The number of neutrons (N) in an atom is equal to the difference between the mass number (A) and the atomic number (Z). This relationship arises from the definition of these quantities and the composition of atomic nuclei.
The atomic number (Z) of an atom represents the number of protons in its nucleus. It defines the element itself since elements are distinguished by the number of protons they possess. For example, carbon has an atomic number of 6, indicating it has 6 protons.
The mass number (A) of an atom represents the total number of protons and neutrons in its nucleus. It reflects the overall mass of the atom. For instance, a carbon isotope with 6 protons and 8 neutrons has a mass number of 14.
Since the mass number (A) includes both protons and neutrons, the difference between A and Z must be the number of neutrons. Mathematically, we can express this relationship as:
N = A - Z
For example, in the case of carbon, with an atomic number (Z) of 6 and a mass number (A) of 14:
N = 14 - 6 N = 8
Thus, carbon-14 contains 6 protons and 8 neutrons. This relationship applies to all atoms, where the number of neutrons can be determined by subtracting the atomic number from the mass number.