Question
Question 6
Technetium-99m is a radioactive isotope commonly used in medicine as a radioactive tracer. A radioactive tracer is an isotope injected into the body to help create images for diagnosis of health problems. Technetium-99m has a half-life of 6 hours. If a patient receives a dose of technetium-99m one morning, about what percentage of the technetium-99m will be left in the patient's body 12 hours later?
a
12.5%
b
25.0%
c
6.25%
d
93.8%
Technetium-99m is a radioactive isotope commonly used in medicine as a radioactive tracer. A radioactive tracer is an isotope injected into the body to help create images for diagnosis of health problems. Technetium-99m has a half-life of 6 hours. If a patient receives a dose of technetium-99m one morning, about what percentage of the technetium-99m will be left in the patient's body 12 hours later?
a
12.5%
b
25.0%
c
6.25%
d
93.8%
Answers
GPT-4o mini
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%**.
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%**.