The maximum number of electrons that can occupy a particular shell is determined by the formula 2n², where 'n' is the principal quantum number, or the shell number. This rule arises from the principles of quantum mechanics, which govern the behavior of electrons in an atom. The principal quantum number, n, defines the energy level or shell, and each energy level can accommodate a certain number of electrons. The first shell (n=1) can hold up to 2 electrons, the second shell (n=2) up to 8 electrons, the third shell (n=3) up to 18 electrons, and so on. This arrangement is due to the distribution of electrons in various subshells and orbitals within a shell, each with its own capacity to hold electrons. The electron capacity of each shell influences the chemical properties of elements, as atoms tend to react in ways that achieve a stable electronic configuration, often involving full outer shells.

While neutrons are neutrally charged and do not directly influence the chemical properties of an atom, they play a critical role in the stability of the nucleus. Neutrons act as a buffer between the positively charged protons, mitigating the electrostatic repulsion between them. This buffering effect is crucial in larger nuclei where the repulsive forces between numerous protons would otherwise destabilize the nucleus. In addition, the neutron-to-proton ratio is a key factor in the stability of isotopes. Isotopes with too many or too few neutrons compared to protons tend to be unstable and can undergo radioactive decay. Neutrons also contribute to the overall mass of the atom and, therefore, its mass number. In nuclear reactions, neutrons play a pivotal role, as they can initiate and sustain nuclear chain reactions, particularly in nuclear reactors and atomic bombs.

The atomic number of an element, which is the number of protons in the nucleus of its atoms, uniquely identifies the element. This is because the number of protons determines the fundamental properties of the element, including its chemical behavior and place in the Periodic Table. Each element has a distinct atomic number, making it a unique identifier. The atomic number cannot change for a given element; altering the number of protons in the nucleus would transform the atom into a different element. For example, removing one proton from a nitrogen atom (atomic number 7) would turn it into a carbon atom (atomic number 6). This characteristic makes the atomic number a fundamental and unchangeable property that defines each element. The concept of atomic number is crucial in chemistry for classifying and understanding the behavior of different elements.

Electrons are arranged in shells or energy levels around the nucleus due to the quantum mechanical nature of electrons. These shells represent regions where electrons are most likely to be found, and each shell corresponds to a specific energy level. The arrangement in shells is determined by the principles of quantum mechanics, particularly the Pauli Exclusion Principle and the Aufbau Principle. According to these principles, electrons fill lower energy levels first before moving to higher levels. The stability of an atom is significantly influenced by this electron arrangement. Atoms are most stable when their outermost shell is full, as in the case of noble gases. Atoms with incomplete outer shells tend to be more reactive, as they seek to achieve stability by gaining, losing, or sharing electrons through chemical reactions. This electron arrangement and the resulting quest for stability drive much of chemical bonding and reactivity.

Isotopes are variants of a particular chemical element that have the same number of protons (and thus the same atomic number) but different numbers of neutrons. This variation in neutron count leads to different mass numbers for the isotopes. Despite these differences in mass, isotopes of an element exhibit nearly identical chemical properties because they have the same electron configuration. However, their physical properties, such as melting points, boiling points, and densities, can differ due to the difference in mass. Isotopes play a crucial role in various fields. In chemistry and biology, certain isotopes are used as tracers to track chemical processes and biological pathways. In medicine, radioactive isotopes are used in diagnostic imaging and cancer treatment. In environmental science, isotopes help in understanding climatic and geological processes. The study of isotopes thus provides a wealth of information across various scientific disciplines.