Question

Technetium-99m is an ideal radioisotope for scanning organs because it has a half-life of \(6.0 \mathrm{~h}\) and is a pure gamma emitter. Suppose that \(80.0 \mathrm{mg}\) were prepared in the technetium generator this morning. How many milligrams of technetium- \(99 \mathrm{~m}\) would remain active after the following intervals? a. one half-life b. two half-lives c. \(18 \mathrm{~h}\) d. \(24 \mathrm{~h}\)

Short answer

a. 40.0 mg b. 20.0 mg c. 10.0 mg d. 5.0 mg

Step-by-step solution

– Understanding Half-Lives

The half-life of a radioactive isotope is the time required for half of the isotope to decay. For technetium-99m, this half-life is 6.0 hours.

– Calculating After One Half-Life

After one half-life (6.0 hours), half of the original sample remains. Thus, if the initial amount is 80.0 mg, the amount remaining is: 80.0 mg / 2 = 40.0 mg

– Calculating After Two Half-Lives

For two half-lives (12.0 hours), half of the 40.0 mg remains: 40.0 mg / 2 = 20.0 mg

– Calculating After 18 Hours

18 hours is 3 half-lives (because 18/6=3). Halving 20.0 mg (the amount remaining after two half-lives): 20.0 mg / 2 = 10.0 mg

– Calculating After 24 Hours

24 hours is 4 half-lives (because 24/6=4). Halving 10.0 mg (the amount remaining after 18 hours): 10.0 mg / 2 = 5.0 mg

Key concepts

technetium-99m

Technetium-99m is a widely used radioisotope in the medical field. It is primarily employed for diagnostic imaging, particularly in nuclear medicine for scanning organs and bones. This isotope is ideal for such purposes because it has a relatively short half-life of 6 hours, which makes it safe for patients as the body gets rid of it quickly.

Moreover, technetium-99m emits only gamma rays, which penetrate tissues but do not cause ionizing damage as alpha or beta particles might. This makes it effective and safe for imaging, resulting in clear and precise diagnostic images without significant risk to the patient.

radioactive decay

Radioactive decay is the process through which unstable atomic nuclei lose energy by emitting radiation. This process can result in the transformation of one element into another. There are several types of radioactive decay including alpha, beta, and gamma decay.

In the context of technetium-99m, it decays by emitting gamma radiation, which is high-energy electromagnetic radiation. This transition enables the isotope to move from a higher energy state to a more stable lower energy state. Understanding the nature of radioactive decay helps in grasping how and why technetium-99m is used in medical applications.

half-life calculation

The half-life of a radioactive substance is the time required for half of the radioactive atoms in a sample to decay. For technetium-99m, the half-life is exactly 6.0 hours. This means that every 6 hours, the amount of the radioisotope decreases by half.

Let's break down the calculations from the exercise:
- After one half-life (6 hours), 80 mg of technetium-99m reduces to 40 mg.
- After two half-lives (12 hours), 40 mg reduces to 20 mg.
- After three half-lives (18 hours), 20 mg reduces to 10 mg.
- After four half-lives (24 hours), 10 mg reduces to 5 mg.

These calculations are essential in both medical and scientific contexts for understanding how long a radioisotope will remain active in the human body or in any given environment.

gamma emitter

A gamma emitter is a type of radioactive substance that emits gamma rays during its decay process. Gamma rays are a form of high-energy electromagnetic radiation. They are highly penetrating and can pass through soft tissue and bones, making them particularly useful for medical imaging.

Technetium-99m is classified as a pure gamma emitter, meaning it does not emit dangerous alpha or beta particles. This makes it safe for use within the human body for diagnostic purposes. The emitted gamma rays are captured by a gamma camera to form detailed images of internal organs.

This characteristic of technetium-99m is why it is so valuable in nuclear medicine, providing clear imaging while minimizing potential health risks.