SOLUTION: Radium-226 is a radioactive element with a half-life of 1600 years. How much of a 1000 g sample of the element will be present after 6400 years? How long will it take for the 1

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Radium-226 is a radioactive element with a half-life of 1600 years. How much of a 1000 g sample of the element will be present after 6400 years? How long will it take for the 1      Log On

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 Question 191308: Radium-226 is a radioactive element with a half-life of 1600 years. How much of a 1000 g sample of the element will be present after 6400 years? How long will it take for the 1000 gram sample to decay to 1 gram? Answer by ankor@dixie-net.com(15624)   (Show Source): You can put this solution on YOUR website!Radium-226 is a radioactive element with a half-life of 1600 years. How much of a 1000 g sample of the element will be present after 6400 years? : The half-life decay formula: A = Ao(2^(-t/h)) where: Ao = initial amt A = resulting amt after t years h = half-life of substance t = time in years : A = 1000(2^(-6400/1600)) A = 1000(2^-4) A = 1000 * .0625 A = 62.5 grams after 6400 yrs : : How long will it take for the 1000 gram sample to decay to 1 gram? 1 = 1000(2^(-t/1600)) Divide both sides by 1000 and we can write this: 2^(-t/1600) = 2^(-t/1600) = .001 log(2^(-t/1600)) = log(.001) *log(2) = log(.001) *.30103 = -3 Multiply both sides by 1600, results -.30103t = -4800 t = t = 15,945.25 yrs for 1000 g to decay to 1 g ; : Check by using this in the following equation with a calc A = 1000(2^(-15945.25/1600)) A = 1.000; confirms our solution