What changes occur to the atomic number and mass of a nucleus during each of the following decay scenarios? (a) an \(\alpha\) particle is emitted (b) a \(\beta\) particle is emitted (c) Y radiation is emitted (d) a positron is emitted (e) an electron is captured

Understanding alpha decay is essential to grasp changes in an atom's nucleus. When an alpha particle, consisting of 2 protons and 2 neutrons, is emitted, the atom undergoes a significant transformation. As a result, the atomic number, representing the number of protons, decreases by 2, thus altering the element to a different one. Simultaneously, the atomic mass number decreases by 4, given the loss of both protons and neutrons. Importantly, this form of decay can be easily shielded, as alpha particles have limited penetration power and can be stopped by a sheet of paper.

One common example of alpha decay is the transformation of uranium-238 into thorium-234. This process contributes to the natural radioactive decay series and is crucial for fields like geology and archaeology for dating ancient objects.

Beta decay occurs when a neutron in the nucleus is converted into a proton and a beta particle, which is essentially an electron, is emitted. This reaction increases the atomic number by 1, because there is one more proton in the nucleus, yet it does not affect the atomic mass number, as the mass of an electron is negligible compared to that of protons and neutrons. Beta decay is further categorized into beta-minus and beta-plus decay, depending on whether an electron or positron is emitted.

Digging deeper, beta-minus decay is a response by the nucleus to an excess of neutrons, whereas beta-plus decay, also known as positron emission, corrects a surplus of protons. Beta particles have greater penetration power than alpha particles but can still be stopped by materials like aluminum.

Gamma decay is fascinating because it involves no change in the atomic or mass numbers of an atom. When gamma rays, which are high-energy photons, are emitted, they carry away excess energy from an excited atomic nucleus. This process typically follows alpha or beta decay, which can leave the nucleus at higher energy levels. While gamma radiation does not alter the identity of the atom, it does result in a more stable nucleus.

Due to their high energy, gamma rays are highly penetrating and require dense materials, like lead or thick concrete, for shielding. Their ability to pass through most substances makes them useful in medical imaging and treatment but also poses significant health risks if not managed properly.

Positron emission, or beta-plus decay, is a less common type of beta decay wherein a proton is transformed into a neutron, releasing a positron—the antiparticle of an electron. This intriguing occurrence decreases the atomic number by 1 but leaves the atomic mass unchanged. Positrons are antimatter; they annihilate upon encountering electrons, producing gamma radiation.

In the world of medicine, positron emission is ingeniously harnessed in PET scans (Positron Emission Tomography), an imaging technique that uses radioactive tracers to visualize metabolic processes in the body. Understanding positron emission also contributes to our knowledge of fundamental particle physics and the workings of the universe.

Electron capture is a less intuitive process, but it plays a vital role in nuclear transformations. In this process, an electron from an atom's inner shell is drawn into the nucleus, where it combines with a proton to form a neutron, hence reducing the atomic number by 1. The mass number remains the same, as the capture does not add or remove nucleons from the nucleus. This capture usually leads to an excited nucleus that then releases energy, often in the form of an X-ray or a subsequent gamma ray emission.

Electron capture is particularly significant in the decay of some isotopes used in medical diagnostics and the study of neutrino masses. This process is also a form of nature's balancing act, as it tends to occur in nuclei with a high proton-to-neutron ratio.