Chapter 9: Problem 35
In a diagnostic test for leukemia, a person receives \(4.0 \mathrm{~mL}\) of a solution containing selenium- \(75 .\) If the activity of the selenium-75 is \(45 \mu \mathrm{Ci} / \mathrm{mL}\), what dose, in \(\mu \mathrm{Ci}\), is given?
Short Answer
Expert verified
The dose given is 180 μCi.
Step by step solution
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Radioactivity
Radioactivity is the process by which unstable atomic nuclei release energy in the form of particles or photons. Elements like selenium-75 are radioactive because their nuclei are not stable and thus undergo radioactive decay. Medical diagnostics often use radioactive isotopes like selenium-75 because they emit radiation that can be detected and measured to provide critical information about bodily functions or to diagnose diseases like leukemia.
This radiation can be in the form of alpha particles, beta particles, or gamma rays. The unit used to measure radioactivity is the curie (Ci), and one μCi (microcurie) is one-millionth of a curie, which indicates a very small amount of radioactivity suitable for medical tests. Understanding radioactivity helps in understanding how these diagnostic tests work and what the readings signify.
In leukemia diagnostic tests, a small, controlled amount of a radioactive substance is administered to the patient. The goal is to use the emitted radiation to gather information about the disease's presence and progression without causing harm.
This radiation can be in the form of alpha particles, beta particles, or gamma rays. The unit used to measure radioactivity is the curie (Ci), and one μCi (microcurie) is one-millionth of a curie, which indicates a very small amount of radioactivity suitable for medical tests. Understanding radioactivity helps in understanding how these diagnostic tests work and what the readings signify.
In leukemia diagnostic tests, a small, controlled amount of a radioactive substance is administered to the patient. The goal is to use the emitted radiation to gather information about the disease's presence and progression without causing harm.
Dose Calculation
Dose calculation in medical diagnostics is crucial for ensuring patient safety while achieving accurate results. The concept revolves around determining how much of a radioactive substance, in this case selenium-75, is administered to a patient. This is typically done by calculating the product of the volume of the solution administered and the activity per unit volume (mL).
In our exercise, we have:
Volume of the solution, \( V = 4.0 \text{ mL} \) and Activity of selenium-75 per milliliter, \( A = 45 \text{ μCi/mL} \)
To find the total dose, we use the formula:
\( \text{Total Dose} = V \times A \)
Substituting the given values:
\( \text{Total Dose} = 4.0 \text{ mL} \times 45 \text{ μCi/mL} \)
Multiplying these gives:
\( \text{Total Dose} = 180 \text{ μCi} \)
This calculation tells us that the patient receives a dose of 180 μCi of selenium-75. Proper dose calculation ensures the patient receives enough of the radioactive substance to be effective but not so much that it could cause harm.
In our exercise, we have:
Volume of the solution, \( V = 4.0 \text{ mL} \) and Activity of selenium-75 per milliliter, \( A = 45 \text{ μCi/mL} \)
To find the total dose, we use the formula:
\( \text{Total Dose} = V \times A \)
Substituting the given values:
\( \text{Total Dose} = 4.0 \text{ mL} \times 45 \text{ μCi/mL} \)
Multiplying these gives:
\( \text{Total Dose} = 180 \text{ μCi} \)
This calculation tells us that the patient receives a dose of 180 μCi of selenium-75. Proper dose calculation ensures the patient receives enough of the radioactive substance to be effective but not so much that it could cause harm.
Selenium-75
Selenium-75 is a radioactive isotope of selenium, widely used in medical diagnostics. Its use leverages its ability to emit gamma radiation, which can be detected with special equipment to diagnose conditions such as leukemia. Selenium-75 has a half-life of about 119.78 days, meaning that every 119.78 days, half of the selenium-75 atoms will have decayed into another element.
Gamma rays emitted by selenium-75 allow doctors to trace its movement and location within the body, helping them to identify abnormal areas where these rays are concentrated. Because it has this property, it becomes useful in scans that image organs or tissues.
Special precautions are taken when dealing with selenium-75 to protect both the patient and healthcare providers from excessive radiation. This underscores the importance of accurate dose calculations to balance diagnostic effectiveness with safety. Therefore, understanding selenium-75's properties and handling is crucial in its application in the medical field.
Gamma rays emitted by selenium-75 allow doctors to trace its movement and location within the body, helping them to identify abnormal areas where these rays are concentrated. Because it has this property, it becomes useful in scans that image organs or tissues.
Special precautions are taken when dealing with selenium-75 to protect both the patient and healthcare providers from excessive radiation. This underscores the importance of accurate dose calculations to balance diagnostic effectiveness with safety. Therefore, understanding selenium-75's properties and handling is crucial in its application in the medical field.
