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Radioactivity and Half-Life

Formulas Used

  1. A sample of liquid Na-24 from the turbine of a sodium-cooled reactor starts with an activity of 59 Ci. Given that Na-24 has a short half-life of only 15 hours, what will the sample’s activity have dropped to after 6.3 hours have passed?
  2. In the medical test known as a PET scan, the patient is injected with a small amount of the isotope F-18, which has a half-life of 109.8 minutes. If the patient is initially injected with a dose of 8.28 mCi of F-18, how much of that activity will remain in a patient’s body 3.96 hours after the injection?
  3. Iodine-131, one of the isotopes that is produced in a fission reactor, has a half-life of 8.0 days. If 517 mCi of I-131 were to be accidentally released from a reactor, how long would it take for the sample’s activity to dwindle to only 63.6 mCi?
  4. The C-14 in a living tree produces 15.3 beta counts per minute per gram of carbon. After the tree dies, its C-14 is no longer replenished, and the existing C-14 decays with a half-life of 5730 years. If a wooden bowl is found to be producing only 10.4 beta counts per minute per gram of carbon, how much time has passed since the tree from which the bowl was made died?
  5. Suppose that scientists at the site of a nuclear accident which occurred 15.4 years ago discover that the area exposes inhabitants to 14 mrem per hour from Cs-137. Given that the half-life of Cs-137 is 30.17 years, what would the exposure have been at the time of the accident?
  6. A scientist using a Geiger-Mueller tube discovers that the decay rate of a particular isotope drops from 222 counts/min to 12.8 counts/min in two readings taken 160 minutes apart. What is the half-life of the isotope she is measuring?

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