Elements: Radioactive Decay in Smoke Detectors

Americium-241 is a synthetic isotope made in nuclear reactors around the world. Chances are you have been in close proximity to this radioactive isotope thousands of time in your life because it is used in household smoke detectors. 241Am^{241}\rm Am is an alpha emitter whose decay obeys a first order rate-law (as do all nuclear decays) with a half-life of 432.6 years. What is the rate constant of its decay? How much 241Am^{241}\rm Am would remain of a 25mg sample if it were left for 300 years.


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