2.950 mg sample of technetium-99 m is used for a diagnostic test. technetium- 99 m has a half-life of 6.0 hr , how much of the technetium-99 sample remains 24.0 hr after the test? Answer Answer:

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**Step 1: Write the decay formula**

The decay of a radioactive substance is given by  
$$
N(t) = N_0 \left(\frac{1}{2}\right)^{\frac{t}{T_{1/2}}}
$$  
where:
- $$ N(t) $$ is the remaining amount after time $$ t $$,
- $$ N_0 $$ is the initial amount,
- $$ T_{1/2} $$ is the half-life.

**Step 2: Identify the given values**

- Initial mass $$ N_0 = 2.950 $$ mg  
- Half-life $$ T_{1/2} = 6.0 $$ hr  
- Time elapsed $$ t = 24.0 $$ hr

**Step 3: Determine the number of half-lives elapsed**

$$
\frac{t}{T_{1/2}} = \frac{24.0}{6.0} = 4
$$

**Step 4: Substitute the values into the decay formula**

$$
N(24.0\ \text{hr}) = 2.950 \left(\frac{1}{2}\right)^4
$$

**Step 5: Calculate the remaining amount**

Since  
$$\left(\frac{1}{2}\right)^4 = \frac{1}{16}$$, we have:
$$
N(24.0\ \text{hr}) = 2.950 \times \frac{1}{16} = \frac{2.950}{16} \text{ mg}
$$

**Step 6: Perform the division**

$$
\frac{2.950}{16} \approx 0.1844 \text{ mg}
$$

**Final Answer:**  
Approximately $$0.1844$$ mg of technetium-99m remains after 24.0 hours.
After 24 hours, about 0.1844 mg of technetium-99m remains.

2.950 mg sample of technetium-99 m is used for a diagnostic test. technetium- 99 m has a half-life of 6.0 hr , how much of the technetium-99 sample remains 24.0 hr after the test? Answer Answer:

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