The half-life of technetium-99m is 6 hours, which means that every 6 hours, half of the substance decays.
To find out how much will be left after 12 hours, we can calculate the number of half-lives that occur in that time period:
\[ \text{Number of half-lives} = \frac{\text{Total Time}}{\text{Half-life}} = \frac{12 \text{ hours}}{6 \text{ hours}} = 2 \]
Now, let's determine how much of the original amount remains after 2 half-lives. The remaining percentage can be calculated as follows:
- After the first half-life (6 hours), 50% remains.
- After the second half-life (another 6 hours), you take half of the remaining amount:
\[ \text{Remaining amount after 2 half-lives} = 50% \times \frac{1}{2} = 25% \]
Thus, after 12 hours, approximately 25.0% of the technetium-99m will be left in the patient's body.
The answer is b) 25.0%.