Question

You have 8,560 grams of a radioactive kind of rubidium. If its half-life is 15 minutes, how much will be left after 45 minutes?

Answer 1

The half-life of the radioactive substance indicates that every 15 minutes, half of the remaining amount will have decayed.

We start with 8,560 grams of rubidium. To find out how much remains after 45 minutes, we can determine how many half-lives fit into 45 minutes:

\[
\text{Number of half-lives} = \frac{45 \text{ minutes}}{15 \text{ minutes/half-life}} = 3
\]

Now, we will apply the half-life decay process. After each half-life, the amount of the substance will be halved. We can calculate the remaining amount after each of the 3 half-lives:

1. After the first half-life (15 minutes):
\[
\text{Remaining} = \frac{8560}{2} = 4280 \text{ grams}
\]

2. After the second half-life (30 minutes):
\[
\text{Remaining} = \frac{4280}{2} = 2140 \text{ grams}
\]

3. After the third half-life (45 minutes):
\[
\text{Remaining} = \frac{2140}{2} = 1070 \text{ grams}
\]

Therefore, after 45 minutes, the amount of radioactive rubidium remaining is **1,070 grams**.