Key Points

This law states that the properties of elements are a periodic function of their atomic weights. Mendeleev's table successfully predicted the existence and properties of then-undiscovered elements.

The Modern Periodic Law states that the physical and chemical properties of the elements are periodic functions of their atomic numbers. This is the fundamental principle of the modern periodic table.

The modern periodic table consists of 7 horizontal rows called periods, which correspond to the principal quantum number $n$. It also has 18 vertical columns called groups, where elements have similar valence electron configurations and chemical properties.

Elements are classified into four blocks (s, p, d, f) based on the type of atomic orbital into which the last electron enters. This classification helps in understanding their properties.

Comprising Groups 1 (alkali metals, $ns^1$) and 2 (alkaline earth metals, $ns^2$), these are highly reactive metals with low ionization enthalpies that readily form cations.

These elements belong to Groups 13 to 18 and have the general outer electronic configuration $ns^2np^{1-6}$. This block includes metals, non-metals, and metalloids.

These are elements of Groups 3 to 12, characterized by the filling of inner $d$ orbitals with a general configuration of $(n-1)d^{1-10}ns^{0-2}$. They are metals that exhibit variable oxidation states and form colored ions.

These are the Lanthanoids (filling of $4f$ orbitals) and Actinoids (filling of $5f$ orbitals). They are placed separately at the bottom of the periodic table and are all metals.

Atomic radius generally decreases across a period from left to right due to an increase in effective nuclear charge. It increases down a group because of the addition of a new principal energy level (shell).

A cation is smaller than its parent atom (e.g., $Na^+ < Na$) due to fewer electrons and greater nuclear pull. An anion is larger than its parent atom (e.g., $Cl^- > Cl$) due to increased electron-electron repulsion.

These are atoms and ions that have the same number of electrons, such as $O^{2-}, F^-, Ne,$ and $Na^+$. Among isoelectronic species, the radius decreases as the nuclear charge increases.

Ionization enthalpy is the energy required to remove an electron from an isolated gaseous atom. It generally increases across a period and decreases down a group.

The first ionization enthalpy of Beryllium ($Be$) is higher than Boron ($B$) due to a stable, fully-filled $2s$ orbital. Nitrogen ($N$) has a higher value than Oxygen ($O$) due to a stable, half-filled $2p$ orbital.

This is the enthalpy change when an electron is added to a neutral gaseous atom. It generally becomes more negative across a period and less negative down a group.

The electron gain enthalpy of Chlorine ($Cl$) is more negative than that of Fluorine ($F$). This is because the incoming electron experiences less repulsion in the larger $3p$ orbital of chlorine compared to the compact $2p$ orbital of fluorine.

Electronegativity is the ability of an atom in a compound to attract shared electrons. It increases across a period from left to right and decreases down a group.

Metallic character increases down a group and decreases across a period. Non-metallic character increases across a period and decreases down a group.

Oxides of elements on the extreme left of a period are basic (e.g., $Na_2O$), those on the extreme right are acidic (e.g., $Cl_2O_7$), and those in the center can be amphoteric (e.g., $Al_2O_3$) or neutral.