Plutonium has a half life of $2.4 \times 10 ^ { 4 }$ years. How long does it take for $99.0 \%$ of the plutonium to decay?

Question

Quizplus · Accepted Answer

To find the time it takes for 99.0% of plutonium to decay, we can use the formula for exponential decay, $N = N_0(1/2)^{t/T}$, where $N$ is the final amount, $N_0$ is the initial amount, $t$ is the time, and $T$ is the half-life. For 99.0% decay, $N/N_0 = 0.01$. Solving for $t$, we get $t = T \log_2(N_0/N) = 2.4 \times 10^4 \times \log_2(100) = 2.4 \times 10^4 \times 6.64 \approx 1.6 \times 10^5$ years.

Plutonium Has a Half Life Of 2.4×1042.4 \times 10 ^ { 4 }2.4×104

Plutonium Has a Half Life Of $2.4 \times 10 ^ { 4 }$