Question

a certain radioactive isotope has a halflife of approximately 2000 years. How many years to the nearest year would be required for a given amount of this isotope to decay to 60% of that amount?

Answer 1

Given that the half-life is about 2000 years, you know that it takes that much time for any given amount of the isotope to decay half the original amount, which is explained by the equation
\[\large\frac{1}{2}=e^{2000k}~~\implies~~\color{red}k=\cdots\]
Find \(k\), the relative decay factor. Then use this \(k\) to determine the time \(t\) that it takes for the amount to decay to 60% its original amount:
\[\large0.6=e^{\color{red}kt}\]

Answer 2

thank you