Isotopes are variants of a particular chemical element that have the same number of protons but different numbers of neutrons in their atomic nuclei. This means that isotopes of an element have the same atomic number (which determines the element's identity) but different mass numbers.
The mass number of an isotope refers to the total number of protons and neutrons in the atomic nucleus. It is denoted by the symbol "A" and is usually written as a superscript to the left of the atomic symbol. For example, the most common isotope of carbon is carbon-12, written as ¹²C. Carbon-12 has six protons and six neutrons, so its mass number is 12.
The atomic weight (also known as the relative atomic mass) of an element is a weighted average of the masses of all the naturally occurring isotopes of that element. It takes into account the abundance (relative occurrence) of each isotope in nature. Atomic weight is typically listed below the element's symbol in the periodic table. For example, the atomic weight of carbon is approximately 12.01.
The atomic weight of an element can be calculated using the following formula:
Atomic weight = (mass₁ × abundance₁) + (mass₂ × abundance₂) + ...
Where mass₁, mass₂, etc., are the mass numbers of the isotopes, and abundance₁, abundance₂, etc., are the relative abundances of the isotopes in nature. The atomic weight is expressed in atomic mass units (u) or unified atomic mass units (u), where 1 atomic mass unit is defined as 1/12th the mass of a carbon-12 atom.
In summary, isotopes have the same atomic number but different mass numbers due to varying numbers of neutrons. The mass number represents the total number of protons and neutrons in an isotope's nucleus, while atomic weight is the weighted average of the masses of all the naturally occurring isotopes of an element, taking into account their relative abundances.