An important component of smoke detectors is the $\alpha$ emitter ²⁴¹Am. The rate constant for the decay of this isotope is 1.6 x 10^-3 yr^-1. If a smoke detector starts with1.8 x 10^-4 g of the isotope, how long will it take until 1.0 x 10^-4 g of americium remains?

Question

Quizplus · Accepted Answer

Using the first-order decay formula $ t = \frac{\ln(\frac{N_0}{N})}{k} $, where $ N_0 = 1.8 \times 10^{-4} $ g, $ N = 1.0 \times 10^{-4} $ g, and $ k = 1.6 \times 10^{-3} $ yr$^{-1}$, the time $ t $ is calculated to be approximately 370 years.

An Important Component of Smoke Detectors Is The α\alphaα Emitter 241Am

An Important Component of Smoke Detectors Is The $\alpha$ Emitter ²⁴¹Am