A patient is administered 20 mg of iodine-131. how much of this isotope will remain in the body after 48 days if the half-life of for iodine-131 is 8 days?

To determine how much iodine-131 remains in the body after 48 days, we can use the concept of radioactive decay and the half-life formula. The half-life formula is given by:

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

where:
- \( N(t) \) is the remaining quantity of the substance after time \( t \).
- \( N_0 \) is the initial quantity of the substance.
- \( t \) is the time elapsed.
- \( T_{1/2} \) is the half-life of the substance.

Given:
- \( N_0 = 20 \) mg (initial amount of iodine-131)
- \( T_{1/2} = 8 \) days (half-life of iodine-131)
- \( t = 48 \) days (time elapsed)

Now, plug in the values:

\[
N(48) = 20 \times \left(\frac{1}{2}\right)^{\frac{48}{8}}
\]

Simplify the exponent:

\[
\frac{48}{8} = 6
\]

So:

\[
N(48) = 20 \times \left(\frac{1}{2}\right)^6
\]

\[
N(48) = 20 \times \frac{1}{64}
\]

\[
N(48) = \frac{20}{64} = 0.3125 \text{ mg}
\]

Therefore, after 48 days, approximately **0.3125 mg** of iodine-131 will remain in the body.

Would you like more details or have any questions?

---

Here are 5 related questions:
1. What is the general process of radioactive decay?
2. How do we calculate the half-life of a substance if not given?
3. What are the health implications of iodine-131 in the body?
4. How does the decay of iodine-131 differ from other isotopes used in medicine?
5. Can the decay formula be applied to other elements? If so, how?

**Tip:** Understanding the half-life concept can also help in other real-life applications, such as pharmacokinetics (drug metabolism in the body).

Learn how to calculate the remaining amount of iodine-131 in the body after 48 days using the half-life formula. This problem involves radioactive decay concepts and exponential decay formulas. Suitable for advanced high school students and anyone interested in nuclear physics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation