Magnesium-27 has a half-life of 9.45 min. How many grams of a 200 g sample will remain after 120 min?

Round your answer to the nearest hundredth of a gram.

To solve this problem, we need to use the formula for exponential decay, which is given by:

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

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

Given:
- Initial mass \(N_0 = 200\) grams,
- Half-life \(t_{1/2} = 9.45\) minutes,
- Time elapsed \(t = 120\) minutes.

Let's calculate how many grams of Magnesium-27 will remain after 120 minutes.

First, we find the number of half-lives that have passed:

\[
\frac{t}{t_{1/2}} = \frac{120}{9.45}
\]

Now, let's calculate the remaining mass \(N(t)\):

\[
N(t) = 200 \times \left(\frac{1}{2}\right)^{\frac{120}{9.45}}
\]

Let's compute this step-by-step.After 120 minutes, approximately **0.03 grams** of the 200-gram sample of Magnesium-27 will remain.

Would you like further details, or do you have any questions?

Here are 5 related questions to consider:
1. How does the half-life of a substance affect the decay process over time?
2. What are some real-life applications of half-life calculations in nuclear physics or medicine?
3. How would the remaining mass change if the half-life were different, say 20 minutes instead of 9.45 minutes?
4. What mathematical models are used for substances that do not follow simple exponential decay?
5. How does environmental exposure affect the half-life of radioactive substances?

**Tip:** When working with half-life problems, always ensure you correctly convert time units and understand the exponential decay formula.

Learn how to calculate the remaining mass of Magnesium-27 after 120 minutes using the exponential decay formula. This problem involves a 200-gram sample with a half-life of 9.45 minutes. Discover the step-by-step solution and gain insights into the decay process of radioactive substances. Suitable for Grades 10-12 students studying nuclear physics or chemistry.

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