# Explain why your “radioactive decay” curve is not perfectly smooth; in other words, besides the fact that this is not really radioactive and you are shaking a tray instead of the passage of real time, why are real radioactive decay curves very predictable?

Discussion

Plot a line graph with the number of “radioactive” particles left (you must start with 200 at time = 0. Subtract the first amount that flipped over for the first 5,000 years. Then subtract the second amount from that number — not the 200 — at 10,000 years, etc.) versus time (on the horizontal axis). Be sure that it is properly labeled and titled.

Explain why your “radioactive decay” curve is not perfectly smooth; in other words, besides the fact that this is not really radioactive and you are shaking a tray instead of the passage of real time, why are real radioactive decay curves very predictable?

What do mathematicians call the shape of this curve?

If the half-life of your sample is 5,000 years, calculate the value for k, the rate constant. Be sure to show your calculations.

Assume that your “radioactivity” was C-14 (carbon-14, carbon with mass number 14) and that it undergoes beta decay. Write the balanced nuclear equation for this reaction.

Carbon dating can be used to get a measurement of the age of a carbon-containing sample. (Scientists actually use mass spectroscopy and measure ratios of isotopes, which is a bit more complicated than can be replicated here.) Using the curve you created in Step 1, determine the age of a sample with this amount of radioactivity left:

75%

50%

25%

0%