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
25.0%
b
12.5%
c
93.8%
d
6.25%
To find the percentage of technetium-99m left in the patient's body 12 hours later, we need to determine how many half-lives have passed.
Since technetium-99m has a half-life of 6 hours, after 6 hours, half of the initial amount will remain. This means that after 12 hours (2 half-lives), 25% (50% x 50%) of the initial amount will remain.
Therefore, the correct answer is a) 25.0%.
To determine the percentage of technetium-99m left in the patient's body 12 hours later, we need to consider the half-life of technetium-99m.
Given that technetium-99m has a half-life of 6 hours, it means that after 6 hours, half of the radioactive tracer will decay. After another 6 hours (a total of 12 hours), another half of the remaining radioactive tracer will decay.
To calculate the percentage remaining, we can use the following formula:
Percentage remaining = (Initial amount) * (0.5)^(time / half-life)
In this case, the initial amount is 100%, since it represents the full dose of technetium-99m initially injected into the patient's body. The time is 12 hours, and the half-life is 6 hours.
Substituting these values into the formula, we get:
Percentage remaining = (100%) * (0.5)^(12 hours / 6 hours)
Simplifying the equation, we have:
Percentage remaining = (100%) * (0.5)^2
Percentage remaining = (100%) * 0.25
Percentage remaining = 25%
Therefore, the correct answer is:
a) 25.0%
To calculate the percentage of technetium-99m left in the patient's body after 12 hours, we need to determine how many half-lives have passed.
Given that the half-life of technetium-99m is 6 hours, after 6 hours, half of the initial dose will remain in the patient's body. After another 6 hours (total of 12 hours), another half of the remaining dose will decay, leaving one-fourth (25%) of the initial dose in the patient's body.
Therefore, the correct answer is option a) 25.0%.