"Radioactive" Dice - Half Life Lab

After many years of doing the classic penny/skittle half-life lab, I was ready for something more. At it's best, all that lab was able to do was confirm that flipping a coin indeed gives you a 50/50 result and removing half of the sample each time results in a half-life curve. I wanted something where students were actually discovering something with the lab rather than confirming it.

I realize that replacing the 2-sided coin for a 6-sided dice isn't a brand new idea but I really like how the half life is no longer just "1 roll". Now that I have a 3D printer, I decided that it was time to take this lab concept and put my own spin on it :)

In this post, I will detail the investigation and share different ways to make or purchase "radioactive" dice kits of your own.

Radioactive Dice - Half Life Lab (pdf)
File Size:	698 kb
File Type:	pdf

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Radioactive Dice - Half Life Lab (editable)
File Size:	620 kb
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CLICK HERE to download 3D Files or purchase premade kits

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Set Up

All radioactive elements have a property called half-life. Half-life can be defined as the amount of time it takes for one-half of the original sample to decay and this time varies based on the element.

To represent our radioactive atoms, this lab uses dice that have one colored face. When one of these “atoms” is rolled with the colored face up, we say that it has decayed into one of its daughter elements and can be removed from the sample.

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Procedure

1. Place all 100 “radioactive” dice into a cup and roll them out into a box lid to prevent losing them off the table.
2. Carefully count the number of dice that are showing their colored side face-up and remove these from the sample.
3. After removing these “decayed atoms” from the sample, place all remaining dice back in the cup and roll again.
4. Repeat steps 2 and 3 until there are no more dice remaining.

The diagram/table below shows this process if you started with 30 dice

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Data

For each roll, students count up the number of newly decayed and record the totals in a data table. There is space in the lab for 20 rolls. In my experience, that is enough to get them to a point where either all dice have "decayed" or it's close enough that the students get the idea.

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Graph

One of the main objectives for this lab is to provide students with an opportunity to create a half-life curve from real data. In the pdf, students are provided with a preset axes to graph both the "total undecayed" and the "total decayed" by hand.

The dotted lines placed at 100, 50, 25, and 12.5 dice are to help students use the graph to estimate the half-life observed in their lab data. By fitting a curve to the data and marking where that line intersects these dotted lines, the half-life of the "radioactive" dice is just the average horizontal spacing between the marks.

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Questions

The lab concludes with a series of analysis questions that connect the lab with the traditional half-life problem solving examples that students should know how to do. For example:

• If you started with 1,200 dice, how many would you expect to have after 4 half-lives have elapsed?
  
• Based on your estimated half-life for these dice, how many rolls would that take? (4 half-lives)
  
• If these dice had 2 radioactive faces instead of 1, how would that affect the number of rolls it would for half of the sample to decay? Why? 
  
• Since actual radioactive elements are not dice, we measure half-life in seconds, minutes, days or years. For example, the half-life of Carbon-14 is 5,730 years. If you have a 40 g sample of that is 17,190 years old...
  
  • How many half-lives have elapsed? (how many times can 5,730 go into 17,190?)
    
  • What percentage of the sample is still undecayed Carbon-14? 
    
  • How many grams of Carbon-14 remain undecayed? 
    
  • Carbon-14 becomes Nitrogen-14 through beta decay. Assuming all decayed atoms are now Nitrogen-14, how many grams of Nitrogen-14 are in the sample?

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Extensions

While not captured in the write up, one of my favorite discussions that comes out of this data is how we actually measure the radioactive half life. Even though we often graph the total number of atoms that are "decayed" or "undecayed", that isn't a value that is easily measured in real life. Instead, the true data is more analogous to the "newly decayed" column. It is the number of events per unit of time that can be measured with geiger counter to see how the activity changes over the lifespan of the element. Some groups even noticed this on their own by making a "graph" using the decayed dice from each round :)

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Materials - 3D Printed

For this lab, I 3D printed a set of 100 "radioactive" dice for each of the lab stations in my room. The primary benefit of doing it this way is since each die only has one non-black side, it is very easy to determine when each one has "decayed". It also allowed me to make each set a different color so that I could easily reunite any dice that were found on the floor without having to count each set to figure out which one is missing. While it seems like a lot, having a sample size of 100 ensures that there is enough for the data to make a nice graph. It also makes for an easy leap to percentages for students that need this extra support

To make completing and storing the kits a little easier, I also designed and printed a big version of the die that is the perfect size to fit four 5x5 layers of the dice. Putting them away in this fashion is a quick and easy way to count up the 100 dice and determine if any are missing. It also just looks more official this way :)

These models are posted for free in the standard places if you want to print your own or I have the option to purchase these kits premade and shipped to you in any colors that you want. Everything can be found in the link below :)

CLICK HERE for 3D Printed Models/Kits

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Materials - Homemade

While it looks really cool and I think my students definitely appreciated it, the fancy die design isn't really required to do this lab. You can also do a similar investigation with standard 6-sided dice and just modify the language in the lab so that they are looking for a six (or any number that you decide should indicate that the atom has decayed). If you want to make it more permanent, you could even use a sharpie to color one side of each die to make it easier to spot. If you build your own kits in this way, you will just need to buy LOTS of dice so that each group can get 100 :)

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Files

Radioactive Dice - Half Life Lab (pdf)
File Size:	698 kb
File Type:	pdf

Download File

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Radioactive Dice - Half Life Lab (editable)
File Size:	620 kb
File Type:	docx

Download File

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