Question

Element X decays radioactively with a half life of 9 minutes. If there are 170 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 26 grams?

Answer 1

Element X decays radioactively with a half-life of 9 minutes. To decay from 170 grams to 26 grams, it will take approximately 4 half-lives or 36 minutes.

Step-by-step explanation:

To find the time it takes for Element X to decay from 170 grams to 26 grams, we can use the concept of half-life.

The half-life of Element X is 9 minutes. This means that in every 9 minutes, half of the amount of Element X will decay.

Since we want to decay from 170 grams to 26 grams, we need to determine how many half-lives it will take. Starting with 170 grams, we divide it by 2 until we reach a value close to 26 grams:

1. 170/2 = 85
2. 85/2 = 42.5 (approximately)
3. 42.5/2 = 21.25 (approximately)
4. 21.25/2 = 10.625 (approximately)

It will take approximately 4 half-lives for Element X to decay from 170 grams to 26 grams. Since each half-life is 9 minutes, the total time it will take is 4 x 9 = 36 minutes.