Question

lab #5 understanding radioactivity

Experimental Procedure: Note: Samale.salculations were done by the instructor, Please see below. Simply do what the instructor has done! This is a simple and fun home project. We will call it the Decay Game. Get 100 pennies. Think of them as a new radioactive isotope. We will call it Coinium isotope. One coin decays” when it comes up tails. Start with all your 100 coins by tossing them on the floor or a large table. Remove the coins that decayed (tails). Toss the remainder and remove the ones that decayed and so forth. On a Microsoft Excel sheet (or similar program, such as Google Sheets), make a table of the number of remaining coins versus the number of years (throws). Make a plot of the data points, where the horizontal axis represents the number of years (number of throws) and the vertical axis represents the remaining coins. Continue plotting your points until your sample decays to zero. Connect the points in a smooth curve that runs evenly between the points (but not necessarily touches all the points (see sample plot provided). Excel should be able to take care of that. From the table of data, what is the half-life of your sample? Does this number agree with your graph? Explain. For how many years will your Coinium isotope decay until you have only one coin? From the graph, predict the number of coins left after 3 years after 5 years. How many years did it take for the sample to decay to zero? What is your conclusion? What did you learn?

Answer 1

Conclusion : like the number of coins remaining decrease smoothly with trials ( roughly reducing to 50% ( halfing ) every throw ,the number of radio active atoms remaining also decrease smoothly and reduce to 50% of value for each "half time " Example if X has half life of 2 years than 50% of X decays every two years ( at end of 2 years 50% ,at end of 4 years 25 % ( which is 50 % of 50 % ) 6 years 12.5% and so on)
Date: count data Start t=0 years 1 100 Hat decay equation 4 Time inyear Number after tyears & N(+) = No e starting value where t= 0.693 do t/ 2 58 24 12 F 3 3 4 (100) 5 6 case 1) after 1 year 58 conum left 58 = 100 e a what is half life of sample ? Ans Time at which Share there are so е coins left 58 100 In 0.58 = -2 (2=0.545) 58 SD t2 = 0.69 1. 26 years > 0.545 Part 2) 2 years Case 2) after 24 coinium Left el -21 24 at time 9 m 0.24 = - 2X 0.97 years croughly) To agree with our graphs Ans should be around 12 years as Ctoss number) 1.2 the value of coins remaining is so [50% or half of the initial value] Theoritical calculation from data will calculate Half life for Average it 3or4 samplings and out X= 0.71 Left Case 3) After 3 years 12 In (0.12) 2e-3 we dz 0.7 ts, a lyear

case 4 after 4 years 7 left In 20.07) = 6-41 = 0.66 loos years remained Averaging out 1.26€ 1.05+ 0.97+ 1 4 a Tol years Curve all the Half life from data- from Graph number of com after 3 year, syears ( The point i your plot u not Smooth your graph is Just joining sample points. YIL The graph should be like Least squares fitting exponential curve Y= a e a ebre to so let me help you out here as well. 0.7t Y= 100 e Theoritical calculation t time until only I to get the con remain 2 A = 0.693 lo) 0.63 decay equation N(t) = No e at to graph equation 0.63 + value after Too in oool= -xt t=- noool 0.63 3 • 3 year by looking at graph 8 year (thirteen) 5 year Theoritically it will take a long time for sample to go zeso, as we have such a small number (100) compared to atoms ~(1020-1015) or more.