Oxygen-15, used in PET scans, has a 2.0-min half-life. A...

Oxygen-15, used in PET scans, has a 2.0-min half-life. A hospital cyclotron produces $2.60 \mathrm{mg}$ of ${ }^{15} \mathrm{O} .$ (a) It's delivered to the diagnostic facility 6.0 min later. How much ${ }^{15} \mathrm{O}$ remains at this time? (b) After another $4.0 \mathrm{~min}$, the ${ }^{15} \mathrm{O}$ is injected into a patient. How much is there at that point?

Oxygen-15, used in PET scans, has a 2.0-min half-life. A hospital cyclotron produces $2.60 \mathrm{mg}$ of ${ }^{15} \mathrm{O} .$
(a) It's delivered to the diagnostic facility 6.0 min later. How much ${ }^{15} \mathrm{O}$ remains at this time? (b) After another $4.0 \mathrm{~min}$, the ${ }^{15} \mathrm{O}$ is injected into a patient. How much is there at that point?

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Key Concepts

Cyclotron Production of Radionuclides

This concept involves the use of a cyclotron, a type of particle accelerator, to produce radioactive isotopes for medical applications. It is a key method for generating short-lived isotopes that are otherwise not found in nature, which are then used in diagnostic imaging techniques such as PET scans.

Exponential Decay Equation

This is the mathematical formula used to calculate the remaining quantity of a radioactive substance over time. The equation, N(t) = N0 × (1/2)^(t/T½), where N0 is the initial quantity, t is the elapsed time, and T½ is the half-life, succinctly models how the substance decays exponentially.

Radioactive Decay

This is a process in which an unstable atomic nucleus loses energy by emitting radiation. Over time, the quantity of the radioactive substance decreases as the nuclei decay into more stable forms. This decay process is random at the level of single atoms but predictable in large numbers, and it follows a specific mathematical law.

Half-Life

This is the time required for half of a sample of a radioactive substance to decay. It is a characteristic property of each radioactive isotope and is used to determine how quickly the substance decays. The concept of half-life is fundamental in calculations related to radioactive decay processes.

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