Suppose 40% of a radioactive substance remains after 2 years.Assume that ln 0.4 = -0.9 and find the decay constant.
A) 0.225
B) 0.45
C) 0.6
D) 1.8
E) 3.6

Question

Quizplus · Accepted Answer

The decay of a radioactive substance is given by the formula $N(t) = N_0e^{kt}$, where $N(t)$ is the amount of substance at time $t$, $N_0$ is the initial amount, $k$ is the decay constant, and $t$ is the time. Given that 40% remains after 2 years, we have $0.4N_0 = N_0e^{2k}$. Dividing both sides by $N_0$ and taking the natural logarithm, we get $\ln(0.4) = 2k$. Substituting $\ln(0.4) = -0.9$, we find $-0.9 = 2k$, so $k = -0.9 / 2 = -0.45$. The decay constant is positive by convention, so the correct answer is $0.45$.

Suppose 40% of a Radioactive Substance Remains After 2 Years