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# Half-lives

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1. Half-lives Objective 5

2. Half-lives • The time it takes for one-half of a radioactive isotope (a sample) to decay

3. Let’s say the half life of isotope A-5 is 1 minute. You have 10 pounds of it. How much is left after 1 half-life? 5 lbs How much is left after the second half-life? 2.5 lbs How much is left after the third half-life? 1.25 lbs How much is left after the fourth half-life? 0.625 lbs How much is left after the fifth half-life? 0.3125 lbs How much is left after the sixth half-life? 0.15625 lbs Does it ever go away??? Example Problem 1

4. Half-life GraphExponential Decay Tritium = H-3 t1/2 = 4500 days = 12.3 years

5. Calculating Half Life • AE = Ao * 0.5t/t1/2Where AE = amount of substance leftAo = original amount of substancet = elapsed timet1/2 = half-life of the substance • Note: Unit for time does not matter as long as both as same.

6. Example • You are given 157 grams of C-14, how much of C-14 would be left after 2000 years? The half-life of C-14 is 5730 years. AE = 157 * 0.5(2000/5730)

7. Amount of C-14 left after 2000 years would be 123 grams.

8. Example Problem 2 You have a 100.0 grams sample of Radium-222. It has a half-life of 3.8 days. How many grams will be left after 2 weeks?

9. 7.8 grams of Radium-222 is left after 2 weeks

10. References • http://wwwchem.csustan.edu/chem3070/images/tritium.gif