Problem 74 - Chemistry The Science in Context

Question

Several isotopes of arsenic are used in medical imaging. Which isotope, \(^{72}\) As or \(^{77}\) As, is more likely to be useful for PET imaging?

Step-by-Step Solution

Answer

Answer: \(^{72}\) As is more suitable for PET imaging because it undergoes positron emission (β+ decay) with a half-life of approximately 26 hours, whereas \(^{77}\) As decays through electron capture and does not undergo positron emission.

Step 1: Positron emission is a type of radioactive decay in which a proton in the nucleus of an atom is converted into a neutron, and a positron is emitted. This can be represented by the general equation: $$ _{Z}^{A}X \rightarrow _{Z-1}^{A}Y + _1^0e $$ where X is the original atom, Y is the result of decay, A is the mass number, Z is the atomic number, and e represents the emitted positron. For isotopes to be useful in PET imaging, they must undergo positron emission. #Step 2: Isotope Decay Modes#

To determine the decay modes of the given isotopes of arsenic, \(^{72}\) As and \(^{77}\) As, you can consult a reference table or source (such as a textbook or database) that lists the decay modes of isotopes. #Step 3: Comparing Decay Modes for \(^{72}\) As and \(^{77}\) As#

Step 2: After consulting a reference source, we find that: - \(^{72}\) As undergoes positron emission (β+ decay) with a half-life of approximately 26 hours. - \(^{77}\) As undergoes electron capture, not positron emission, with a half-life of about 38.8 hours. #Step 4: Determining the Suitable Isotope for PET Imaging#

Since \(^{72}\) As undergoes positron emission, it is suitable for PET imaging, while \(^{77}\) As is not, as it decays through electron capture. Therefore, the more likely isotope to be useful for PET imaging is \(^{72}\) As.

Key Concepts

Positron Emission Tomography

Positron Emission Tomography, commonly known as PET, is a sophisticated imaging technique used in medical diagnostics to observe metabolic processes in the body. The core of a PET scan lies in the detection of gamma rays emitted indirectly by a positron-emitting radionuclide (tracer), which is introduced into the body on a biologically active molecule.

In the context of PET imaging, radioactive isotopes are carefully selected to have the property of positron emission. This process involves a proton in the nucleus being converted into a neutron and simultaneously releasing a positron, the antimatter counterpart of an electron. When a positron encounters an electron, annihilation occurs, producing a pair of gamma rays that move in approximately opposite directions. These gamma rays are detected by the PET scanner and used to construct detailed images of the tracers’ concentration within the body. This information is invaluable for diagnosing and monitoring a range of diseases, including cancer and neurological disorders.

Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation in the form of particles or electromagnetic waves. There are several types of decay, including alpha, beta, and gamma decay. Specifically, for PET imaging, we are interested in beta-plus decay, or positron emission.

During positron emission, a proton in the nucleus is converted into a neutron and a positron (\( _{1}^{0}e \) or \beta^+). This emitted positron travels a short distance before it interacts with an electron, leading to the production of two gamma photons. These photons are detected by the PET scanner, allowing for the generation of images.

The isotope’s decay mode and half-life are critical factors in its suitability for medical imaging. Isotopes with too short a half-life can decay before imaging is possible, while those with too long a half-life pose prolonged radiation risks. The ideal isotope for PET has a perfect balance: a half-life long enough to perform the diagnostic procedure but short enough to minimize radiation exposure.

Isotopes of Arsenic

Arsenic has several isotopes, each with different properties and potential applications. When discussing isotopes for PET imaging, it's important to focus on their mode of decay and half-life. Isotopes that undergo beta-plus decay (positron emission) are the ones of interest.

The understanding of decay modes comes from consulting reliable nuclear databases or textbooks, which indicate that arsenic-72 (\( ^{72}As \)) undergoes positron emission suitable for PET, while arsenic-77 (\( ^{77}As \) does not. This is essential because PET imaging relies on the detection of gamma rays from positron annihilation events. An isotope that undergoes electron capture, like arsenic-77, does not emit positrons and is therefore not useful for PET.

In summary, for PET applications, an ideal isotope is one that has a suitable half-life and undergoes positron emission, making arsenic-72 a potential candidate for such medical imaging diagnostics, as it fits the required characteristics.