AP Chemistry - Nuclear Worksheet #4
Half-Life Calculations
1.         What is meant by the term half-life?
2. Strontium-90 has a half-life of 28 years. How long will it take for all of the strontium-90 presently on earth to be reduced to 1/32 of its present amount?
3. The half-life of cesium-137 is 30 years. Of an initial 100 g sample, how much cesium-137 will remain after 300 years?
4. You are at a dinner party and your host brings out a bottle of brandy for which he paid a great deal of money because he was told that it was bottled in the time of Napoleon (1769-1821). Since you are a research chemist you are asked if there is any way in which the age of the brandy can be determined. You assert that tritium(H3) dating is the way to do it. Ordinary water contains a very small amount of tritium that is formed in the earth's atmosphere by reactions involving cosmic rays. Tritium disintegrates by beta-emission at a rate equal to that at which it is formed. Water exposed to the atmosphere will contain a constant tritium content. Since brandy contains water, it should be possible to estimate its age. Since tritium in the bottle will not be replaced after it decays, the older the brandy, the lower its tritium content should be. You agree to test a sample of your host's brandy. You find that the sample has a tritium content of 30.6% of that of present-day water. How long ago was the brandy bottled?
 t½ for H3 = 12.3 years
5. A 24.0 g sample of Ra-226 is supplied to a lab in the year 2000. In the year 2040, it is noted that only 20.0 g of Ra-226 remains. What is the half-life of Ra-226?
6. What specific property of radiation is used by the Geiger counter? 
7. What radiation units (common and SI) are used to describe the activity of a sample of radioactive material? 
8. What is the name of the radiation unit that equals 1 disintegration/s?
9. What radiation units (common and SI) are used to describe the quantity of energy absorbed by a mass of tissue?

10. Explain how it is possible to determine the age of uranium-bearing rocks. 
11.  If radioactive wastes must be stored for seven half-lives before disposal
The t1/2 = 14.26 days       

a) how long must P-32 be held? 
b) what fraction of the P-32 originally set side remains after this time?

12. Woven rope sandals found in a cave in Oregon were analyzed by radiocarbon dating methods. The specific activity of the carbon was found to be 850 Bq/g. What is the age of these sandals?  Normal activity for C-14 is 918 Bq/g and the t1/2 = 5730 y.