Write a partial decay series for Th-232 undergoing these sequential decays. $$ \alpha, \beta, \beta, \alpha $$

Alpha decay is a type of radioactive decay where an unstable atomic nucleus emits an alpha particle and transforms into a new nucleus. An alpha particle consists of two protons and two neutrons, which is equivalent to a helium-4 nucleus. During this process, the mass number of the atom (the total number of protons and neutrons) decreases by four and its atomic number (the number of protons) decreases by two.

This can be represented in a nuclear equation, where the parent nuclide (in this case, Thorium-232 or \textsuperscript{232}Th) will release an alpha particle (\textsuperscript{4}He) to form a new nuclide. Here's how the equation looks:\[\textsuperscript{232}_{90}Th \rightarrow \textsuperscript{4}_{2}He + \textsuperscript{228}_{88}Ra\]
The product of this reaction, in the exercise, is Radium-228. Alpha decay often occurs in the heavy elements found in the lower part of the periodic table.

Beta decay is another form of radioactive decay where a beta particle is emitted. Beta particles can be either electrons or positrons, and the decay can happen in two ways: beta-minus (\textsuperscript{\beta-}) or beta-plus (\textsuperscript{\beta+}) decay. In \textsuperscript{\beta-} decay, a neutron is converted into a proton and an electron, where the electron is then emitted from the nucleus, while in \textsuperscript{\beta+} decay, a proton is converted into a neutron and a positron.

During beta decay, the atomic number of the nuclide will increase by one if it's a \textsuperscript{\beta-} decay, or decrease by one if it's a \textsuperscript{\beta+} decay. The mass number, however, remains unchanged. For instance, when Radium-228 (from the previous alpha decay) undergoes \textsuperscript{\beta-} decay, it transforms into Actinium-228:\[\textsuperscript{228}_{88}Ra \rightarrow \textsuperscript{0}_{-1}e + \textsuperscript{228}_{89}Ac\]
By emitting a beta particle, Ra-228 changes its composition to become Ac-228, with an increased atomic number due to the gained proton.

Nuclear chemistry is the field of chemistry that deals with the reactions and processes involving the atomic nucleus. It encompasses the study of radioactive decay, fission, fusion, and the synthesis of new elements — essentially, the changes in the composition of atomic nuclei. Nuclear chemistry has immense implications in various fields ranging from energy production through nuclear power plants, to medical treatments via radiotherapy and diagnostic imaging, as well as applications in tracing mechanisms within a chemical reaction or biological system by using radioisotopes.

Understanding nuclear equations, such as those for alpha and beta decay, is fundamental to mastering nuclear chemistry. It requires knowledge of the stability of atomic nuclei and the ways in which they can transform to achieve more stable configurations. The decay series exercise embodies the principles of nuclear chemistry by showcasing the sequential transformations that occur as unstable isotopes strive for stability.

Radioactive isotopes, or radionuclides, are variants of elements with an unstable combination of neutrons and protons in their nuclei, leading to spontaneous emission of radiation as they change to a more stable configuration. A wide array of radioactive isotopes exist, each with its specific mode of decay, half-life — the time it takes for half of a given sample to decay — and radiation type emitted.

Medical imaging, cancer treatment, radioactive dating, and power generation are just a few applications that rely on the unique properties of radioactive isotopes. The decay series, as presented in the exercise with Th-232, is a common method to demonstrate the conversion of an isotope through successive radioactive processes until reaching a stable form. Understanding these processes is crucial in various scientific and industrial fields that utilize radioactive isotopes.