Lab 2  Radioactive Decay In this lab you will investigate radioactive decay by using pennies to simulate decaying nuclei. In this lab, a penny will decay when it comes up heads (although you might not have known that this happened to pennies). You will investigate the half-life of pennies and you will take a look at probability with regard to small numbers and large numbers. The difference is important. When you throw 8 pennies, you would expect 4 pennies to come up heads the most often, but sometimes different numbers of heads will occur. You would actually be surprised if 4 pennies came up heads every time.

Procedure: 1. You will throw 8 pennies for each decay cycle. A decay cycle for this lab will be until you have 1 or 0 pennies left. You will do 50 of these decay cycles. This sounds like a lot but each cycle can be done in much less than a minute even when taking the required data Set up a data table to do this quickly. A sample follows.

2. For each trial, record the number of heads that shows up on the first throw. Also record the number of throws that is required to have one or no pennies left.

Analysis

1. Find the total number of pennies that `decayed' on the first throw by adding the "Number Decayed 1^st Time."

 2. The total number of pennies you threw on the first throw is 50 trials times 8 pennies each trial. Find the percent of the total number of pennies thrown which 'decayed" the first time.

3. Draw a bar graph of the number of pennies which decay on the first throw showing the number of trials where a given number of pennies "decayed." (If 2 decayed on the first throw 6 times, draw a bar up from the horizontal axis 6 units at the 2 position.)

4. Find the average number of throws required for 1 or 0 pennies to be left. This is the average value of three half-lives.

5. Draw a bar graph of the number of throws needed to get 1 or 0 pennies showing the number of trials when it took a given number of throws. (If twice it took 7 times to have only 1 or 0 left, then draw a bar 2 units long at 7.)

Conclusions 

1. Is the total number of pennies which decayed on the first throw expected? Theoretically 50% would decay each throw; did this happen?

2. Comment on whether the expected number of heads came up on the first throw on a particular trial. Choose a trial at random, say trial 34, and see if the expected number of heads showed up. Did you expect this?

3. Comment on whether the first half-life of the pennies is expected. One would expect half the pennies to decay on the first throw; did this happen?

4. Is the time for three half-lives expected?

5. Discuss error, if any, in this lab.

6. In radioactive decay. you do not know which particular atom is going to decay, but you known that a certain percentage is going to decay in a given amount of time. Does this lab show this kind of decay?

Further information:

When a nucleus decays, with an alpha or beta particle, it turns into another kind of atom. Many times this atom is radioactive so it decays, too. The nucleus changes from one kind to another in a set path toward a stable nucleus. This path of changes is called a decay series. Some isotopes have longer half-lives than other so more atoms of that variety will exist than of the shorter half-life isotopes. For instance, if one isotope has half-life of a minute and another an hour, more atoms would exist of the hour half-life isotope because they don't decay as fast.