Question

The half life of plutonium is 14.4 years. If 100g of plutonium are present initially, determine the quantity present after 10 years. When will the quantity drop under 5 mg?

Answer 1

First find the relative decay factor \(k\):
\[\frac{1}{2}=e^{14.4k}~~\implies~~k=\frac{1}{14.4}\ln\frac{1}{2}\]
Use this \(k\) to solve for the time \(t\):
\[5=100e^{kt}~~\implies~~t=\frac{1}{k}\ln\frac{5}{100}\approx\cdots\]