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Answer:
- Option 4. 8.5%
Explanation:
The<em> half-life </em>time of a radiactive isotope (radioisotope) is a constant value, meaning that the amount of the radioisotope that decays will be (1/2) raised to the number of half-lives passed.
Naming A₀ the initial amount to the radioisotope, you can build this table to find the amount left.
Number of half-lives amount of radiosotope left
0 A₀
1 (1/2) × A₀
2 (1/2)×(1/2)×A₀ = (1/2)² × A₀
3 (1/2)³ ×A ₀
4 (1/2)⁴ × A₀
n (1/2)ⁿ × A₀
Now calculate the number of half-lives the strontium-90 sample has passed after 100 years:
- n = 100 years / 28.1 years ≈ 3.5587
Hence, the amount of strontium-90 is:
In percent, that is:
Rounding to two significant figures, that is 8.5%.
<u>Conclusion</u>: <em>The percent of strontium-90 left after 100 yeaers is 8.5% </em>(choice number 4).