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The atomic mass number is a fundamental concept in chemistry that provides information about the composition of an atom's nucleus. It counts the total number of protons and neutrons present in the nucleus. Protons are positively charged particles, while neutrons have no charge, and together they account for nearly all of the atom's mass because electrons are much lighter in comparison. Every atom of a particular element has the same number of protons, known as the atomic number, but the number of neutrons can vary, leading to different isotopes of the same element.

For example, carbon has an atomic number of 6, which means every carbon atom has 6 protons. However, the most common isotope of carbon, carbon-12, has 6 neutrons. Therefore, its atomic mass number is the sum of protons and neutrons, which is 12. Another isotope, carbon-14, has 8 neutrons, giving it an atomic mass number of 14. Simply put, the formula to calculate an atomic mass number is: \( Atomic\ mass\ number = Number\ of\ protons + Number\ of\ neutrons \).

Relative atomic mass, commonly known as atomic weight, is a crucial concept for comparing the mass of atoms of different elements. Unlike the atomic mass number, which is an integer for all atoms, the relative atomic mass is not always an integer. It is defined as the weighted average mass of an element's isotopes according to their natural abundance in atomic mass units (amu), which are units defined on a scale where 12 amu is the mass of a carbon-12 atom.

To calculate the relative atomic mass, you multiply the mass of each isotope by its abundance percentage, then add these values together. The formula for calculating relative atomic mass is as follows: \( Relative\ atomic\ mass = \sum (isotope\ mass \times fractional\ abundance) \). This value gives us an average mass that represents a collective picture of an element's isotopes as they occur naturally.

Elements often exist as a collection of different isotopes – atoms with the same number of protons but differing numbers of neutrons. This variation in neutron number results in different atomic mass numbers for the isotopes. The isotopic distribution of an element describes the abundance of each isotope relative to the total amount of the element in any given natural sample.

Understanding isotopic distribution is vital for calculating the relative atomic mass of an element. This is because the overall atomic weight is a reflection of the masses of all the isotopes, weighted by their respective abundances. Take chlorine for instance, with two primary isotopes: chlorine-35 and chlorine-37. About 75.77% of natural chlorine is chlorine-35, while 24.23% is chlorine-37. Therefore, these percentages will be used as weighting factors in the calculation of chlorine's atomic weight from the isotopic masses.

Protons and neutrons are the building blocks of atomic nuclei and play a key role in defining the identity and mass of an atom. Protons are positively charged particles, while neutrons lack an electrical charge and are neutral. The number of protons in the nucleus of an atom identifies the element: for example, all atoms with 6 protons are carbon atoms. The number of neutrons, on the other hand, contributes to the mass of an atom and determines the isotope of that element.

In terms of mass, protons and neutrons are quite similar, although a neutron is very slightly more massive than a proton. This small difference, however, does not affect the atomic mass number calculation significantly, since both protons and neutrons have a mass close to 1 amu. For most practical purposes, the combined number of protons and neutrons gives the approximate atomic mass of an isotope, understanding that electrons contribute negligibly to the mass.