Determine the particle emitted and write the balanced nuclear equation for each of the following nuclear transformations: (a) sodium-24 to magnesium-24; (b) \({ }^{128} \mathrm{Sn}\) to \({ }^{128} \mathrm{Sb}\); (c) lanthanum-140 to barium-140; (d) \({ }^{228} \mathrm{Th}\) to \({ }^{224} \mathrm{Ra}\).

When we dive into the realm of nuclear physics, we encounter various types of radioactive decay. One of these fascinating processes is the beta-plus decay. Simply put, beta-plus decay occurs when a proton within an unstable nucleus is transformed into a neutron, releasing a positively charged beta particle, known as a positron, and a neutrino.

The general equation for beta-plus decay is as follows:\[^{A}_{Z}X \rightarrow ^{A}_{Z-1}Y + ^{0}_{+1}e + u_e\]In this equation, \(^{A}_{Z}X\) is the unstable isotope that undergoes decay, \(^{A}_{Z-1}Y\) represents the new isotope formed, \(^{0}_{+1}e\) stands for the emitted positron, and \(u_e\) is the neutrino.

This type of decay is crucial in the field of medicine, particularly in positron emission tomography (PET) scans, which utilize the emitted positrons to create detailed images of the body.

Nuclear transformation is a fascinating process that involves changing one element into another. This process is at the heart of many nuclear reactions, including the radioactive decay paths and artificial transmutation. It is the change in the identity or characteristics of an atomic nucleus that occurs when it is bombarded with an energetic particle.

For instance, the transformation of Sodium-24 into Magnesium-24, as seen in the textbook exercise, is a result of beta-plus decay. The atomic number changes due to the emission of a positron, which effectively converts a proton into a neutron, thereby transforming the nucleus from one element to another without altering the mass number.

Understanding nuclear transformation is essential, not only for comprehending radioactive decay but also for grasping how elements are formed in stars and how scientists create new elements in laboratories.

Stepping further into the quantum field, positron emission is a type of beta decay in which a proton in an unstable atomic nucleus is converted into a neutron while releasing a positron. But what exactly is a positron? It’s a subatomic particle with the same mass as an electron but with a positive electric charge (hence the name 'beta-plus').

Here’s what happens during positron emission:\[^{A}_{Z}X \rightarrow ^{A}_{Z-1}Y + ^{0}_{+1}e\]When a positron is emitted from the nucleus, the atom's atomic number decreases by one since a proton has been converted into a neutron, thereby producing a different element, as is the case with sodium turning into magnesium in our textbook example.

Positron emission is instrumental in several applications, most notably in medical imaging techniques like PET scans which take advantage of this phenomenon to assist in the diagnosis and treatment planning of various health conditions.