Problem 66 - Chemistry The Science in Context

Question

A patient is administered mercury-197 to evaluate kidney function. Mercury- 197 has a half-life of \(65 \mathrm{h}\). What fraction of an initial dose of mercury-197 remains after 6 days?

Step-by-Step Solution

Answer

Answer: Approximately 26.34% of the initial dose of mercury-197 would remain after 6 days.

Step 1: Convert days to hours

To find out how many hours have passed after 6 days, we simply multiply the number of days by the number of hours in a day: Hours passed = 6 days × 24 hours/day = 144 hours.

Step 2: Calculate the number of half-lives elapsed

Divide the total number of hours passed by the half-life of mercury-197 to find the number of half-lives that have elapsed: Number of half-lives = 144 hours / 65 hours/half-life ≈ 2.2154.

Step 3: Find the remaining fraction of the initial dose

Using the formula for radioactive decay, we can find the remaining fraction of the initial dose. The formula is: Remaining fraction = (1/2)^(Number of half-lives) Remaining fraction = (1/2)^2.2154 ≈ 0.2634 Hence, about 26.34% of the initial dose of mercury-197 would remain after 6 days.

Key Concepts

Half-life

Understanding half-life is crucial for grasping how radioactive substances decay over time. The half-life of a radioactive element is the time required for half of the radioactive atoms in a sample to decay. It is a fixed property of the substance and does not change over time.
For example, in the context of radioactive decay, if a substance has a half-life of 65 hours, like mercury-197, then every 65 hours, only half of the original amount of mercury-197 will remain.
This concept is applied in various fields like medicine, archaeology, and nuclear physics, as it helps predict the behavior of unstable atoms.

• Half-life allows scientists to estimate how long a radioactive substance will remain active.
• It's commonly represented in decay equations, such as Remaining Fraction = (1/2)^{Number of half-lives}.
• Understanding half-life is essential when working with radioactive materials.

Mercury-197

Mercury-197 is a radioactive isotope of mercury used particularly in medical applications.
In medical diagnostics, mercury-197 is used as a tracer due to its distinguishable radioactive signature. It helps physicians assess the function of organs by tracking the movement and accumulation of radiation in the body.
Mercury-197 is known for its relatively short half-life of 65 hours, which makes it suitable for these medical evaluations because it does not linger long within the body.
Some key features of mercury-197 include:

• It is a gamma emitter, making its detection easy with suitable equipment.
• The short half-life reduces the long-term radiation exposure risk for patients.
• Being a heavy element, mercury-197 is easily absorbed in tissues, which aids in medical imaging.

Kidney Function Evaluation

Radioactive isotopes like mercury-197 are employed in evaluating kidney function due to their ability to travel through specific body systems.
In this process, the isotope is introduced to the body, where it is filtered by the kidneys.
Doctors measure the rate at which the substance passes through the kidneys, which reveals important details about the kidneys' performance. This method is advantageous because:

• It provides a non-invasive way to assess kidney function.
• The test can detect abnormalities in how kidneys filter blood.
• It offers precise measurements of kidney filtration rate.

Understanding this process is essential for diagnosing and monitoring various kidney-related conditions effectively. Ensuring accurate evaluations helps in determining the best treatments and monitoring treatment progress over time.