Question

The following isotopes (listed with their half-lives) have been used in the medical and biologic sciences. Arrange these isotopes in order of their relative decay activities: \({ }^{3} \mathrm{H}\) ( 12.2 years), \({ }^{24} \mathrm{Na}\) ( 15 hours), \({ }^{131} \mathrm{I}(8\) days \(),{ }^{60} \mathrm{Co}(5.3\) years \(),{ }^{14} \mathrm{C}\) ( 5730 years \()\).

Short answer

The isotopes arranged in order of their relative decay activities, from highest to lowest, are: \({ }^{24} \mathrm{Na} > { }^{131} \mathrm{I} > { }^{60} \mathrm{Co} > { }^{3} \mathrm{H} > { }^{14} \mathrm{C}\).

Step-by-step solution

1. Identify the half-lives of each isotope

: First, let's write down the half-lives for each isotope: - \({ }^{3} \mathrm{H}\): 12.2 years - \({ }^{24} \mathrm{Na}\): 15 hours - \({ }^{131} \mathrm{I}\): 8 days - \({ }^{60} \mathrm{Co}\): 5.3 years - \({ }^{14} \mathrm{C}\): 5730 years

2. Convert half-lives into a common unit

: To easily compare the half-lives, we should convert them into a common unit. Let's convert all of them into hours. - \({ }^{3} \mathrm{H}\): 12.2 years * 365 days/year * 24 hours/day = 106824 hours - \({ }^{24} \mathrm{Na}\): 15 hours - \({ }^{131} \mathrm{I}\): 8 days * 24 hours/day = 192 hours - \({ }^{60} \mathrm{Co}\): 5.3 years * 365 days/year * 24 hours/day = 46488 hours - \({ }^{14} \mathrm{C}\): 5730 years * 365 days/year * 24 hours/day = 50207400 hours

3. Order isotopes based on half-lives

: Now that we have all half-lives in hours, we can order the isotopes by comparing their half-lives. Remember that the shorter the half-life, the higher the decay activity. So, we will order them from the shortest to the longest half-life: - \({ }^{24} \mathrm{Na}\) (15 hours) - \({ }^{131} \mathrm{I}\) (192 hours) - \({ }^{60} \mathrm{Co}\) (46488 hours) - \({ }^{3} \mathrm{H}\) (106824 hours) - \({ }^{14} \mathrm{C}\) (50207400 hours) Finally, we have arranged the isotopes in order of their relative decay activities, from the highest decay activity to the lowest: \({ }^{24} \mathrm{Na} > { }^{131} \mathrm{I} > { }^{60} \mathrm{Co} > { }^{3} \mathrm{H} > { }^{14} \mathrm{C}\)

Key concepts

Radioactive Decay

Radioactive decay is a fundamental concept in nuclear chemistry where unstable atomic nuclei release energy by emitting radiation in the form of particles or electromagnetic waves. This process occurs naturally in several isotopes and is used in various scientific and medical applications.

To measure how quickly a radioactive isotope decays, we use the term 'half-life', which is the time needed for half of the radioactive nuclei in a sample to decay. For example, if a sample has a half-life of 1 hour, after 1 hour only half of the sample remains, after 2 hours only a quarter remains, and so on.

In the context of the given exercise, the half-life serves as an inverse indicator of decay activity: the shorter the half-life, the more active the isotope is in terms of decay. Understanding half-life is crucial in determining how long a radioactive isotope will remain active or how quickly it needs to be replaced or disposed of safely.

Nuclear Chemistry

Nuclear chemistry is the branch of chemistry that deals with changes in the nucleus of elements. These changes often lead to transformations from one element to another and are accompanied by energy changes. This energy can be harnessed for various purposes such as electricity generation, medical treatments, and scientific research.

Converting the half-lives of isotopes into a common unit, such as hours, allows chemists to accurately calculate the amount of an isotope needed for a particular time frame. In medical treatments, for example, the dosage of radioactive isotopes must be carefully calculated to ensure that it is effective yet safe for the patient.

Nuclear chemistry also involves meticulous safety protocols because of the potential hazards of ionizing radiation. Professionals in this field must understand the rates of radioactive decay to prevent contamination and unnecessary radiation exposure.

Medical Isotopes

Medical isotopes are specific types of isotopes that are used within the healthcare sector, particularly for diagnostic imaging and treatment of diseases. One of the most widely known applications is in the field of nuclear medicine, where isotopes are used to diagnose and treat illnesses such as cancer.

For instance, some isotopes can be used in very small quantities as tracers to visualize specific organs or tumors, while others can be employed to target and destroy malignant cells. The half-lives of these isotopes are critical to their medical use. A half-life that is too short could be ineffective before reaching the target, whereas a half-life that is too long could mean unnecessary exposure to radiation for the patient.

Understanding how to compare the half-lives and activities of medical isotopes helps in selecting the most appropriate isotope for a given medical procedure, ensuring both efficacy and patient safety.

Biological Applications of Isotopes

Isotopes have significant applications in biology as well, beyond their medical uses. They can be used as tracers to follow the pathways of biochemical reactions or substances within an organism. By tracking these isotopes, biologists can study the metabolic processes and gain insights into nutrient absorption, enzyme functions, and even the spread of contaminants in the environment.

For example, Carbon-14 ({ }^{14} C), with its half-life of 5730 years, is used in radiocarbon dating to determine the age of archaeological samples. Tritium ({ }^{3} H), although it has a much shorter half-life, can be used to label molecules in cellular or pharmacological studies.

The choice of isotope for any biological application depends on factors such as the half-life, decay mode, and biological compatibility, hence the importance of understanding these properties and their implications for biological research and applications.