Question

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%

Answer 1

• Option 4. 8.5%

Step-by-step 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:

• n = 100 years / 28.1 years ≈ 3.5587

Hence, the amount of strontium-90 is:

`((1)/(2))^(3.5587)A_0=0.08486A_0`

In percent, that is:

`(0.08486A_0/A_0).100=8.486%`

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).