Radioactive Decay and Half Life Simulation 2/17 Integrated Science 2 Redwood High School Name: Period: Background I t was not until the end of the 1800 s that scientists found a method for determining the actual age of rocks, mi era s a d fossi s. They fou d that radioactive e eme ts decay, or cha ge to other e eme ts by givi g off partic es a d e ergy at a co sta t a d measurab e rate. Scie tists a so fou d that for each differe t radioactive e eme t, the rate of cha ge as fixed a d ot at a affected by such thi gs as pressure or temperature of the surrou di g e viro me t. The decay process is so regu ar that it ca itera y be used to determi e the passage of time, ike the ticki g of a c ock. I this activity, you i use a mathematica mode to study the process of radioactive decay a d exami e ho it ca be used to determi e the age of a cie t earth materia s - particu ar y fossi s. It i be he pfu to remember that the term half-life refers to the time required for half of the atoms of a given mass of substance to decay to a stable e d product. Focus Questions Describe ha f- ife a d radioactive decay, a d ho are they re ated to o e a other? What is the re atio ship bet ee specific e eme ts a d their ha f- ives? Ho ca radioactive decay a d ha f- ife be used to ca cu ate age? Procedure 1. Obtai the ecessary materia s for your ab group from the supp y tab e. This shou d i c ude a shoebox ith a id, i side pa e s umbered 1-4, ye o popcor ker e s, a d b ack popcor ker e s. 2. Cou t out 100 ye o ker e s. Doub e-check your cou t. 3. P ace the 100 ye o cor ker e s i to the empty shoebox. Cover the box. Ho d the box eve a d give it a sharp, si g e shake. 4. Ope the box a d remove a the ye o ker e s that have the sma e d poi ted to ard side 1. Cou t a d record the removed cor (Side 1 Test). For each shake, subtract corn removed from the number of yellow kernels in the box before the shake. Record this number as corn remaining. 5. Rep ace each ye o ker e removed ith a b ack ker e. Rep ace the id, shake the box agai, a d o ce agai remove the ye o ker e s poi ti g to ard side 1. Cou t a d record the removed cor. Subtract this figure from the umber remai i g from the previous shake. Record this e figure i the data tab e u der cor remai i g. Rep ace a removed ye o ker e s ith b ack ker e s. 6. Repeat this process u ti a of the ye o ker e s have bee removed from the box. 7. Remove a the b ack ker e s a d restock the box ith 100 ye o ker e s. Repeat the above procedures except this time after each shake remove the ye o ker e s that are poi ted to ard both side 1 and side 2. 8. Co ti ue this procedure u ti a of the cor has bee removed from the box. Radioactive Decay and Half Life Simulation
9. Repeat the e tire procedure for a third time, except this time remove the kernels that are facing sides 1, 2 and 3. Cou t the cor remai i g a d record each of your observatio s i the data tab e. Repeat u ti a the cor has bee removed from the shoebox. 2
Data/Results Radioactive Decay Simu atio - Data Tab e Starti g Cor Cou t: Shake # Side 1 Test Side 1 and 2 Test Side 1, 2 and 3 Test yellow corn yellow corn yellow corn yellow corn yellow corn yellow corn removed remaining removed remaining removed remaining 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Analysis and Conclusions 1. Co struct a graph to i ustrate your data. The graph shou d compare number of shakes verses number of yellow corn remaining. The graph shou d i c ude the data from a three tria s as recorded i each co um of your data tab e. (Remember, bar graphs are used for disco ti uous data, i e graphs for co ti uous data.) Attach graph to back of your ab. 2. Write a brief paragraph summarizi g the data i ustrated i your graph. 3
3. a) For the first data set (side 1 o y) ho ma y shakes ere required before ha f of the ye o ker e s ere remai i g i the box? b) For the seco d data set (sides 1 a d 2) ho ma y shakes ere required before ha f of the ye o ker e s ere remai i g i the box? c) For the third data set (sides 1, 2 a d 3) ho ma y shakes ere required before ha f of the ye o ker e s ere remai i g i the box? 4. Comp ete the fo o i g tab e, i dicati g hat each of the compo e ts of the ab ere simu ati g ith respect to radioactive decay. Component In Simulation Ye o ker e s i box duri g the simu atio What It Represents Ye o ker e s that have bee removed B ack ker e s i box duri g the simu atio Ye o ker e s remai i g after a y give shake A si g e shake The cha ge from removi g o y side 1 ker e s to either sides 1 a d 2 or sides 1, 2, a d 3 Shoebox Half Life Use your new understanding of radioactive decay and half-life to perform the following calculations. 5. Suppose a radioactive e eme t has a ha f- ife of 30 days. a. Ho much of a 4 gram samp e i be u cha ged (sti radioactive) after 60 days? (Sho your ork.) b. After 90 days? (Sho your ork.) c. After 120 days? (Sho your ork.) 6. Suppose a radioactive e eme t has a ha f- ife of 10,000 years. a. What perce t of the materia i be u cha ged (sti radioactive) after 20,000 years? (Sho your ork.) b. After 30,000 years? (Sho your ork.) 4
7. Create a tab e fi ed ith va ues ref ecti g the fo o i g: the cha ges that occur over 10 mi io years to a i itia samp e of te pou ds of a radioactive e eme t that has a ha f ife of 2 mi io years record amou t of radioactive a d stab e e eme t prese t i itia y, a d after each ha f- ife. 8. Describe ha f- ife a d radioactive decay, a d ho are they re ated to o e a other? 9. Describe ho radioactive decay a d ha f- ife ca be used to ca cu ate the age of fossi s? 5