher can also collec scores ha sudens earned in he game. Summaive assessmen will consis of quesions/problems on he chaper es Texas Insrumens Incorporaed 7 educaion.i.com