trontium-90 has a life of 29 days. If a sample that originally had 1000 grams of Strontium-90 has decayed to 15 grams. APPROXIMATELY how old is the sample?

Answer 1

A rather easy formula to use in these types of problems is FR = 0.5ⁿ

FR = fraction remaining

n = number of half lives that have elapsed.

In the current problem we have (or can find) the fraction remaining, so we can easily find the number of half lives that have elapsed. From this we can calculate the age of the sample.

FR = 15 g/1000 g = 0.015

Solving for n we have

0.015 = 0.5ⁿ

log 0.015 = log 0.5 n

n = 6.06 half lives have elapsed

Since each half life is 29 days, the age of the sample is...

6.06 half lives x 29 days/half life = 175.7 days = 176 days old

Answer 2

By definition, the half-life of a radioactive isotope is the time required for half of a given amount of this isotope to decay. For instance, in the case of strontium-90 whose half-life is 29 days, only 50% of the original amount of isotope would remain after 29 days (1 half-life), only 25% of the original amount would remain after 58 days (2 half-lives), only 12.5% would remain after 87 days (3 half-lives) and so on.

More generally, the amount of isotope remaining after any amount of time can be expressed by the following equation:

In this equation, N(t) is the amount of isotope remaining at any time t, N₀ is the starting amount, and t_1/2 is the half-life. Therefore, for this particular problem, we can set this equation up as follows, then solve for t:

15 g = (1000 g)(1/2)^{t/29 d}; t = 176 days old

I hope this helped!