Question

Each of the following isotopes is radioactive: (a) \(\frac{28}{15} \mathrm{P}\) (b) \(45 \mathrm{K} ;\) (c) \(^{73} \mathrm{Zn}\). Which would you expect to decay by 30 . \(\beta^{+}\) emission?

Short answer

The isotope \( ^{73}Zn \) is the one most likely to decay by \( \beta^{+} \) emission.

Step-by-step solution

Understanding Beta Plus Decay

In a Beta Plus decay, a proton is converted into a neutron in the nucleus. In this process, a positron (represented as \( \beta + \)) and a neutrino are emitted. This changes the atomic number (Z) and the mass number (A). The atomic number decreases by 1 while the mass number stays the same.

Analyze the Isotopes

We've given the following isotopes: (a) \( \frac{28}{15}P \) (b) \( 45 K \) (c) \( ^{73}Zn \). The atomic number is the number at the bottom of given isotope, while the mass number is the number at the top. For \( \frac{28}{15}P \), the atomic number is 15 and the mass number is 28. For \( 45 K \), we know that the atomic number of K (Potassium) is 19, thus the mass number is 45. For \( ^{73}Zn \), we know that the atomic number of Zn (Zinc) is 30, thus the mass number is 73.Analyzing the atomic numbers and mass numbers, we can conclude that \( \frac{28}{15}P \) and \( 45 K \) have more neutrons than protons while \( ^{73}Zn \) has more protons than neutrons. Since a Beta Plus decay is caused by an excess of protons, \( ^{73}Zn \) is likely to decay by \( \beta^{+} \) emission.

Final Thoughts

An isotope that has more protons than neutrons in its nucleus can undergo positron emission, or β+ decay. The nucleus will convert a proton into a neutron and a positron. The positron is then emitted from the atom's nucleus. Since \( ^{73}Zn \) has more protons than neutrons in its nucleus, it can undergo \( \beta^{+} \) emission.

Key concepts

Radioactive Isotopes

Radioactive isotopes, also known as radioisotopes, are versions of chemical elements that have an unstable combination of protons and neutrons in their nucleus, which makes them radioactive. The ratio of neutrons to protons determines the stability of a nucleus; when this ratio is imbalanced, the nucleus seeks stability through the process of radioactive decay.

For example, in the exercise provided, the isotope of Zinc (\( ^{73}Zn \) ) is described as having more protons than neutrons. This imbalance prompts it as a candidate for beta plus decay (\( \beta^{+} \) emission), which is one of several mechanisms by which a nucleus can decay toward a more stable state. Understanding the neutron-proton ratio is crucial for predicting the type of decay an unstable isotope will undergo and this ratio forms the basis of much of the work conducted in nuclear chemistry.

Positron Emission

Positron emission, also known as beta plus decay (\( \beta^{+} \) decay), occurs when a proton in an unstable nucleus is transformed into a neutron. This process emits a positron, the antimatter counterpart of the electron, along with a neutrino, which is an almost massless and chargeless particle.

In this form of decay, the atomic number of the isotope decreases by one, but the mass number remains unchanged because a proton (which contributes to the atomic number) is converted into a neutron (which does not affect the atomic number). For instance, zinc-73 (with 30 protons) becomes copper-73 (with 29 protons) after emitting a positron. The phenomenon of positron emission is not only significant in the field of nuclear chemistry but also in practical applications such as medical diagnostic imaging, specifically in positron emission tomography (PET) scans.

Nuclear Chemistry

Nuclear chemistry is the subfield of chemistry focused on the reactions and properties of atomic nuclei, including radioactive decay, fission, and fusion. In understanding nuclear chemistry, it's essential to grasp the concepts of isotopes and radioactive decay, such as alpha decay, beta decay (including beta plus and beta minus), and gamma decay.

The stability, half-life, and energy release associated with the different forms of decay are key topics within this area of study. For example, the beta plus decay illustrated in the exercise shows an application of nuclear chemistry concepts to determine the behavior of an unstable isotope (\( ^{73}Zn \) ). By exploring how and why certain isotopes undergo specific decay processes, we deepen our understanding of atomic structure and the forces acting within the nucleus, leading to groundbreaking applications in energy production, medical treatments, and beyond.