In \(\beta\) -decay, an electron comes out from an atom. The electron comes out due to nuclear change, not from the orbit of the atom. It may be explained by the fact that on \(\beta\) -decay, (a) the atomic number increases by one unit. (b) the mass number remains unchanged. (c) the atomic species get changed. (d) the atomic species remains unchanged.

Understanding radioactive decay is fundamental in the study of nuclear chemistry. It refers to the process by which an unstable atomic nucleus loses energy by emitting radiation. This emission can include alpha particles, beta particles, gamma rays, or other particles. Specifically, beta decay is one such type of radioactive decay where an electron, known as a beta particle, is ejected from the nucleus. This occurrence signifies a transformation internally within the nucleus where a neutron is converted into a proton, or vice versa. This process is spontaneous and results in the transmutation of one element into another, effectively changing the nature of the atom.

It is essential to recognize that during radioactive decay, the nucleus is seeking a more stable configuration. As a result, the atoms of some elements exist in nature with unstable combinations of protons and neutrons, leading them to undergo radioactive decay over time. Through beta decay, the atom achieves greater stability. Radioactive materials have a range of half-lives - the time required for half of the radioactive atoms to decay - which can be seconds, years, or even millions of years.

Nuclear chemistry is the branch of chemistry that deals with the reactions and transformations that occur in the nucleus of an atom. It encompasses a variety of processes, including radioactive decay, nuclear fission, and nuclear fusion. In nuclear reactions, unlike ordinary chemical reactions that involve electrons and result in the formation of different molecules, the protons and neutrons within an atomic nucleus are altered.

One of the fascinating aspects of nuclear chemistry is that it can lead to changes in the identity of elements, as seen with beta decay. These changes are at the heart of many applications, such as in medicine with the use of radioactive isotopes for diagnosing and treating diseases, or in energy where nuclear reactions power our nuclear reactors. What sets nuclear chemistry apart is the significant energy involved in these processes, due to the change in the nucleus, which dwarfs the energy changes in molecular reactions.

The atomic number is a fundamental property of an element and plays a significant role in its chemical behavior. Defined as the number of protons in the nucleus of an atom, the atomic number determines the identity of an element. For example, carbon atoms always have six protons, giving them an atomic number of six. During beta decay, this number changes since either a proton is added or removed from the nucleus.

In the context of beta decay, when a neutron turns into a proton, the atomic number increases by one, as evidenced in solution step 2. This seemingly small change has profound implications because it means the atom has transformed into a different element. As all elements are organized by their atomic number on the periodic table, a change in atomic number effectively moves the atom to a new position on this table.

The mass number, sometimes referred to as the nucleon number, is another crucial term in nuclear chemistry. It represents the total number of protons and neutrons, known collectively as nucleons, in an atomic nucleus. It's important to note that the mass number is not the same as the atomic mass, which is the actual mass of an atom and might include the small weight contributed by electrons.

The significance of the mass number in beta decay becomes clear when noting that despite a neutron being transformed into a proton (or vice versa), the number of nucleons remains unaffected. This maintenance of the mass number, as discussed in solution step 3, is essential in understanding that while the element's identity changes, the atom doesn't gain or lose its overall nucleon content.

Delving into atomic species transformation offers a clearer picture of what happens during beta decay. This phenomenon is an incredible aspect of nuclear chemistry that involves changing one type of atom into another. In beta decay, as a neutron is converted into a proton within the nucleus, it alters the atomic number, which as we've learned, defines the element types. This means the original atomic species has been transformed into a new one.

Using an everyday analogy, imagine changing an apple into an orange merely by rearranging its internal composition. In gamma decay, radioactive atoms undergo a similar incredible transformation, albeit through different processes. The ability of elements to transmute through natural radioactive processes is a central theme in the study of nuclear reactions and underpins various technological applications, from energy production to medical imaging and treatments.