Unit 49: Exponential Decay & Half-Life
Practice Problems
Note: problem difficulty is ranked using a star system.
(*) One-star problems are fundamental to the unit, and can be done relatively quickly. Use these problems to introduce yourself to the material.
(**) Two-star problems are more difficult, and require an understanding of one or two key concepts. Use these problems to test your understanding of the material.
(***) Three-star problems are the most difficult, and require some creative thinking in addition to a deep familiarity with multiple key concepts. Use these problems to challenge yourself; if you can complete one of these, you’re on your way to mastering the material.
*Q49.1) An isotope has a half-life of 1200 years. What’s its decay constant?
*Q49.2) An isotope has a decay constant of 0.02 s⁻¹. What’s its decay constant in units of min⁻¹?
**Q49.3) ²³⁸U has a half-life of 4.5 billion years. How long will it take for 80% of the active nuclei in a sample of ²³⁸U to decay?
**Q49.4) You find an old bone on an archaeological dig and send it to a lab for carbon dating. Results reveal the bone to contain 42% the concentration of ¹⁴C that’s found in the bones of living creatures. Given that the half-life of ¹⁴C is 3700 years, estimate the age of the remains.
***Q49.5) Two patients, Alice and Bob, are administered ¹³¹I as part of a treatment for hyperthyroidism. ¹³¹I has a biological half-life in Bob of 4 days and a biological half-life in Alice of 2 days (she has a faster metabolism). If Alice is initially given twice as much ¹³¹I as Bob, how long will it take until both patients have the same amount of ¹³¹I in their systems? Note: ¹³¹I has a physical half-life of 8 days.