Technetium-99 is prepared from \(^{98}\) Mo. Molybdenum- 98 combines with a neutron to give molybdenum- \(99,\) an unstable isotope that emits a \(\beta\) particle to yield an excited form of technetium- 99 , represented as \(^{99} \mathrm{Tc}^{*}\). This excited nucleus relaxes to the ground state, represented as \(^{99} \mathrm{Tc}\), by emitting a \(\mathrm{y}\) ray. The ground state of \(^{99} \mathrm{Tc}\) then emits a \(\beta\) particle. Write the equations for each of these nuclear reactions.

Neutron capture is a nuclear process where an atomic nucleus absorbs a neutron, becoming a heavier isotope. This reaction is pivotal in nuclear chemistry and reactor design, as it plays a crucial role in forming elements and isotopes.

For example, in the production of technetium-99, a stable isotope of molybdenum, molybdenum-98 (^{98}Mo), absorbs a neutron and transforms into molybdenum-99 (^{99}Mo), an unstable isotope. It's important to note that this process doesn't change the atomic number, which denotes the identity of the element, but instead increases the mass number by one due to the added neutron.

Beta decay is a common type of radioactive decay involving the emission of beta particles. During this process, a neutron is changed into a proton within the nucleus, and an electron – the beta particle – along with an antineutrino are ejected.

For molybdenum-99, this transformation leads to the creation of a new element, technetium-99 (^{99}Tc), albeit in an excited state, noted as technetium-99*. This fundamental shift results in a changing atomic number while the mass number remains constant. This is a quintessential event that accurately showcases one of the methods through which elements are transformed on the periodic table.

After the beta decay of molybdenum-99, the resulting technetium-99 is in an excited state with excess energy. This state is unstable, and the nucleus releases this surplus energy in the form of gamma rays – pure electromagnetic energy – to transition to a stable or 'ground' state.

Gamma rays don't alter either the atomic or mass numbers of a nucleus, as they occur without any particle emission. The discharge of these rays can be detected and measured, and their study is a cornerstone in nuclear physics to understand the internal workings of atomic nuclei. Gamma emission is also used in medical imaging techniques, such as PET scans, due to its ability to pass through the human body, providing a non-invasive diagnostic tool.

Technetium-99 (^{99}Tc) is a radioisotope of great interest in medical diagnostics, particularly for its use in radiopharmaceuticals for imaging applications. The production of this isotope follows a sequence of nuclear reactions beginning with neutron capture by molybdenum-98 and subsequent beta decay to form excited technetium-99. Following a gamma emission to reach a stable state, it undergoes a second beta decay, but it's important to note that the most stable form of technetium-99 eventually decays into ruthenium-99 (^{99}Ru), closing the cycle of transformations.

The entire process is critical not only for creating useful isotopes but also for shedding light on fundamental nuclear physics, the principles of which enable multiple applications in science, medicine, and industry.