Isotopes of the same element have different physical properties because the difference in the number of neutrons affects the atomic mass, which in turn influences physical properties like density, melting point, and boiling point. For example, heavier isotopes typically have higher densities. The variation in neutron count also affects the nuclear stability of isotopes, influencing properties such as radioactive decay rates. However, these physical differences do not affect chemical properties, as chemical reactions involve electrons in the outer shells of atoms, not the nucleus. Since isotopes of an element have the same atomic number, they possess the same number of electrons and thus exhibit identical chemical behaviors. This distinction between physical and chemical properties is a crucial aspect of understanding isotopes in chemistry.

The concept of mass number applies to molecules through the calculation of molecular mass. Molecular mass is the sum of the mass numbers of all the atoms in a molecule. For example, in a water molecule (H₂O), there are two hydrogen atoms and one oxygen atom. Assuming the most common isotopes, each hydrogen atom has a mass number of 1 (1 proton and 0 neutrons), and the oxygen atom typically has a mass number of 16 (8 protons and 8 neutrons). Therefore, the molecular mass of water is (2×1) + 16 = 18. This calculation is crucial in many areas of chemistry, including stoichiometry, where it helps determine the proportions of elements in reactions and the mass of reactants and products. Understanding the mass numbers of individual atoms is thus essential for calculating the molecular mass of compounds.

Two different elements can indeed have the same mass number, as mass number is the sum of protons and neutrons in the nucleus, and different combinations of these particles can yield the same total. For instance, consider carbon-14 (6 protons and 8 neutrons) and nitrogen-14 (7 protons and 7 neutrons). Both of these isotopes have a mass number of 14, but they are different elements because their atomic numbers (number of protons) differ. This scenario illustrates that while the mass number can be the same for different elements, it is the atomic number that fundamentally distinguishes one element from another. The concept of different elements sharing the same mass number is especially important in understanding nuclear reactions, where transmutation of elements can occur.

Atomic number and mass number are key tools in identifying unknown elements in a sample, particularly in analytical chemistry. The atomic number can be determined through spectroscopic techniques, such as X-ray fluorescence or atomic absorption spectroscopy, where the unique spectral lines of each element serve as a fingerprint. Once the atomic number is known, the identity of the element is established, as each element has a unique atomic number. Mass spectrometry is used to determine the mass number by measuring the mass-to-charge ratio of ions. This technique can differentiate isotopes of an element, allowing for a more precise identification, especially in cases where isotopic composition is relevant. These methods are integral in fields like environmental analysis, forensic science, and material science, where precise identification of elements is crucial.

Atomic number is fundamental in determining an element's position in the periodic table. The periodic table is arranged in order of increasing atomic numbers. This arrangement means that elements are sequenced based on the number of protons in their nucleus. As the atomic number increases, new electron shells are required to accommodate the increasing number of electrons (which is equal to the number of protons in a neutral atom). This progression leads to the formation of periods (horizontal rows) in the periodic table. Additionally, elements with similar atomic numbers tend to exhibit similar chemical properties because they have a similar number of valence electrons, contributing to the grouping of elements into columns known as groups or families. Thus, the atomic number not only determines an element’s placement in the periodic table but also its chemical behavior.