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Radioactive Half Life

Exponential Decay of Radioactive and other substances

The Half Life of anything is the amount of time that the substance's total amount is halved. A common real world example of half life is the decay of radioactive substances.

Formula for Half Life

y = 100(½)x
  • x represents the interval between half lives
  • y = the current amount
  • Example
    If a radioactive substance has a half life of 1 day, and there is 100 grams of this substance
    • to find the amount in 1 day
      • current amount= (starting amount)(½)(days passed)
      • current amount= 100(½)¹ = 50 grams
    • to find the amount in 2 days
      • current amount = (100)(½)2 = 25 grams
    • to find the amount in 5 days
      • current amount = (100)(½)5 = 3.125 grams


      Example Two (Interval of 10 minutes)

      If the the half life of substance X is 10 minutes and substance X starts out at a total of 100 grams then
    • at t =0, the current amount =100 grams
    • t = 10 mins, current amount =50 grams
    • t = 20 mins, there is 25 grams
    • t = 30 mins, 12.5 grams
    • and so on and so forth.
    It should be noted that the total substance will never actually become zero since half of anything, no matter how small and insignificant a number, is still not ZERO. Therefore, the half life of radioactive and other substances approaches zero, getting closer and closer to zero but never actually reaching it. See the interactive demo just below for a real time example of how half of a number never actually reaches zero.
    Problem 1 A certain substance has a half life of 1 hour, if you start with 1000 grams of the substance, how much will you have in 1 hour?
    Answer

    Radioactive Half Life

    Problem 2) Technetium-99m is a radioactive substance used to diagnose brain, thyroid liver and kidney diseases. This radioactive substance has a half life of 6 hours. If there are 200 mgs of this technetium-99m, how much will there be in 6 hours?
    Answer