Half Life Chemistry Problems - Nuclear Radioactive Decay Calculations Practice Examples
The Organic Chemistry Tutor・12 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.
