background [prelab assignment (10 points) due at the beginning of lab]

describe 2 methods using graphical analysis to determine the half-life of a radioactive isotope (hint:  see content of lab report).

purpose

compare the determination of the half-life based on:

• the decay constant
• its definition (i.e.  analyze the graph:  # radioactive isotope versus time)

relate the # of faces on a dice to the half-life & decay constant

 

materials

6- or 10- sided dice;  20 dice / group

cup (to shake dice)

methods / data analysis

initially, simulate 100 radioactive isotopes by rolling a group of 20 dice, 5 times. 

pick a specific value on the dice, which represent the decay of the radioactive isotope

adjust # remaining radioactive isotopes accordingly; repeat till less than 20 dice remain

each set of dice rolls represent an interval of time, while # dice in sample represent # radioactive isotope in the sample

combine the data between groups & among classes

 

Content of lab report [35 points; no lab report revisions]

data analysis  -  for 6 or 10 sided dice  (20 points)

• determine & compare the half-life. 

• graphs:  for a 6- or10- sided dice   
  • # dice in sample versus # dice roll;  determine half-life based on definition - using your group's data
  • ln (# dice in sample)  versus  # dice roll; determine half-life based on relationship between half-life and decay constant - using your group's data
  • # dice in sample versus # dice roll - for 6- versus 10- sided dice - using other groups' data
• statistical comparsion of preceding methods for 6-sided dice versus 10-sided dice (use multiple t-test or 2-anova; using other groups' data); conclusion based on p-value.

discussion  (15 points)

what is the (qualitative) relationship between the number of sides on the dice (i.e. 6 versus 10) and the (simulated) decay constant ?  refer to your data to support your response.

what is the (qualitative) relationship between the number of sides on the dice (i.e. 6 versus 10) and the (simulated) half-life ? refer to your data to support your response.

rationalize the relationship between the (i) decay constant versus half-life using your class notes and (ii) # sides on a dice versus decay constant (or half-life) using concepts from probability.

resources

lab activity source (examples):  site 1  &  site 2  [access 4 / 2009]