Classification of Elements & Periodicity in Properties – JEE Main Formula Sheet & Class 12 Notes

Historical Development — Triads, Octaves, and Mendeleev's Table

Why Periodic Table History Is Tested in JEE Main as One-Mark Facts

Döbereiner's Triads (1829): Johann Döbereiner grouped elements into triads where the atomic mass of the middle element was approximately the arithmetic mean of the first and third. Classic examples: Li–Na–K (atomic masses 7, 23, 39 — mean of 7 and 39 is 23 ✓), Ca–Sr–Ba, Cl–Br–I. This was the first recognition of numerical relationships between elements but was limited to only a few groups.

Newlands' Law of Octaves (1865): John Newlands arranged elements in increasing atomic mass and observed that every eighth element had properties similar to the first — analogous to musical octaves. This worked for lighter elements (up to calcium) but broke down for heavier elements where two elements were forced into the same slot. The law was not accepted by the scientific community at the time.

Mendeleev's Periodic Law (1869): Dmitri Mendeleev stated that the properties of elements are a periodic function of their atomic masses. His table had elements arranged in rows (periods) and columns (groups). The greatest achievement was leaving gaps for undiscovered elements and predicting their properties — eka-boron (later scandium), eka-aluminium (gallium), and eka-silicon (germanium) were all discovered with properties remarkably close to Mendeleev's predictions. Limitations: could not explain the position of hydrogen, isotopes, and anomalous pairs like Ar–K, Co–Ni, Te–I where atomic mass order conflicts with property similarity.

Electronic Configuration and Position in the Periodic Table

Why Configuration-Position Mapping Is a Core JEE Main Skill

Every element's position in the periodic table is uniquely determined by its electronic configuration. The period number equals the principal quantum number (n) of the outermost shell. The group number is determined as follows: for s-block elements, group = number of valence electrons (Group 1 for ns¹, Group 2 for ns²). For p-block elements, group = 10 + number of valence electrons (e.g., ns²np¹ → Group 13, ns²np⁶ → Group 18). For d-block elements, group = number of (n–1)d electrons + ns electrons. For f-block elements (lanthanoids: 4f filling, period 6; actinoids: 5f filling, period 7), they are placed in Groups 3 but listed separately.

The type of block an element belongs to is determined by the subshell receiving the last electron: last electron in s → s-block; last in p → p-block; last in d → d-block; last in f → f-block. JEE Main frequently gives an electronic configuration and asks for period, group, and block — or gives period and group and asks for configuration. This mapping skill is fast and reliable once the rules are internalised. Download the Free PDF for a systematic configuration-to-position conversion table.

Atomic Radius — Covalent, Metallic, and van der Waals Radii

Why Atomic Radius Trends and Exceptions Are JEE Main Staples

Atomic radius cannot be measured directly (atoms have no sharp boundary), so it is defined operationally. Covalent radius: half the distance between the nuclei of two covalently bonded atoms of the same element in a molecule (e.g., half the Cl–Cl bond length in Cl₂). Metallic radius: half the distance between the nuclei of two adjacent atoms in a metallic crystal. van der Waals radius: half the distance between the nuclei of two non-bonded atoms of adjacent molecules — always larger than covalent radius for the same element.

Trend across a period (left to right): atomic radius generally decreases. As we move across a period, the number of protons increases (increasing nuclear charge) while electrons are added to the same shell (same shielding). The increased effective nuclear charge pulls the electron cloud inward, reducing the radius. Trend down a group: atomic radius increases. A new shell is added at each period, increasing the distance of the outermost electrons from the nucleus, and the increased shielding by inner shells more than compensates for the increased nuclear charge.

Important exceptions: Noble gases have the largest van der Waals radii in their period but are not compared with covalent radii of other elements (noble gases do not form covalent bonds under normal conditions). The atomic radius of Ga (135 pm) is slightly less than Al (143 pm) despite Ga being below Al — this is because the 3d electrons in Ga provide poor shielding, so effective nuclear charge experienced by the 4p electron in Ga is higher than expected. Similarly, Ge has a smaller radius than might be expected. This is called the d-block contraction.

Ionic Radius and Isoelectronic Series

Why Ionic Radius Comparisons Are a Direct JEE Main Question Type

Ionic radius is the radius of an ion in an ionic crystal. It differs from atomic radius based on the charge of the ion. Cations are always smaller than the parent atom — loss of electrons reduces electron-electron repulsion, and the remaining electrons are held more tightly by the same nuclear charge. The outermost shell may also be completely removed (e.g., Na⁺ has the configuration of Ne). Anions are always larger than the parent atom — addition of electrons increases electron-electron repulsion without changing nuclear charge, so the electron cloud expands.

Isoelectronic species are atoms or ions with the same number of electrons but different nuclear charges. For isoelectronic species, the ionic radius decreases as the nuclear charge (atomic number) increases — more protons pull the same number of electrons more tightly. Classic isoelectronic series tested in JEE Main: N³⁻, O²⁻, F⁻, Ne, Na⁺, Mg²⁺, Al³⁺ — all have 10 electrons. Ionic radius order: N³⁻ > O²⁻ > F⁻ > Ne > Na⁺ > Mg²⁺ > Al³⁺ (decreasing as atomic number increases from 7 to 13). Another common series: S²⁻, Cl⁻, Ar, K⁺, Ca²⁺ — all have 18 electrons. Radius order: S²⁻ > Cl⁻ > Ar > K⁺ > Ca²⁺.

Ionisation Enthalpy — Trends, Values, and Critical Exceptions

Why Ionisation Enthalpy Exceptions Are the Most-Tested Topic in This Chapter

Ionisation enthalpy (IE) is the minimum energy required to remove the most loosely bound electron from an isolated gaseous atom in its ground state. It is always positive (endothermic). The first ionisation enthalpy (IE₁) removes the first electron; IE₂ removes the second from the resulting cation; IE₂ > IE₁ always, since the cation has a higher effective nuclear charge for fewer electrons.

Trend across a period: generally increases left to right, because increasing nuclear charge with the same shielding increases the energy needed to remove an electron. Trend down a group: generally decreases, because the outermost electron is farther from the nucleus and more shielded by inner shells.

Exceptions — these are the most important JEE Main content in this section:

Be > B (IE₁): Beryllium (1s²2s²) has a fully filled 2s subshell, which is more stable than the half-filled 2p¹ configuration of Boron. The 2p electron in B is also slightly higher in energy and more effectively shielded by the 2s electrons, making it easier to remove than B's electron. So IE₁(Be) > IE₁(B), despite B being to the right of Be. Same reasoning applies to Mg > Al.

N > O (IE₁): Nitrogen (1s²2s²2p³) has a half-filled 2p subshell — three electrons in three separate p orbitals (Hund's rule). This half-filled configuration is extra stable due to exchange energy. Oxygen (1s²2s²2p⁴) has a paired electron in one 2p orbital, and the electron-electron repulsion in that paired orbital makes it easier to remove an electron from O than from N. So IE₁(N) > IE₁(O). Same reasoning applies to P > S.

These four exceptions — Be > B, N > O, Mg > Al, P > S — appear in virtually every JEE Main paper from this chapter. Download the Free PDF for a complete IE₁ trend table with all exceptions highlighted.

Electron Gain Enthalpy — Trends and the Fluorine Anomaly

Why Electron Gain Enthalpy Exceptions Are Critical for JEE Main

Electron gain enthalpy (EGE, also called electron affinity) is the enthalpy change when an electron is added to an isolated gaseous atom to form a monovalent anion. It is negative (exothermic) when energy is released on adding the electron — this means the anion is more stable than the atom. Some elements (noble gases, alkaline earth metals with filled shells) have positive EGE, meaning energy must be supplied.

Trend across a period: EGE generally becomes more negative (more exothermic) from left to right, because higher effective nuclear charge means the atom holds an extra electron more strongly. Trend down a group: EGE generally becomes less negative, because the extra electron is added to a larger orbital farther from the nucleus, with more shielding — the attraction is weaker.

The fluorine anomaly — a critical JEE Main exception: Chlorine has a more negative EGE than fluorine, even though F is above Cl in Group 17 and has a higher electronegativity. This seems contradictory. The reason: fluorine is an extremely small atom (atomic radius 64 pm). When an extra electron is added to fluorine, the resulting F⁻ ion is very compact, and the electron-electron repulsion in this tiny space is very high. This repulsion partially offsets the nuclear attraction, giving a less negative EGE for F compared to Cl. The same pattern appears in Group 16: S has a more negative EGE than O for the same reason.

Noble gases have positive (endothermic) EGE — they already have fully filled stable configurations and have no tendency to gain electrons. Alkaline earth metals (Group 2) also have positive or very small negative EGE because their ns² shells are full and any electron must enter a higher-energy np orbital.

Electronegativity — Pauling Scale and Periodic Trends

Why Electronegativity Comparisons Are Tested in Every JEE Main Paper

Electronegativity is the tendency of an atom in a chemical bond to attract the shared pair of electrons towards itself. Unlike ionisation enthalpy and electron gain enthalpy, electronegativity is not a directly measurable property — it is a derived concept. The most widely used scale is the Pauling scale, where fluorine (the most electronegative element) is assigned a value of 4.0 and all other values are relative to this.

Trend across a period: electronegativity increases left to right. As nuclear charge increases across a period with the same shielding, the atom pulls bonding electrons towards itself more strongly. Trend down a group: electronegativity decreases. The bonding electrons are farther from the nucleus and more shielded, reducing the pull. Noble gases are not assigned electronegativity values on the Pauling scale (they generally do not form bonds under standard conditions).

Electronegativity directly governs bond polarity, the direction of dipole moments, the acidic strength of hydrides and oxoacids, and the oxidising power of elements. In oxoacids, higher electronegativity of the central atom (or more electronegative substituents) increases the acid strength. The difference in electronegativity between two bonded atoms predicts whether the bond is covalent (Δχ < 1.7), polar covalent (Δχ 1.7–3.2), or ionic (Δχ > 3.2). Download the Free PDF for the complete electronegativity table with periodic trends illustrated.

Valency, Oxidation States, and Periodic Trends in Chemical Properties

Why Valency and Oxidation State Trends Are Directly Tested in JEE Main

Valency is the combining capacity of an element. For s- and p-block elements, the valency in a period first increases from 1 to 4 and then decreases from 4 to 0 (or increases from 4 to a maximum of the group number, depending on which valence is considered). For example, across Period 3: Na(1), Mg(2), Al(3), Si(4), P(3 or 5), S(2, 4, or 6), Cl(1, 3, 5, or 7), Ar(0).

Metallic and non-metallic character: Metallic character decreases across a period (left to right) and increases down a group. Non-metallic character shows the opposite trend. The most metallic element is francium (Fr) or, among stable and abundant elements, caesium (Cs). The most non-metallic element is fluorine (F). The diagonal line separating metals from non-metals passes through B, Si, As, Te, and At — these elements along the diagonal are called metalloids (they show properties intermediate between metals and non-metals).

Periodic trends in oxides: Oxides of metals are basic; oxides of non-metals are acidic; oxides of metalloids are amphoteric. Across a period, the nature of oxides changes from basic (Na₂O) through amphoteric (Al₂O₃) to acidic (P₄O₁₀, SO₃, Cl₂O₇). Down a group, metallic oxides become more basic (e.g., MgO is less basic than BaO; SiO₂ is less acidic than CO₂ is a non-metal oxide — actually CO₂ > SiO₂ in acidic nature). Periodic trends in hydrides: The thermal stability of hydrides decreases down a group (bond enthalpy decreases as atomic size increases). The acidic strength of binary hydrides increases across Period 3 (PH₃ < H₂S < HCl) and increases down a group for the same family (HF < HCl < HBr < HI — due to decreasing bond enthalpy making H–X easier to ionise, though HF is an exception in aqueous solution due to strong H-bonding).

Screening Effect, Effective Nuclear Charge, and Shielding

Why These Concepts Explain Every Periodic Trend

The effective nuclear charge (Z*) experienced by a valence electron is less than the actual nuclear charge (Z) because inner electrons partially shield (screen) the valence electrons from the nucleus. Z* = Z – σ, where σ is the shielding constant. Slater's rules provide a method to calculate σ, but the conceptual understanding is more important for JEE Main: electrons in the same shell shield each other poorly (contribution ≈ 0.35 each), while electrons in inner shells shield much more effectively (contribution ≈ 0.85 for n–1 shell, ≈ 1.00 for n–2 and inner shells).

As we move across a period, nuclear charge Z increases by 1 at each step, but shielding σ increases by only about 0.35 (electrons added to the same shell). So Z* increases across a period, explaining why atomic radius decreases, ionisation enthalpy increases, and electronegativity increases going left to right. As we move down a group, a new electron shell is added. Despite the increased nuclear charge, the increased shielding by the additional inner shell more than compensates, so Z* increases only slowly down a group — but the much greater distance of the valence electrons from the nucleus dominates, causing atomic radius to increase and IE and electronegativity to decrease down a group.

Diagonal Relationship and Anomalous Properties of Second-Period Elements

Why Diagonal Pairs Are Important for JEE Main Inorganic Questions

The diagonal relationship describes the similarity in properties between certain pairs of elements in the second and third periods that are diagonally adjacent in the periodic table. The pairs are: Li–Mg, Be–Al, B–Si, and C–P. This similarity arises because moving one period down increases atomic radius (reducing polarising power) while moving one group to the right increases charge density — the two effects roughly cancel, giving similar charge-to-radius ratios (ionic potential) for the diagonal pair.

Examples of diagonal similarity: Li resembles Mg — both form normal oxides (not peroxides), both form nitrides (Li₃N and Mg₃N₂) directly with N₂, both have organometallic chemistry. Be resembles Al — both form amphoteric oxides, both form covalent compounds, both are dissolved by NaOH. B resembles Si — both form acidic covalent oxides, both form volatile hydrides with similar properties.

Anomalous properties of second-period elements arise because these elements (Li, Be, B, C, N, O, F) are significantly smaller and more electronegative than their heavier congeners, and they can only accommodate a maximum of 4 bond pairs (no d-orbitals available in the n=2 shell). This means they cannot expand their octet — unlike P, S, Cl which can use 3d orbitals. So PCl₅ and SF₆ can exist but NCl₅ and OF₄ cannot. Nitrogen can form only 4 bonds maximum (as in NH₄⁺) while phosphorus can form 5 or 6 (as in PCl₅ or [PF₆]⁻). Download the Free PDF for a complete diagonal relationship summary.