Half Life Chemistry Problems - Nuclear Radioactive Decay Calculations Practice Examples

The Organic Chemistry Tutor2 minutes read

The text discusses the decay of Iodine 131, Sodium 24, and Oxygen 15, providing information on their half-lives, rates of decay, and equations to calculate the final amount after a specific time period. It highlights the mathematical relationships between decay constants, initial amounts, and final amounts in radioactive decay scenarios.

Insights

  • Iodine 131 has a half-life of 8 days, with 12.5 grams remaining from an initial 200 grams after 32 days, following an exponential decay model.
  • Sodium 24 decays from 750 grams to 50 grams in 60 hours due to its half-life of 15 hours, governed by a rate constant of 0.04621, as described by a logarithmic decay equation.

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Recent questions

  • What is the half-life of Iodine 131?

    8 days

  • How much Iodine 131 remains after 32 days?

    12.5 grams

  • What is the rate constant K for Iodine 131?

    0.08664

  • How long does it take for Sodium 24 to decay from 750 grams to 50 grams?

    60 hours

  • What fraction of Oxygen 15 remains after five half-lives?

    1/32

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Summary

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Radioactive Decay Rates and Half-Lives Explained

  • Iodine 131 has a half-life of 8 days.
  • If there are 200 grams of iodine 131, after 32 days, 12.5 grams will remain unchanged.
  • The rate constant K for iodine 131 is 0.08664.
  • The equation to find the final amount of iodine 131 after 32 days is AF = 200 * e^(-0.08664 * 32) = 12.501 grams.
  • Sodium 24 has a half-life of 15 hours.
  • It will take 60 hours for 750 grams of sodium 24 to decay to 50 grams.
  • The rate constant K for sodium 24 is 0.04621.
  • The equation to find the time for 750 grams of sodium 24 to decay to 50 grams is Ln(50/800) = -0.04621t, resulting in t = 60 hours.
  • Oxygen 15 has a half-life of 2 minutes.
  • After five half-lives, 3.125% of the sample remains, which is equivalent to 1/32 as a fraction.
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