Periodic Table of Elements

Cheatsheet Content

Periodic Table: Classification & Trends (JEE Mains) The periodic table organizes elements based on their atomic number (Moseley's Law: properties are periodic functions of atomic number) into periods and groups, reflecting electron configurations and chemical properties. Periods (Horizontal Rows): Indicate the principal quantum number ($n$) of the valence shell. There are 7 periods. Groups (Vertical Columns): Elements in the same group have similar outermost shell electronic configurations and thus similar chemical properties. There are 18 groups. Blocks: Based on the differentiating electron's subshell. s-block (Gr. 1 & 2): Valence electron enters s-orbital. Alkali metals ($ns^1$) and Alkaline earth metals ($ns^2$). p-block (Gr. 13-18): Valence electron enters p-orbital. Includes Boron family ($ns^2np^1$) to Noble gases ($ns^2np^6$). d-block (Gr. 3-12): Differentiating electron enters $(n-1)d$ subshell. Transition elements. General config: $(n-1)d^{1-10}ns^{0-2}$. f-block (Lanthanides & Actinides): Differentiating electron enters $(n-2)f$ subshell. Inner transition elements. General config: $(n-2)f^{1-14}(n-1)d^{0-1}ns^2$. JEE Mains Important Periodic Trends 1. Atomic Radius ($r$) Across a Period (L to R): Decreases. Effective nuclear charge ($Z_{eff}$) increases, pulling electrons closer. Down a Group (Top to Bottom): Increases. New shells are added, shielding effect increases. Covalent Radius: Half the internuclear distance between two identical atoms bonded by a single covalent bond. Metallic Radius: Half the internuclear distance between two adjacent metal atoms in a metallic lattice. Van der Waals Radius: Half the internuclear distance between two non-bonded atoms of adjacent molecules. (Largest among all radii for a given element). Ionic Radius: Cations ($M^+$): Smaller than parent atom due to loss of electron(s) and increased $Z_{eff}$. Anions ($X^-$): Larger than parent atom due to gain of electron(s) and increased electron-electron repulsion. Isoelectronic Species: For isoelectronic species, ionic radius decreases with increasing nuclear charge ($Z$). E.g., $O^{2-} > F^- > Na^+ > Mg^{2+} > Al^{3+}$. 2. Ionization Enthalpy ($\Delta_i H$) Energy required to remove the most loosely bound electron from an isolated gaseous atom. Across a Period: Generally increases. $Z_{eff}$ increases, making electron removal harder. Exceptions: $IE_1$ of Group 13 ($ns^2np^1$) is less than Group 2 ($ns^2$) due to easier removal of $p$-electron. $IE_1$ of Group 16 ($ns^2np^4$) is less than Group 15 ($ns^2np^3$) due to half-filled $p$-orbital stability in Group 15 and repulsion in Group 16. Down a Group: Generally decreases. Atomic size increases, shielding increases, making electron removal easier. Successive Ionization Enthalpies: $IE_1 3. Electron Gain Enthalpy ($\Delta_{eg} H$) Energy released or absorbed when an electron is added to an isolated gaseous atom. Usually negative (exothermic). Across a Period: Becomes more negative (more exothermic). $Z_{eff}$ increases, greater attraction for incoming electron. Down a Group: Becomes less negative (less exothermic). Atomic size increases, less attraction for incoming electron. Exceptions: Group 17 (Halogens) have highly negative $\Delta_{eg}H$. Group 18 (Noble Gases) have positive $\Delta_{eg}H$ (endothermic) due to stable filled subshells. Group 2 (Alkaline Earth Metals) and Group 15 (Nitrogen family) also have positive or slightly positive $\Delta_{eg}H$ due to stable $s^2$ or half-filled $p^3$ configurations. Chlorine (Cl) has a more negative $\Delta_{eg}H$ than Fluorine (F) due to smaller size of F leading to inter-electronic repulsion in its compact $2p$ subshell. Similarly, S > O. 4. Electronegativity (EN) Tendency of an atom to attract shared electron pair in a covalent bond. (Pauling scale is common). Across a Period: Increases. $Z_{eff}$ increases. Down a Group: Decreases. Atomic size increases, less attraction for bonded electrons. No Units: It's a relative concept. Most Electronegative: Fluorine (F) is 4.0. Related to metallic/non-metallic character: High EN = non-metallic; Low EN = metallic. JEE Mains Key Points & Exceptions Diagonal Relationship: Elements of 2nd period show similarities with elements of 3rd period in the next group (e.g., Li-Mg, Be-Al, B-Si). Due to similar charge/radius ratio. Anomalous Behavior of 2nd Period Elements: (Li, Be, B, C, N, O, F). Smallest size, high electronegativity, high ionization enthalpy. Absence of d-orbitals (max covalency 4). Can form $p\pi - p\pi$ multiple bonds (C, N, O, F). Lanthanide Contraction: Poor shielding effect of $4f$ electrons causes a steady decrease in atomic/ionic radii from La to Lu. Consequences: Similar radii of elements in 2nd and 3rd transition series (e.g., Zr/Hf, Nb/Ta). Similar chemical properties of elements in 2nd and 3rd transition series. Difficulty in separation of lanthanides. Oxidation States: s-block: Fixed oxidation states (+1 for Gr. 1, +2 for Gr. 2). p-block: Variable oxidation states. Inert pair effect prominent down the group (e.g., +1 for Tl in Gr. 13, +2 for Pb in Gr. 14). d-block: Exhibit variable oxidation states (due to participation of $(n-1)d$ and $ns$ electrons). Acidity of Oxides: Across a period: Increases (Basic $\to$ Amphoteric $\to$ Acidic). Down a group: Decreases (Acidic $\to$ Basic). E.g., $Na_2O$ (basic), $Al_2O_3$ (amphoteric), $SO_2$ (acidic). Important Formulas & Concepts Effective Nuclear Charge ($Z_{eff}$): $Z_{eff} = Z - S$, where $Z$ is atomic number and $S$ is screening constant (Slater's Rules, though detailed calculations often not required for JEE, focus on trends). Electronegativity Scales: Pauling Scale: $X_A - X_B = 0.208 \sqrt{\Delta E}$ where $\Delta E$ is resonance energy in kcal/mol. Mulliken Scale: $X_M = \frac{IE + EG}{2}$ (IE = Ionization Enthalpy, EG = Electron Gain Enthalpy, in eV). Electropositivity/Metallic Character: Tendency to lose electrons. Opposite of Electronegativity. Increases down a group, decreases across a period.