Write a nuclear equation for positron emission by each nuclide. (a) C-11 (b) N-13 (c) O-15

Beta decay is a type of nuclear process in which an unstable atom undergoes transformation to become more stable. During this process, a beta particle, which can be an electron or its antiparticle a positron, is emitted. In the specific case of positron emission, a proton inside the atom's nucleus is converted into a neutron, and a positron is released. This transformation causes the atom's atomic number to decrease by one, leading to the creation of a new element, whereas the mass number remains unchanged. In essence, the core of the atom, known as the nucleus, is rejigged to reach a tad more stable configuration.

Positron emission is a captivating form of beta decay as it involves the emission of antimatter, a counterpart to electrons with a positive charge. Because of its nature, positron emission is extensively used in medical imaging, specifically in positron emission tomography (PET) scans, helping doctors to spot active organs and tissues.

Nuclear equations are pivotal in illustrating the changes occurring inside an atom's nucleus during nuclear reactions. The equation consists of symbols that represent the isotopes involved in the reaction along with the particles emitted or absorbed. Nuclear equations allow us to concisely convey the concept of the conservation of nucleon number and electric charge in these reactions.

In the case of positron emission, the nuclear equation demonstrates the transformation of the original nucleus to a new nucleus and a positron (\( _{+1}^{0}e \)). The fundamentals of writing nuclear equations include balancing both the mass numbers (top numbers) and atomic numbers (bottom numbers) on both sides of the reaction arrow. For example, when carbon-11 emits a positron, the equation shows that the carbon transforms into boron-11, with no change in mass number but a decrease in atomic number.

Nuclear chemistry delves into the heart of the atom, dealing with the changes that occur within nuclei. It encompasses a broad range of phenomena, including radioactivity, fission, and fusion, along with their applications, effects, and the transformation of elements. In the study of positron emission, nuclear chemistry allows us to understand the underlying principles that govern this specific type of nuclear instability and the conditions under which a nucleus will emit a positron.

Grasping the intricacies of nuclear chemistry is crucial for unlocking a variety of technological advances, particularly in energy production and medicine. By unraveling the secrets of the atomic nucleus, chemists can craft new materials, devise innovative cancer treatments and contribute to energy solutions through nuclear power.

Isotopes are atoms of the same element that differ in the number of neutrons within their nucleus, giving them unique mass numbers. Despite these differences, isotopes of an element share the same number of protons, ensuring they have identical chemical properties. Some isotopes are stable, while others are unstable, or radioactive, often resulting in phenomena such as positron emission as they seek stability.

For instance, Carbon-11, Nitrogen-13, and Oxygen-15 are all radioactive isotopes undergoing positron emission. Understanding isotopes is not just a curiosity—it's essential in numerous fields, including geology for dating rocks, in medicine for treatments and diagnostics, as well as in physics and chemistry for a variety of research purposes. Isotopes provide us a deeper insight into the building blocks of our world, explaining why some atoms undergo radioactive decay while others remain unchanged for eons.