Isotope Structure

The atomic number, also called the proton number, is the number of protons in the nucleus. It is given the symbol $Z$:

$Z=\text{number of protons}$

The number of protons determines which element an atom belongs to. For example, every carbon nucleus has six protons, so carbon has atomic number 6.

Counting all the nucleons

The mass number, also called the nucleon number, is the total number of protons and neutrons in the nucleus. It is given the symbol $A$:

$A=\text{number of protons}+\text{number of neutrons}$

Therefore, the number of neutrons can be found by subtraction:

$\text{number of neutrons}=A-Z$

Mass number is a count of particles in one nucleus, so it is always a whole number. It is not the same as the decimal relative atomic mass that may appear on a periodic table.

Reading standard nuclear notation

An isotope is written in the form

${}^{A}_{Z}X$

where $X$ is the element's chemical symbol, $A$ is written at the upper left and $Z$ is written at the lower left.

Consider ${}^{13}_{6}\mathrm{C}$. The symbol $\mathrm{C}$ identifies carbon. Its atomic number is 6, so its nucleus contains 6 protons. Its mass number is 13, so the nucleus contains 13 nucleons altogether. The neutron number is therefore $13-6=7$. The notation describes the nucleus; it does not directly state the number of electrons.

How the notation identifies isotopes

Isotopes are atoms of the same element whose nuclei contain the same number of protons but different numbers of neutrons. Their nuclear symbols therefore have the same chemical symbol and the same lower number, $Z$, but different upper numbers, $A$.

For example, ${}^{12}_{6}\mathrm{C}$ and ${}^{13}_{6}\mathrm{C}$ are both carbon because each has 6 protons. Carbon-12 has $12-6=6$ neutrons, whereas carbon-13 has $13-6=7$ neutrons. The extra neutron changes the mass number but not the identity of the element.

By contrast, two nuclei with different atomic numbers are different elements, even if their mass numbers happen to be equal. The proton number—not the total number of nucleons—is what fixes the element's identity.