Write a series of nuclear equations in which Al-27 reacts with a neutron and the product undergoes an alpha decay followed by a beta decay.

Neutron capture is a type of nuclear reaction in which an atomic nucleus absorbs a free neutron. This process often occurs in nuclear reactors and stars, where free neutrons are abundantly available. When a nucleus captures a neutron, its mass number increases by one, but its atomic number remains the same, since neutrons carry no charge.

For instance, the aluminum isotope \( _{13}^{27}Al \) captures a neutron \( _{0}^{1}n \) to become \( _{13}^{28}Al \). The neutron capture process is crucial in nuclear chemistry and astrophysics, as it can lead to the formation of heavier elements and contribute to the nucleosynthesis in stars. Moreover, understanding neutron capture is important for the safety and efficiency of nuclear reactors.

Alpha decay is a type of radioactive decay in which an unstable atomic nucleus emits an alpha particle, which is essentially a helium nucleus consisting of two protons and two neutrons. This emission results in the decrease of the mass number by four and the atomic number by two.

Considering the example from the exercise, \( _{13}^{28}Al \) undergoes alpha decay to produce \( _{11}^{24}Na \) and an alpha particle \( _{2}^{4}He \).

Alpha decay is significant in understanding the stability of nuclei and is commonly observed in heavy elements. This form of decay can be dangerous if ingested or inhaled, as alpha particles are highly ionizing but have low penetration power. Nevertheless, it is less hazardous externally due to their low penetration, making them easy to shield.

Beta decay is a process by which a nucleus changes its identity by changing a neutron into a proton while ejecting an electron (beta particle) and an antineutrino. In the case of beta-minus decay, it increases the atomic number by one but keeps the mass number the same.

Following the steps in our example, \( _{11}^{24}Na \) undergoes beta decay, transforming into \( _{12}^{24}Mg \), with the emission of an electron and an antineutrino. This transition can be depicted as \( _{11}^{24}Na \rightarrow _{12}^{24}Mg + _{-1}^{0}e \).

Beta decay is essential for the stability of the nucleus and plays a key role in the lifespan of certain elements. It is also a common decay mode for neutron-rich nuclei. In addition to study in physics, beta decay has practical applications in medicine, such as in radiotherapy and radiopharmaceuticals.