Question

how much of a radioactive kind of promethium will be left after 20 days if you start with 9,056 grams and the half - life is 5 days? grams

Explanation:

Step1: Determine the number of half - lives

The formula to find the number of half - lives $n$ is $n=\frac{t}{T}$, where $t$ is the total time and $T$ is the half - life. Here, $t = 20$ days and $T=5$ days. So $n=\frac{20}{5}=4$.

Step2: Use the radioactive decay formula

The formula for radioactive decay is $N = N_0\times(\frac{1}{2})^n$, where $N_0$ is the initial amount, $n$ is the number of half - lives, and $N$ is the remaining amount. We know that $N_0 = 9056$ grams and $n = 4$. So $N=9056\times(\frac{1}{2})^4$.
First, calculate $(\frac{1}{2})^4=\frac{1}{16}$. Then $N = 9056\times\frac{1}{16}$.
$9056\div16 = 566$.

Answer:

566