Using Dice to Model the Radioactive Half-life of an Isotope                   

 

Procedures (trial one: Oneortwoium)

 

In this trial each of the dice represents one gram of the parent isotope Oneortwoium. 

Each shaking event will represent one year of time.

Dice that land on 1 or 2 will be represent one gram of daughter isotope.

 

1.  Your group should have 60 dice, one of which is a different color.  Count them to make sure

      they are all there. 

 

2.  Place all of the dice in the container you have been given and shake them up well and then

     pour them out onto your lab bench.

 

3.  Remove all the dice that land on 1, or 2.  Each of these represents one gram of daughter

     isotope.

 

4.  Count the number of dice remaining after the first shake and record this number on your data

     table in the column labeled “Grams of Oneortwoium”.  This represents the number of grams

   of remaining Oneortwoium.

 

5.  Take the remaining dice (the ones that landed on 3 - 6) which represent the ones that did

     not decay, and return them to the container and shake them up again.

 

6.  Pour the dice onto your lab bench again and repeat steps 3 – 5.

 

7.  Continue this process for ten shakes, or until all of the dice have “decayed”.

 

 

Procedures (trial two: Justsixium)

 

In this trial each of the dice represents one gram of the parent isotope Justsixium. 

Each shaking event will represent one year of time.

Dice that land on 6 will be represent one gram of daughter isotope.

 

8.  Repeat the steps above, starting over again with all 60 dice.  This time you will imagine that

    each of the dice represents a gram of Justsixium. 

 

    This time, instead of removing dice that land on 1, or 2, you will only remove dice that land

    on 6.

 

9.  After each shake, count the number of dice that have not decayed and write this on your data

     table in the column labeled “Grams of Justsixium”

 

10. Continue this process for ten shakes, or until all of the dice have “decayed” to 6.

 

      Pay attention to when the one mismatched dice decays.  Put a box around the value on the

     data table when this one finally decayed.

 

 

Half-life Lab                                                             Name ____________________

 

Data Table

 Number of Years              Grams of Oneortwoium                        Grams of Justsixium

(1 shake =   5yrs)         (1 dice = 1 gram of Oneortwoium)        (1 dice = 1 gram of Justsixium)

 

            0                                       80                                                       80

 

  _____5______                ______» 50_______                       _______» 65______

 

  ______10_____               _______________                                         _______________

 

  _____15_____                 _______________                                         _______________

 

  ____20_____                         _______________                                   _______________

 

  _____25_____                 _______________                                         _______________

 

  _____30_____                 _______________                                         _______________

 

  _____35_____                 _______________                                         _______________

 

  _____40_____                 _______________                                         _______________

 

  _____45_____                 _______________                                         _______________

 

  _____50_____                 ______» 0______                              _______» 10______

 

11.  Graph the data for the decay of Oneortwoium on the graph paper provided.

      Draw a smooth best-fit curve through the data and label the curve “Oneortwoium”

 

12. Graph the data for the decay of Justsixium on the graph paper provided.

      Draw a smooth best-fit curve through the data and label the curve “Justsixium”.

 

Questions

1.  To find the half-life of each isotope, see how many years (shakes) it took it to reduce itself

     from 80g to 40g.       Half-life of Oneortwoium:_____ » 8______

                                    Half-life of Justsixium:      _____» 17_______

2. How many more years did it take to reduce the amount of isotope from

   40g to 20g (50% to 25%)?      Oneortwoium:___ » 8___  Justsixium:      ____» 17____

   You should find that this is the same amount of time as one half-life.

 

3.  Which isotope would be more radioactive? Choose the one that decays the fastest since it gives off more particles in a given amount of time

 

4.  If Oneortwoium had too many neutrons to be stable, what type of particle would it emit?

Electron emission

 

   If Justsixium had too a large nucleus that was too large to be stable, what type of particle

   would it emit?  Hint: too big = 84 or more protons

 

 

 

Questions (continued)

 

5.  If you walked in in the middle of this lab and found that your lab partners were part way

     through “trial one: Oneortwoium” and they only had 8 of the original 80 dice left in their        

    box, how many shakes would you estimate that they had completed? _________________

 

    If each shake was equal to one year, how many years would this be? ________________

 

 

6.  About how many half-lives does it take any parent isotope to be reduced to 3.1% of its original

    amount?  ________  

 

    If you had only 3.1% of the original amount of Justsixium, how old would the sample be? _____

    (remember that one shake = one year)

 

7.  If you started with 60g of Justsixium, how many grams would you expect to have left

     after 15 years? ___________

 

     If you started with 1000g of Justsixium, how many grams would you expect to have left

     after 15 years? ___________

 

8.  If you started with 60g of Oneortwoium, how many grams would you expect to have left

     after 15 years? ___________