Question

The half-life of a radioactive kind of cerium is 32 days. How much will be left after 160 days, if you start with 57,728 grams of it?

Answer 1

After 160 days, 1,804 grams of the radioactive cerium with a half-life of 32 days will remain from the original 57,728 grams, based on the regular halving that occurs with each half-life period.

Step-by-step explanation:

The half-life of a radioactive substance is the time it takes for half of the radioactive nuclei to decay. When we start with 57,728 grams of a radioactive kind of cerium with a half-life of 32 days, we can determine how much will be left after 160 days by calculating how many half-lives that period represents.

Since 160 days is exactly 5 half-lives (160 / 32 = 5), we can simply halve the initial amount 5 times to find the remaining amount:

1. After 1 half-life: 57,728 / 2 = 28,864 grams
2. After 2 half-lives: 28,864 / 2 = 14,432 grams
3. After 3 half-lives: 14,432 / 2 = 7,216 grams
4. After 4 half-lives: 7,216 / 2 = 3,608 grams
5. After 5 half-lives: 3,608 / 2 = 1,804 grams

Therefore, after 160 days, 1,804 grams of the radioactive cerium will be left.