Isotopes of an element are atoms with the same atomic number but different mass numbers; isotopes of an element, therefore, differ from each other only in the number of neutrons within the nucleus. When a naturally occurring element is composed of several isotopes, the atomic mass of the element represents the average of the masses of the isotopes involved. A chemical symbol identifies the atoms in a substance using symbols, which are one-, two-, or three-letter abbreviations for the atoms. The discovery of the periodic recurrence of similar properties among the elements led to the formulation of the periodic table, in which the elements are arranged in order of increasing atomic number in rows known as periods and columns known as groups. Elements in the same group of the periodic table have similar chemical properties. Elements can be classified as metals, metalloids, and nonmetals or as a main-group elements, transition metals, and inner transition metals. Groups are numbered 1–18 from left to right. The elements in group 1 are known as the alkali metals; those in group 2 are the alkaline earth metals; those in 15 are the pnictogens; those in 16 are the chalcogens; those in 17 are the halogens; and those in 18 are the noble gases.

The occurrence and natural abundances of isotopes can be experimentally determined using an instrument called a mass spectrometer. Mass spectrometry is widely used in chemistry, forensics, medicine, environmental science, and many other fields to analyze and help identify the substances in a sample of material. In a typical mass spectrometer, the sample is vaporized and exposed to a high-energy electron beam that causes the sample's atoms to become electrically charged, typically by losing one or more electrons. These cations then pass through a electric or magnetic field that deflects each cation's path to an extent that depends on both its mass and charge. The ions are detected, and a plot of the relative number of ions generated versus their mass-to-charge ratios is made. The height of each vertical feature or peak in a mass spectrum is proportional to the fraction of cations with the specified mass-to-charge ratio.

Dimitri Mendeleev is widely credited with creating the first periodic table of the elements. By the twentieth century, it became apparent that the periodic relationship involved atomic numbers rather than atomic masses. The modern statement of this relationship, the periodic law, is as follows: the properties of the elements are periodic functions of their atomic numbers. A modern periodic table arranges the elements in increasing order of their atomic numbers and groups atoms with similar properties in the same vertical column.

Ida Tacke and Walter Noddack set out to find the elements after German chemists predicted that there should be elements below Manganese in Group 7. They investigated ores containing minerals of ruthenium, tungsten, osmium, and so on, and were able to identify naturally occurring elements that helped complete the table. Rhenium was one of their discoveries, which was one of the last natural elements to be discovered and is the last stable element to be discovered.

In studying the periodic table, you might have noticed something about the atomic masses of some of the elements. Element 43, element 61, and most of the elements with atomic number 84 and higher have their atomic mass given in square brackets. This is done for elements that consist entirely of unstable, radioactive isotopes. The number in square brackets is the atomic mass number of the most stable isotope of that element.