Chapter 8: Problem 61
Fluorine-18 is an isotope used in Positron Emission Tomography (PET) to scan the brain. If a researcher has \(1.50 \mu \mathrm{g}\) of \({ }^{18} \mathrm{~F}\), how long before it decays to \(1.0\) ng? The half-life of \({ }^{18} \mathrm{~F}\) is \(109.8\) minutes. a. \(2.9 \times 10^{-2}\) hours b. 91 hours c. 39 hours d. 19 hours
Short Answer
Step by step solution
Understand the problem
Convert units
Apply the decay formula
Solve for time t
Calculate t in minutes
Convert t to hours
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Half-life Calculation
For instance, the decay of a substance can be described mathematically as follows: \[N(t) = N_0 \left(\frac{1}{2}\right)^{\frac{t}{T_{1/2}}}\]where:
- \( N(t) \): Remaining mass at time \( t \)
- \( N_0 \): Initial mass
- \( T_{1/2} \): Half-life of the substance
Fluorine-18
Fluorine-18 has a relatively short half-life of approximately 109.8 minutes. This is ideal for medical imaging because the isotope decays quickly enough to minimize long-term radiation exposure to patients but allows sufficient time to conduct a PET scan. During its decay, Fluorine-18 releases positrons. When these positrons encounter electrons, they annihilate, producing gamma rays that the PET scanner detects to create detailed images of the body's internal structures and functions.
In practice, this means that handling and storing Fluorine-18 requires stringent safety protocols due to its radioactive nature. Nevertheless, its short lifespan demands efficient logistics to ensure that it is utilized in medical scans soon after production.
Positron Emission Tomography (PET)
PET scans take advantage of the properties of substances like Fluorine-18, which emit positrons during decay. These positrons travel short distances before encountering electrons, resulting in the emission of gamma rays. PET scanners detect these gamma rays to produce comprehensive images of metabolic processes.
PET is predominantly used in oncology, cardiology, and neurology. The scans allow healthcare professionals to detect abnormalities and monitor disease progression by revealing changes in cellular activity. This makes PET a valuable tool for early detection of cancers, brain disorders, and heart diseases, offering insights that other imaging techniques might not reveal.
The precision of PET is remarkable as it doesn't just show structural changes but can illustrate functional activities within tissues. This aspect is pivotal in advancing personalized medicine and treatment plans tailored specifically to a patient's unique physiological conditions.
Unit Conversion in Chemistry
In the context of radioactive decay, converting units like micrograms to nanograms can be crucial. For instance:
- 1 microgram (\(\mu\text{g}\)) = 1000 nanograms (ng)
- This fact helps standardize units for calculations involving changes in mass
Learning to adeptly navigate between units often involves dimensional analysis, allowing for smooth transitions between complex conversions in chemistry problems. Over time, this skill enhances accuracy in laboratory settings and when working with theoretical problems in scientific research.