Question

Cobalt-60 has a half-life of 5.3 years. if a pellet that has been in storage for 26.5 years contains 14.5 g of cobalt-60, how much of this radioisotope was present when the pellet was put into storage?

Answer 1

To determine the initial amount of cobalt-60, we double the final amount of 14.5 g for every half-life that has elapsed which is five, resulting in an initial amount of 232.0 grams.

Step-by-step explanation:

The student's question pertains to the decay of a radioisotope, specifically cobalt-60, which is a topic that falls under the subject of Chemistry. Given that the half-life of cobalt-60 is 5.27 years, we can calculate the initial amount of cobalt-60 present when the pellet was first put into storage. If, after 26.5 years, there is 14.5 grams of cobalt-60 left, this would represent five half-lives (26.5 years ÷ 5.27 years per half-life).

For each half-life, the amount of the substance is halved. This means that after the first half-life, the substance would be 50% of its initial amount, after two half-lives 25%, and so on. Therefore, to find the initial amount, we can repeatedly double the remaining amount for each half-life that has passed.

1. After 5 half-lives, the amount is 14.5 g.
2. After 4 half-lives, we double the amount: 14.5 g × 2 = 29.0 g.
3. After 3 half-lives, double the amount again: 29.0 g × 2 = 58.0 g.
4. After 2 half-lives, double once more: 58.0 g × 2 = 116.0 g.
5. After 1 half-life, the final double: 116.0 g × 2 = 232.0 g.

Therefore, the initial amount of cobalt-60 present when the pellet was put into storage was 232.0 grams.