Throw ten coins onto a flat surface. Move aside all the coins that landed tails-up. Collect the remaining coins. After tossing them once again, remove all coins

Question

Throw ten coins onto a flat surface. Move aside all the coins that landed tails-up. Collect the remaining coins. After tossing them once again, remove all coins landing tails-up. Repeat this process until all the coins have been removed. Can you see how this relates to radioactive half-life? In units of "tosses", what is the average half-life of 25 coins? 50 coins? 1 million coins?

Repeat the preceding activity, but use 10 dimes and 25 pennies. Let the dimes represent a radioactive isotope, such as carbon-14, while the pennies represent a nonradioactive isotope, such as carbon-12. Remove only the dimes when they land heads-up. Collect all the pennies and add them to the dimes that were heads-up. Does the number of pennies affect the behavior of the dimes? Someone gives you two sets of coins. The first set contains 10 dimes and 25 pennies. The second set contains 2 dimes and 25 pennies. Which set of coins has gone through a greater number of tosses? Which set provides the most "radioactivity" after a toss? Which set is analogous to a sample of once living ancient material?

Answer each question and summarize your results in a 2- to 3-page paper. Include a description of your experimental process and include a table of your data.

Answer 1

N = N₀(1/2)^t

 

Where:

• N = the number of coins left after "t" tosses
• N₀ = the initial or starting number of coins
• t = tosses

 

What is the average half-life of 25 coins? 50 coins? 1 million coins?

 

      N = N₀(1/2)^t

      N/N₀ = (1/2)^t

 

      For half-life, the ratio N/N₀ = 1/2 regardless of the

      number of coins you start with.

 

      1/2 = (1/2)^t

      t = 1

 

For the second problem, with dimes and pennies, the number of coins you have is given by:

 

      N = N_p + N_d(1/2)^t

 

      Where:

•       N = the number of coins left (dimes and pennies) after t tosses
•       N_p = the number of pennies, which doesn't change = 25
•       N_d = the initial or starting number of dimes = 10
•       t = tosses

 

      N = N_p + N_d(1/2)^t

      N = 25 + 10(1/2)^t

 

Note that the number of pennies never changes, while the number of dimes gets cut in half with each toss.  Can you finish from here?