Question

The half-life of strontium-90 is 28.1 years. Estimate the percent of a strontium sample left after 100 years.

Answer 1

• 84.9 %

Step-by-step explanation:

1) Half-life is the time for the decay of a sample of matter to half its initial amount.

2) Radioisotopes (radioactive isotopes), such as strontium-90, have constant half-life times.

3) You can relate the time a radioactive samplle has been decaying with the percent of the matter remaining and the number of half-lives elapsed:

`[A]/[Ao]=(1/2)^n`

Where [A]/[Ao] is the ratio ratio of final amount to initial amoun, and n is the number of half-lives elapsed.

Here, n = 100 years / 28.1 years ≈ 3.559

Then:

`[A]/[A_0]=(1/2)^(3.559)=0.08486`

And the percent is 100 × 0.08486 = 84.86% = 84.9 %