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## NUCLEAR CHEMISTRY

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**Rates of Decay & Half Life**• Radionuclides have different stabilities and decay at different rates.**Integrated Rate Equation**where… • A = the amt. of decaying sample remaining at some time, t • Ao= the amt. of sample present at the beginning • k = rate constant; different for each radionuclide • t = time**Integrated Rate Equation**OR… where… • N = # of disintegrations per unit of time; relative activity • No= original activity**HALF-LIFE= the amount of time required for half of the**original sample to decay**HALF-LIFE= the amount of time required for half of the**original sample to decay Daughter Parent**HALF-LIFE**• Half-life = the amount of time required for half of the original sample to decay**Example: Cobalt-60 decays with the emission of beta**particles and gamma rays, with a half-life of 5.27 years. How much of a 3.42 g of cobalt-60 remains after 30.0 years? How do you solve for A???**Example: Cobalt-60 decays with the emission of beta**particles and gamma rays, with a half-life of 5.27 years. How much of a 3.42 g of cobalt-60 remains after 30.0 years?**Uses of Radionuclides**• Radiocarbon dating: the ages of specimens of organic origin can be estimated by measuring the amount of cabon-14 in a sample.**Carbon Cycle**How does C-14 get into living things???**Example: A piece of wood taken from a cave dwelling in New**Mexico is found to have a carbon-14 activity (per gram of carbon) only 0.636 times that of wood today. Estimate the age of the wood. (The half-life of carbon-14 is 5730 years.)**Example: A piece of wood taken from a cave dwelling in New**Mexico is found to have a carbon-14 activity (per gram of carbon) only 0.636 times that of wood today. Estimate the age of the wood. (The half-life of carbon-14 is 5730 years.) t=3744 yrs = 3740 yrs**Uses of Radionuclides*****NOTE: Objects older than 50,000 years have too little activity to be dated accurately using carbon dating; instead the following methods are used: • Potassium-40 decays to argon-40: half-life = 1.3 x 109 years • Uranium-238 decays to lead-206: half-life = 4.51 x 109 years**Example: A sample of uranium ore is found to contain 4.64 mg**of uranium-238 and 1.22 mg of lead-206. Estimate the age of the ore.**Example: A sample of uranium ore is found to contain 4.64 mg**of uranium-238 and 1.22 mg of lead-206. Estimate the age of the ore.