Periodic Table
The periodic table arranges all known elements by increasing atomic number in rows and columns so that elements with similar properties line up.
Definition
The periodic table is a chart of all the elements arranged in order by atomic number, with elements that act alike lined up in the same column. It organizes the $118$ known elements into $7$ horizontal periods and $18$ vertical groups; elements in the same group have the same number of valence electrons and similar chemical properties, and metals sit on the left and center, nonmetals on the right, and metalloids along the staircase line between them. The table is a tabular expression of the periodic law: properties recur periodically as a function of atomic number because electron configurations repeat. It divides into $s$, $p$, $d$, and $f$ blocks according to the subshell being filled, with the lanthanides and actinides ($f$ block) typically set below, and periodic trends in atomic radius, ionization energy, electron affinity, and electronegativity follow from effective nuclear charge and shielding.
Example
Hydrogen is box $1$ in the top left corner, helium is box $2$ in the top right, and gold is box $79$, down in the middle. Lithium, sodium, and potassium are all in group $1$, each with one valence electron, and all react vigorously with water, while fluorine, chlorine, and bromine in group $17$ each have seven valence electrons and all form $-1$ ions. Across period $3$, atomic radius shrinks from sodium ($186\text{ pm}$) to chlorine ($100\text{ pm}$) as nuclear charge climbs from $11$ to $17$ while shielding stays nearly constant, and down group $1$, first ionization energy falls from lithium ($520\text{ kJ/mol}$) to cesium ($376\text{ kJ/mol}$) as the valence electron sits farther from the nucleus.
Key Insight
The table is a map, not just a list; where an element sits tells you a lot about how it behaves before you even look it up. Mendeleev left gaps in his 1869 table for elements nobody had found yet and predicted their properties, and when gallium and germanium were discovered they matched his predictions closely, which convinced chemists the table was real. The table's shape is a direct picture of quantum mechanics, two columns for $s$ orbitals, six for $p$, ten for $d$, fourteen for $f$, and its structure was worked out empirically decades before the theory that explains it existed.