Strontium-90, one of nuclear fission products, has a half-life of 28.8 years, and readily accumulates in bones. If you originally has 10.0 mg of strontium-90, how many grams of strontium-90 remain after 57.6 years?

Question 5 options:

28.8 mg


1.00 mg


57.6 mg


2.50 mg


2.00 mg


5.00 mg

To determine how much Strontium-90 remains after 57.6 years, we can use the formula for exponential decay:

\[
N(t) = N_0 \left( \frac{1}{2} \right)^{\frac{t}{T}}
\]

Where:
- \( N(t) \) is the amount of substance remaining after time \( t \),
- \( N_0 \) is the initial amount of the substance,
- \( t \) is the time elapsed,
- \( T \) is the half-life of the substance.

Given:
- \( N_0 = 10.0 \, \text{mg} \),
- \( T = 28.8 \, \text{years} \),
- \( t = 57.6 \, \text{years} \) (which is exactly 2 half-lives, \( \frac{57.6}{28.8} = 2 \)).

Since 57.6 years is exactly 2 half-lives, the amount of Strontium-90 remaining is:

\[
N(57.6) = 10.0 \times \left( \frac{1}{2} \right)^2 = 10.0 \times \frac{1}{4} = 2.50 \, \text{mg}
\]

So, the amount of Strontium-90 remaining after 57.6 years is **2.50 mg**.

### Correct answer: **2.50 mg**

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Do you want further details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you calculate decay when the time is not a multiple of the half-life?
2. What are the real-world implications of Strontium-90 accumulating in bones?
3. How does the half-life relate to the decay constant in radioactive decay?
4. What is the difference between Strontium-90 and other isotopes in terms of biological impact?
5. How can exponential decay be applied to other fields besides radioactivity?

**Tip:** When calculating decay, if the time isn't an exact multiple of the half-life, logarithms are used for more precision.

Strontium-90, one of nuclear fission products, has a half-life of 28.8 years, and readily accumulates in bones. If you originally have 10.0 mg of strontium-90, how many grams of strontium-90 remain after 57.6 years?

Find out how much Strontium-90 remains after 57.6 years using the half-life formula. The problem explores exponential decay concepts and uses the formula N(t) = N0 * (1/2)^(t/T) for calculating radioactive decay. Suitable for Grades 9-12.

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