Radioactive Decay

The half-life of a radioactive substance is the length of time it takes for half of a given amount of the substance to disintegrate due to radiation. For example, the half-life of radium-226 is 1590 years, so that if today you had 50 grams of radium-226, 1590 years from now there would only be 25 grams left, because half of the 50 grams would have disintegrated.

Problem 1: As above, suppose you have 50 grams of radium-226. Use The Half-Life Calculator to figure how much radium-226 will remain after

  1. 10 years
  2. 50 years
  3. 1000 years
  4. 3000 years
This is an example of exponential DECAY. It works just like exponential GROWTH, which was discussed in our book. The only difference is that the amount is decreasing instead of increasing.

Scientists can determine the age of ancient objects by a method called radiocarbon dating. The bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive isotope of carbon, carbon-14. Vegetation absorbs carbon dioxide, including some carbon-14 molecules, through the atmosphere, and animal life assimilates carbon-14 through the food chain. When a plant or animal dies, it stops replacing its carbon and the amount of carbon-14 begins to decrease through radioactive decay.

The half-life of carbon-14 is approximately 5730 years.

Suppose you found an animal bone, and you wanted to know how old it was. You could have the bone tested for the amount of carbon-14 present. If the lab reported to you that the bone contained 95% of the amount of carbon-14 present in a living animal, then you could estimate that the animal died approximately 424 years ago. (I used the half-life calculator with A = 95, I = 100, and H = 5730, to calculate T = 424.023).

Problem 2: Why did I use A = 95 and I = 100? Could I have used other numbers for A and I?

Problem 3: An archaelogist found a parchment fragment that had about 74% as much carbon-14 as does plant life today. Estimate the age of the parchment.

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