The Half-Life of a Sugar Cube

Problem How can the half-life of a large sample be simulated using sugar cubes?

Materials 250 sugar cubes marked on one side large beaker graph paper

Procedure 1. Count sugar cubes carefully. You must have exactly 250 sugar cubes. If you do not, see your teacher to correct the situation. 2. Put all 250 sugar cubes in the beaker. Gently spill them out on the table. Move any cubes that are on top of other cubes. 3. Count and remove all the sugar cubes that have the colored dot facing up. 4. Put the rest of the sugar cubes back in the beaker and repeat steps 2 & 3. Do this several times, until 10 or fewer sugar cubes remain. 5. Make a table showing the spill number, the number of sugar cubes removed each time, and the number of sugar cubes remaining.

spill # sugar cubes removed sugar cubes remaining

0 0 250 1

6. Make a full-page line graph of spills vs. cubes remaining. Place the number of spills on the X axis and the number of cubes remaining on the Y axis. Start at zero spills with all 250 cubes remaining. See example.

250 Cubes Remaining

0 0 1 2 Spill number

7. Determine the half-life of the decaying sugar cubes in the following way. Assume spills equals years. Find the point on the graph that corresponds to one half of the original sugar cubes. Move vertically down from this point until you reach the horizontal axis. Your answer will be the number of spills. Write the half-life of your sugar cube on your graph.

Conclusion

1. What is the shape of your graph? 2. How many spills are required to remove one half of the sugar cubes? 3. How many spills are required to remove one fourth of the sugar cubes? 4. Assuming spills are equal to years, what is the half-life of the sugar cubes? 5. Using your answer to question 4, how many sugar cubes should remain after 8 years? After 12 years? Do these number agree with your observations? 6. What factors could account for the differences in your observed results and those calculated?

FOR THIS LAB YOU WILL TURN IN A TYPED LAB WITH: TITLE, PROBLEM, MATERIALS, DATA TABLE, A GRAPH (can be drawn if needed), AND THE ANSWERS TO QUESTIONS 1-6.