Question

After three half-lives, a sample contains 20 grams of parent isotopes. How many grams of the parent isotope were present to start?

Answer 1

160 grams

Step-by-step explanation:

Since the sample went through 3 half-lives we have to think about how it would have come to 20 grams of parent isotopes.

We know it cannot be 40, since 40/2 = 20, which is only one half-life.

We also know it can't be 80, since 80/2 = 40 and 40/2 = 20, which is only 2 half-lives.

So we are stuck with 2 answers, 320 and 160.

Since 320 takes 4 half-lives to get to 20 grams (320/2 = 160, 160/2 = 80, 80/2 = 40, 40/2 = 20), we know it cannot be the answer, so we move on to 160.

Let's see.

160/2 = 80, 80/2 = 40, 40/2 = 20

Exactly 3 half-lives!

Clearly the answer to your question of how many grams of the parent isotope was present to start if 20 parent isotopes remained after 3 half-lives is 160!

Have a magnificent day!

Answer 2

The amount of a decaying substance in any time t (at) is calculated by the equation,
at = (a1) x (1/2)^h

where a1 is the original amount and h is the number of half-lives.

Substituting the given values with a1 as the unknown,
20 g = (a1) x (1/2)^3 ; a1 = 160 g

Thuss, there were 160 grams of the isotope at the beginning.