Exam Master Review Sheet - Periodic Classification

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EXAM MASTER FORMULA SHEET

Periodic Classification of Elements

Ultimate Revision for JEE Main, Advanced & NEET

1. Modern Periodic Law & Moseley's Experiment

Modern Periodic Law:

The physical and chemical properties of the elements are periodic functions of their atomic numbers (Z), not atomic mass.

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Mendeleev's Law relied on atomic mass. Anomalous pairs in Mendeleev's table: Ar-K, Co-Ni, Te-I.

Moseley's Equation:

\[ \sqrt{\nu} = a(Z - b) \]

\(\nu\) = Frequency of X-rays, \(Z\) = Atomic Number, \(a, b\) = Constants (\(b \approx 1\) for K-series)

2. Effective Nuclear Charge (\(Z_{eff}\)) & Shielding

The Equation:

\[ Z_{eff} = Z - \sigma \]

\(\sigma\) = Shielding Constant

Shielding Power Order (Penetration Effect):

s > p > d > f

• Across a period: \(Z_{eff}\) increases by ~0.65 units per element.
• Down a group: \(Z_{eff}\) remains almost constant (slight increase).
• Poor Shielding of d & f: Leads to unexpected contractions in atomic radii (e.g., Transition & Lanthanide contractions).

Slater's Rules (Calculating \(\sigma\) for ns/np electrons):

1. Write configuration grouping: (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p)...
2. Electrons in higher groups (right) contribute 0.
3. Electrons in the same group (nth shell) contribute 0.35 each (except 1s = 0.30).
4. Electrons in the (n-1) shell contribute 0.85 each.
5. Electrons in (n-2) or lower shells contribute 1.00 each.

*Note: For nd or nf electrons, all electrons to the left (inner shells) contribute 1.00.

3. Atomic & Ionic Radii

Types of Radii Comparison:

Van der Waals > Metallic > Covalent

Van der Waals radius is defined for noble gases (since they don't form molecules). Hence, noble gases have the largest radius in a period.

Ionic Radii Rules:

• Cations: Always smaller than parent atom (\(M^+ < M\)) due to increased \(Z_{eff}\).
• Anions: Always larger than parent atom (\(X^- > X\)) due to e-e repulsion and decreased \(Z_{eff}\).

Isoelectronic Species: Same number of electrons (e.g., \(N^{3-}, O^{2-}, F^-, Na^+, Mg^{2+}, Al^{3+}\)).
Trend: Radius \(\propto \frac{1}{\text{Atomic Number (Z)}}\). Higher Z means smaller size.

Anomalies due to Poor Shielding:

• Al & Ga: Radius of \(Ga (135\text{pm}) \approx Al (143\text{pm})\) due to poor shielding by 3d electrons in Ga (Transition Contraction).
• 4d & 5d series: Radii are almost identical (e.g., \(Zr \approx Hf\), \(Nb \approx Ta\)) due to poor shielding by 4f electrons (Lanthanide Contraction).

4. Ionization Enthalpy (IE) & Electron Gain Enthalpy

Ionization Enthalpy (\(\Delta_i H\)):

Energy required to remove the most loosely bound electron from an isolated gaseous atom. Always endothermic.

Successive IEs: \(IE_1 < IE_2 < IE_3 \dots\) (drastic jump when core electrons are removed).

Crucial Anomalies (JEE/NEET Favorites):

• Be vs B: \(IE_1(Be) > IE_1(B)\) because 2s electron in Be is more penetrating/stable than 2p electron in B.
• N vs O: \(IE_1(N) > IE_1(O)\) because N has a stable half-filled configuration (\(2p^3\)).
• Period 2 Trend: Li < B < Be < C < O < N < F < Ne

Electron Gain Enthalpy (\(\Delta_{eg} H\)):

Energy change when an electron is added to an isolated gaseous atom. Usually exothermic (negative).

Exceptions (Endothermic/Positive): Noble Gases, Alkaline Earth Metals (Be, Mg), Nitrogen.

Crucial Anomalies:

• Cl > F: \(\Delta_{eg} H\) of Chlorine is more negative than Fluorine. F is too small, leading to high inter-electronic repulsion.
• S > O: Similarly, Sulfur is more negative than Oxygen.
• Halogen Order: Cl > F > Br > I (Most negative to least negative).

5. Electronegativity (EN) Scales

Tendency of an atom to attract shared electrons in a covalent bond. (Unitless).

Pauling Scale (Bond Energy):

\[ X_A - X_B = 0.208 \sqrt{\Delta_{AB}} \text{ (kcal/mol)} \]

\[ X_A - X_B = 0.102 \sqrt{\Delta_{AB}} \text{ (kJ/mol)} \]

Reference: \(X_{Fluorine} = 4.0\)

Mulliken Scale (IE & EA):

\[ X_M = \frac{IE + EA}{2} \text{ (in eV/atom)} \]

Relation: \(X_P \approx \frac{X_M}{2.8}\)

Allred-Rochow (\(Z_{eff}\)):

\[ X_{AR} = 0.359 \frac{Z_{eff}}{r^2} + 0.744 \]

r is covalent radius in \(\text{\AA}\)

6. Chemical Reactivity & Oxides

Basic Oxides

Metals (Left side). React with water to give bases.

\(Na_2O, MgO, CaO, BaO\)

Acidic Oxides

Non-metals (Right side) & High Oxidation state metals.

\(Cl_2O_7, SO_3, CO_2, Mn_2O_7\)

Amphoteric

React with both acids and bases.

\(Al_2O_3, ZnO, BeO, SnO, PbO\)

Neutral Oxides

Neither acidic nor basic.

\(CO, NO, N_2O, H_2O\)

Acidity vs Oxidation State: For oxides of the same element, acidity increases with increasing oxidation state.
E.g., \(MnO\) (Basic) < \(MnO_2\) (Amphoteric) < \(Mn_2O_7\) (Acidic).

Diagonal Relationship: Similar properties between Period 2 and diagonally opposite Period 3 elements. Pairs: (Li, Mg), (Be, Al), (B, Si).
Reason: Similar ionic potential (\(\phi = Charge/Radius\)) and similar EN.

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