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? square grams

## Step 1<br />The problem involves the concept of half-life, which is a term used in nuclear physics to describe the time it takes for half of the atoms in a sample to decay. In this case, the half-life of the radioactive substance, promethium, is given as 5 days. This means that every 5 days, half of the remaining promethium will decay.<br /><br />## Step 2<br />The problem also provides the initial amount of promethium, which is 9,056 grams. We are asked to find out how much of this will be left after 20 days.<br /><br />## Step 3<br />To solve this, we need to calculate how many half-lives have passed in 20 days. Since each half-life is 5 days, we divide 20 by 5 to get 4 half-lives.<br /><br />## Step 4<br />Next, we need to calculate how much promethium will be left after each half-life. After one half-life, half of the original amount will remain. So, after one half-life, we have \( \frac{1}{2} \times 9,056 = 4,528 \) grams.<br /><br />## Step 5<br />After two half-lives, we have \( \frac{1}{2} \times 4,528 = 2,264 \) grams.<br /><br />## Step 6<br />After three half-lives, we have \( \frac{1}{2} \times 2,264 = 1,132 \) grams.<br /><br />## Step 7<br />Finally, after four half-lives, we have \( \frac{1}{2} \times 1,132 = 566 \) grams.