The half-life of strontium-90 is 28.1 years. calculate the percent of a strontium sample left after 100 years.
1. 76%
2. 63%
3. 0.34%
4. 8.5%
5. 82%

Explanation:

The half-life 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:

Hence, the amount of strontium-90 is:

In percent, that is:

Rounding to two significant figures, that is 8.5%.

Conclusion: The percent of strontium-90 left after 100 yeaers is 8.5% (choice number 4).

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