Presentation Transcript

1. Rates of Radioactive Decay

   Drew Sutliff, April Zhang & Xijun Zhu
2. Definitions Isotopes: atoms that contain same number of protons but different number of neutrons Half-life: time required for half of any given quantity of a substance to react Ex: half-life of strontium-90 is 28.8 yrs If we start with 10 g of strontium-90, 5.0 g of that isotope will remain after 28.8 yr, and 2.5 g will remain after anther 28.8 yrs
3. Half-lives Half lives can be as long as billions of years or as short as millionths of a second Half-lives for nuclear decay is unaffected by external conditions such as temperature, pressure, or state of chemical combination Therefore, radioactive atoms cannot be made harmless by chemical reactions Because half-life of any particular nuclide is constant, half-life can be used to determine ages of objects
4. Radiocarbon Dating First, assume that ratio of carbon-14 to carbon-12 in the atmosphere has been constant for at least 50,000 yrs Carbon-14 is incorporated into CO₂, which is turned into more complex carbon molecules through photosynthesis within plants When plants are eaten by animals, carbon-14 is Incorporated taken in by the animals Because living plants and animals constantly take in carbon compounds, they are able to maintain the atmospheric ratio of carbon-14 to carbon-12
5. continued When the organism dies, however, it no longer ingests the carbon compounds used to replenish carbon-14 lost through radioactive decay The ratio of carbon-14 to carbon-12 thus decreases By measuring this ratio to the atmospheric ratio of carbon-14 to carbon-12, we can estimate the age of the object This method cannot be used to date objects older than 50,000 years b/c after that the radioactivity is too low to be measured accurately
6. Other methods of dating Used to check the accuracy of one method with another Counting the rings on the trees It adds a ring each year Using parent and daughter isotopes (one isotope breaks down into another) a.k.a Radiometric dating Ex: it takes 4.5 x 10⁹ yr for half of a sample of uranium-238 to decay to lead-206 Age of a rock with uranium can be determined by measuring the ratio of lead-206 to uranium-238
7. Calculations Based on Half-life Radioactive decay is a first order kinetic process Recall first order rate law is when the rate is proportional to the first power of [A] R = kN Rate of radioactive decay is proportional to the number of radioactive nuclei (N) in the sample The first order rate constant, k, is called the decay constant As a radioactive sample decays, the amount of radiation emanating from the sample decays as well Definitions Activity: the rate at which a sample decays Becquerel (Bq): SI unit for expressing the activity of a particular radiation source (rate at which nuclear disintegrations are occurring) It is defined as one nuclear disintegration per second Curie (Ci): unit of activity defined as 3.7 x 10^10 disintegrations per second (rate of decay of 1g of radium)
8. Calculations All radioactive decay reactions are 1st order. For a 1st order reaction: t= time interval of decay k= decay constant N₀= initial number of nuclei (at time zero) Nt=number of nuclei after time interval Both mass and activity of a particular radioisotope are proportional to number of radioactive nuclei Therefore either ratio of the mass or the ratio of activities can be substituted for Nt/N₀ Half life equation for a nuclear reaction:
9. Questions to ponder… Define Isotope: Atoms with the same number of protons but different numbers of neutrons What does it mean when decay occurs by first order kinetics? (Hint: think R=kN) The rate of decay is proportional to number of nuclides present True/False: (correct the false statement) As a radioactive sample decays, the amount of radiation emanating from the sample stays the same. False. The amount of radiation emanating from the sample decays as well SI unit for expressing the activity of a particular radiation source Becquerel
10. Questions to ponder further… The half life of tritium is 12.3 yr. If 24 mg of tritium is released, what mass of this nuclide will remain after 12.3 yr? 12.1 mg What is 10 curies of radioactivity equivalent to? 3.7 x 10^11 nuclear disintegrations per second If the half life of strontium-90 is 29 years and there is 10g of it, how many grams will remain after 145 years? 0.3125 g Are half-lives affected external conditions such as temperature, pressure, or state of chemical combination? No The rate at which a sample decays is also known as what? Activity
11. Works Cited http://www.idea.wsu.edu/ChemKinetics/first_order.htm http://www2.ucdsb.on.ca/tiss/stretton/CHEM4/APUnit_15_Main.html http://facstaff.gpc.edu/~pgore/geology/geo102/radio.htm http://www.actionbioscience.org/evolution/benton.html