Accelerated Chemistry POGIL: Half-life
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1 Name: Date: Perid: Accelerated Chemistry POGIL: 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. Prerequisites Atmic symbls including mass number, atmic number, and charge. Identify particles in transmutatin equatins, cmplete reactins t bey the cnservatin f mass and nuclear charge. 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 We will walk thrugh calculatins with this equatin and slving fr the variables later in the POGIL. Yu are nt expected t knw hw t use natural lgs n yur wn. Take a deep breath.
2 P O G I L : H a l f - l i f e Page 2 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. Key Questins 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? Mdel 2: Parent and Daughter Atms Key Questins 1. What is the relatinship between a parent atm and a daughter atm? 2. After tw half-lives, hw many parent atms remain radiactive? Hw many daughter atms were frmed? 3. What is the mathematical relatinship between the decay f the parent atm and the frmatin f the daughter element?
3 Mdel 3: Half-life f Candium Activity P O G I L : H a l f - l i f e Page 3 Materials: Skitles and Mike n Ikes Cup & Paper twel Plate Prcedure: 1. Cunt the number f Skittles and recrd it in the data table at 0 half-lives. Place Skittles in cup. 2. Pur Skittles frm yur cup nt paper twel. Recrd the ttal number f S s that result. 3. Place all the nn-s candies in the cup. 4. Replace all the S candies with the same number f Mike n Ikes. Place the Mike n Ikes in the cup. 5. Pur the cup n the desk again. Recrd the ttal number f S s in the data table. 6. Repeat steps 2-4 until there are n Skittles left. This may take mre r less than 10 trials. If it takes mre than 10 trials, cntinue trials n a separate piece f paper. Data Table # f Half-Lives Number f Skittles Number f S s % f Skittles Remaining
4 Graph: P O G I L : H a l f - l i f e Page 4 Graph the % f Skittles remaining (y-axis) versus the number f half-lives (x-axis).draw a smth line r curve thrugh the data pints. With anther clr pen, draw the % pennies that are predicted t remain after each half-life n the same graph. Activity Questins: 1. Cmpare yur tw plts. Hw well did the Skittles simulate half-lives? Explain. 2. Fr the prcess f flipping skittles, what d the S s represent and the nn-s s represent? 3. What represents the parent atm? And daughter atm? 4. Hw many candies wuld yu need t reach at least 14 half-lives?
5 Mdel 4: Half-Lives f Radiactive Elements P O G I L : H a l f - l i f e Page 5 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 Key Questins 1. Why is the number f half-lives and time recrded as zer fr the starting amunt f 24 Na? 2. Hw much time is added t each half-life? Why? 3. Hw much des the mass f radiactive sdium-24 decrease fr each half-life? Why? 4. What happens t the 24 Na atms that decay? (Where d they g?) Practice 1. 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 10.4 hurs? Cmplete the table belw fr yur answer. # Of Half-Lives Time (+ 2.6h) 0h 2.6h 5.2h 7.8h 10.4h Mass 56 Mn 1.0mg 2. 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 3. 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 Amunt f 14 C 0y 1
6 P O G I L : H a l f - l i f e Page 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 [A 0 ] = Amunt f A at time = 0 Key Questins 1. Can yu write the slpe intercept (y = mx + b) equatin fr the half-life graph n the LEFT? Explain yur answer. 2. 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 1. The half-life f 161 Tb is 6.9 days. Hw many grams f an riginal g sample will remain after 2.5 weeks? 2. If yu start with a 325-g sample f 188 Au, hw lng will it take fr 299 g t decmpse? (t 1/2 = 8.8 min) 3. Let us assume a cnstant 14 C/ 12 C ratis f 13.6 disintegratins per minute per gram f living matter. A sample f a petrified tree was fund t give 1.2 disintegratins per minute per gram. Hw ld is the tree? ( 14 C t 1/2 = 5730 years)
7 TEACHER REFERENCE PAGE P O G I L : H a l f - l i f e Page 7 ln[a] = kt + ln[a 0 ] * SUBTRACT ln[a 0 ] ln[a] ln[a 0 ] = kt * SIMPLIFY ln[a] ln[a 0 ] ln [ A A 0 ] = kt Fr half-life, t = t ½ ln [ ] = kt ½ = kt ½ t ½ = k Substitutin ln [ A ] = ( ) t A 0 t ½
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