Find the solution

Question

The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 125 grams of a radioactive isotope, how much will be left after 3 half-lives?

 

Round your answer to the nearest gram.

 

Answer 1

Here is another way to solve the problem.  It gives the same answer:

 

After each half-life has elapsed, you are down to 1/2 of what you started with at the beginning of the half-life interval.

 

After 1 half-life, you are down to 1/2 of the initial amount.

 

After 2 half-lives you are down to 1/2 of 1/2 of the initial amount, which is (1/2)² of the initial amount.

 

Similarly, after 3 half-lives you are down to (1/2)³ of the initial amount.

 

You can see the pattern:  After n half-lives you are down to (1/2)ⁿ of the initial amount.

 

So after 3 half-lives, you are left with

 

(125 g) (1/2)³ = 125/8 g =  15.625 g ≅ 16 g to the nearest gram

Answer 2

Hi Hannah. Just cut the amount in half 3 times (because 3 half-lives have passed).

 

125 --> 62.5

 

62.5 --> 31.25

 

31.25 --> 15.625 g

 

which you have to round up to the nearest gram.