Problem 81 - Chemistry The Central Science In Si Units

Question

Each of the following transmutations produces a radionuclide used in positron emission tomography (PET). (a) In equations (i) and (ii), identify the species signified as "X." (b) In equation (iii), one of the species is indicated as "d." What do you think it represents? (i) \({ }^{14} \mathrm{~N}(\mathrm{p}, \alpha) \mathrm{X}\) (ii) \({ }^{18} \mathrm{O}(\mathrm{p}, \mathrm{X})^{18} \mathrm{~F}\) (iii) \({ }^{14} \mathrm{~N}(\mathrm{~d}, \mathrm{n})^{15} \mathrm{O}\)

Step-by-Step Solution

Answer

(a) X = \(^{11} C\) in (i) and a neutron \(n\) in (ii). (b) "d" represents a deuteron.

Step 1: Analyzing Equation (i)

The nuclear reaction, \(^{14} \mathrm{~N}(\mathrm{p}, \alpha) \mathrm{X}\), involves a nitrogen-14 atom (\(^{14} \mathrm{~N}\)) being bombarded with a proton (\(\mathrm{p}\)) to produce an alpha particle (\(\alpha\)) and another species represented by \(X\). An alpha particle consists of 2 protons and 2 neutrons, which is a helium nucleus (\(^4_2\mathrm{He}\)). To find \(X\), apply conservation of mass and atomic numbers: Mass: 14 (N) + 1 (p) = 4 (alpha) + A (X); Atomic Number: 7 (N) + 1 (p) = 2 (alpha) + Z (X). Solving gives \(A = 11\), \(Z = 6\), identifying \(X\) as \(^{11} \mathrm{C}\).

Step 2: Analyzing Equation (ii)

For the reaction, \(^{18} \mathrm{O}(\mathrm{p}, \mathrm{X})^{18} \mathrm{~F}\), an oxygen-18 atom (\(^{18} \mathrm{O}\)) is bombarded with a proton (\(\mathrm{p}\)) to produce another species \(X\) and fluorine-18 (\(^{18} \mathrm{~F}\)). Apply conservation laws: Mass: 18 (O) + 1 (p) = A (X) + 18 (F); Atomic Number: 8 (O) + 1 (p) = Z (X) + 9 (F). Solving gives \(A = 1\) and \(Z = 0\), indicating \(X\) is a neutron (\(n\)).

Step 3: Analyzing Equation (iii)

In the reaction, \(^{14} \mathrm{~N}(\mathrm{~d}, \mathrm{n})^{15} \mathrm{O}\), nitrogen-14 (\(^{14} \mathrm{~N}\)) interacts with \(d\) to produce a neutron (\(n\)) and oxygen-15 (\(^{15} \mathrm{O}\)). Here, \(d\) represents a deuteron, which is similar to a proton but with an additional neutron (\(^2_1 \mathrm{H}\) or \(\mathrm{d}\)). The transmutation is a deuteron interaction with nitrogen-14, leading to the release of a neutron and the formation of oxygen-15.

Key Concepts

Positron Emission Tomography (PET)

Positron Emission Tomography, or PET, is a fascinating and powerful imaging technique used in medical diagnostics. It allows doctors to look deep inside the body and observe how tissues and organs are functioning in real-time. This non-invasive method uses radioactive isotopes as tracers. These tracers emit positrons, which are tiny particles with a positive charge, similar to electrons but with opposite polarity.

Once injected into the body, these tracers accumulate in targeted areas, commonly areas with high chemical activity, which typically corresponds with disease processes. As the positrons encounter electrons in the body, they annihilate, producing gamma rays that are detected by the PET scanner. This results in detailed 3D images that help in diagnosing and monitoring diseases like cancer.

In the context of nuclear reactions, PET tracers like Carbon-11 ( ^{11}C ) and Fluorine-18 ( ^{18}F ) are produced by transmuting stable atoms into radioactive isotopes. Understanding these reactions ensures the safe and effective use of PET in the medical field, making it a crucial technique in modern diagnostic medicine.

Conservation of Mass and Atomic Numbers

In nuclear reactions, understanding the conservation of mass and atomic numbers is essential. These principles ensure that during a nuclear reaction, although the particles involved may change, the overall balance of mass and the balance of charge remain constant.

When a nuclear reaction occurs, the sum of masses (in terms of atomic mass units) and the sum of atomic numbers (which represents the number of protons) for the reactants must equal the sum for the products. This is the crux of the nuclear equation balancing act.

• For example, in the equation \({ }^{14} \mathrm{~N}( ext{p}, \alpha) \mathrm{X}\), a nitrogen atom is bombarded with a proton, leading to an alpha particle and another species \(X\). Applying the conservation laws, we understand how \(X\), \(^{11} \mathrm{C}\) due to the balanced masses and atomic numbers, emerges from this interaction.

This foundational concept allows scientists to predict the outcomes of nuclear reactions and to ensure that all calculations regarding isotopes are accurate and safe for applications like PET scans.

Deuteron Interactions

Deuterons play a significant role in nuclear reactions, especially in medical imaging applications like producing isotopes for PET scans. A deuteron is an isotope of hydrogen, specifically \(^{2}_1\mathrm{H}\), also referred to as 'd'. It consists of one proton and one neutron, making it twice as heavy as a regular hydrogen nucleus.

In nuclear reactions, deuterons are used to bombard other nuclei - in our example, the use of deuterons in the equation \(^{14} \mathrm{~N}( ext{d}, \text{n})^{15} \mathrm{O}\) results in the transmutation of nitrogen-14 into oxygen-15. This process also liberates a neutron.

The characteristic of deuterons makes them especially useful for creating certain radioactive isotopes necessary in PET imaging. Their role underscores the intricate interactions in nuclear chemistry that contribute to advancements in medical diagnostics, offering improved options for disease detection and monitoring.