Question

question 14 (2 points)
the half - life of polonium - 218 is 3.00 minutes. starting with 1000. g of this pure radioactive isotope in a sealed container, how much lr - 260 remains after 18.0 minutes?
1
a. 1000. g b. 500. g c. 250. g d. 125 g e. 62.5 g
f. 31.3 g g. 15.6 g h. 7.81 i. 750. g j. 3.91g
k. 1.95 g

Explanation:

Step1: Calculate number of half - lives

The half - life $t_{1/2}=3.00$ minutes and the total time $t = 18.0$ minutes. The number of half - lives $n=\frac{t}{t_{1/2}}=\frac{18.0}{3.00}=6$.

Step2: Use radioactive decay formula

The formula for radioactive decay is $N = N_0\times(\frac{1}{2})^n$, where $N_0$ is the initial amount and $N$ is the remaining amount. Here, $N_0 = 1000$ g and $n = 6$. So $N=1000\times(\frac{1}{2})^6$.
$N = 1000\times\frac{1}{64}=15.625\approx15.6$ g.

Answer:

G. 15.6 g