Q: Which equation correctly represents the relationship between the remaining amount of a radioactive substance ($$N$$), the initial amount ($$N_0$$), and the number of half-lives ($$n$$)?

$$N = N_0$ \times \left( \frac{1}{2} \right)^n$$

Q: Which of the following equations can be used to calculate the remaining activity ($$A) of a $$radioactive sample after time $$t$$, given the initial activity ($$A_0) $$and half-life ($$t_{1/2}$$)?

$$A = A_0$ \times \left( \frac{1}{2} \$$right)^{\frac{t}$${t_{1/2}}}$$

Question 1

Technetium-99m is commonly used in medical imaging due to its short half-life. If the half-life of technetium-99m is 6 hours, how much of a 20 mCi dose remains after 12 hours?

Accepted Answer

$$5 \ 	ext{mCi}$$

Question 2

Which equation correctly represents the relationship between the remaining amount of a radioactive substance ($$N$$), the initial amount ($$N_0$$), and the number of half-lives ($$n$$)?

Accepted Answer

$$N = N_0$ 	imes \left( \frac{1}{2} ight)^n$$

Question 3

Why is the short half-life of technetium-99m considered beneficial for patients undergoing medical imaging?

Accepted Answer

It minimizes the duration of radiation exposure to the patient.

Question 4

A patient receives a 20 mCi dose of technetium-99m. After 6 hours, what fraction of the original dose remains?

Accepted Answer

$$\frac{1}{2}$$

Question 5

If a radioactive isotope has a half-life of 6 hours, how many half-lives have passed after 18 hours?

Accepted Answer

$$3$$

Question 6

After 12 hours, what percentage of the original technetium-99m dose remains?

Accepted Answer

$$25\%$$

Question 7

Which of the following best explains why technetium-99m is preferred over isotopes with longer half-lives for diagnostic imaging?

Accepted Answer

It decays quickly, reducing the patient's exposure to radiation after the procedure.

Question 8

A 20 mCi dose of technetium-99m is administered. How much remains after 18 hours? (Half-life = 6 hours)

Accepted Answer

$$2.5 \ 	ext{mCi}$$

Question 9

Which of the following is a real-world advantage of using isotopes with short half-lives in nuclear medicine?

Accepted Answer

They reduce the risk of long-term radiation effects in patients.

Question 10

If a radioactive sample decays to $$\frac{1}{8} of $$its original amount in a certain period, how many half-lives have passed?

Accepted Answer

$$3$$

Question 11

A technetium-99m sample starts at 40 mCi. How much remains after 18 hours? (Half-life = 6 hours)

Accepted Answer

$$5 \ 	ext{mCi}$$

Question 12

Which of the following best describes the concept of half-life?

Accepted Answer

The time required for half of the radioactive atoms in a sample to decay.

Question 13

A patient is given a radioactive tracer with a half-life of 6 hours. If only $$2.5 \ 	ext{mCi}$$ remains after 18 hours, what was the original dose?

Accepted Answer

$$20 \ 	ext{mCi}$$

Question 14

Which of the following equations can be used to calculate the remaining activity ($$A) of a $$radioactive sample after time $$t$$, given the initial activity ($$A_0) $$and half-life ($$t_{1/2}$$)?

Accepted Answer

$$A = A_0$ 	imes \left( \frac{1}{2} \$$right)^{\frac{t}$${t_{1/2}}}$$

Question 15

If a radioactive isotope used in imaging has a half-life that is too long, what is a potential risk for the patient?

Accepted Answer

The patient may be exposed to radiation for a longer period, increasing health risks.

Nuclear Chemistry: Half-Life and Medical Imaging Applications

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