Strontium-90 has a half-life of 28 years. How long will it take for the the Sr-90 to be reduced to 1/32 of its present amount?

To determine how long it will take for strontium-90 (Sr-90) to be reduced to 1/32 of its present amount, we can use the same half-life formula:

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

Here:
- \( N(t) \) is the remaining quantity of Sr-90 after time \( t \).
- \( N_0 \) is the initial quantity of Sr-90.
- \( t \) is the time elapsed.
- \( T_{1/2} = 28 \) years is the half-life of Sr-90.

We are asked to find \( t \) when \( N(t) = \frac{1}{32} N_0 \). This means:

\[
\frac{1}{32} N_0 = N_0 \times \left(\frac{1}{2}\right)^{\frac{t}{28}}
\]

We can simplify by dividing both sides by \( N_0 \):

\[
\frac{1}{32} = \left(\frac{1}{2}\right)^{\frac{t}{28}}
\]

To solve for \( t \), we can rewrite \( \frac{1}{32} \) as a power of 2:

\[
\frac{1}{32} = \frac{1}{2^5} = \left(\frac{1}{2}\right)^5
\]

So, we have:

\[
\left(\frac{1}{2}\right)^5 = \left(\frac{1}{2}\right)^{\frac{t}{28}}
\]

Since the bases are the same, we can equate the exponents:

\[
5 = \frac{t}{28}
\]

Now, solve for \( t \):

\[
t = 5 \times 28 = 140 \text{ years}
\]

It will take **140 years** for the Sr-90 to be reduced to 1/32 of its present amount.

Would you like more details or have any questions?

---

Here are 5 related questions:
1. How does the decay of strontium-90 affect the environment?
2. What are some common uses of strontium-90?
3. How does the decay rate of Sr-90 compare to other radioactive isotopes?
4. What safety measures are taken when handling radioactive materials like Sr-90?
5. Can the half-life of a substance change under different conditions?

**Tip:** When dealing with half-life problems, remember that each half-life reduces the remaining quantity by half, making logarithmic calculations useful.

Learn how to calculate the time it takes for strontium-90 to decay to 1/32 of its initial amount using its half-life of 28 years. This problem involves exponential decay and requires solving exponential equations. Suitable for advanced high school students and beyond.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation