Chapter 5

Chapter Overview

Chemistry is a vast subject that deals with the study of matter, its properties, and the changes it undergoes. The chapter we are about to discuss is an essential part of understanding the fundamental concepts of chemistry. This chapter focuses on the periodic table, which is a tabular arrangement of elements, organized based on their atomic number (number of protons in the nucleus), electron configuration, and recurring chemical properties.

Historical Evolution of the Periodic Classification

The development of the Periodic Table represents one of the most significant achievements in structural chemistry. Before the modern framework was established, several chemists sought to categorize elements based on their atomic masses:

1. Johann Wolfgang Döbereiner (1829) - Law of Triads: Grouped elements into sets of three (triads) with similar chemical properties. He observed that the atomic mass of the middle element was roughly the arithmetic mean of the atomic masses of the other two elements (e.g., Lithium, Sodium, Potassium; Calcium, Strontium, Barium; Chlorine, Bromine, Iodine).
   • Limitation: Applicable only to a few elements known at the time.
2. John Alexander Newlands (1865) - Law of Octaves: Arranged elements in increasing order of atomic mass and noticed that every eighth element had properties similar to the first, analogous to musical notes.
   • Limitation: Held true only up to Calcium ($Z = 20$) and failed to accommodate heavier elements or newly discovered noble gases.
3. Julius Lothar Meyer (1869) - Atomic Volume Curve: Plotted physical properties such as atomic volume, melting point, and boiling point against atomic weight. Alkali metals occupied the peaks, alkaline earth metals occupied the descending slopes, and halogens occupied the ascending slopes.
4. Dmitri Mendeleev (1869) - Mendeleev’s Periodic Law: Stated that "The physical and chemical properties of elements are periodic functions of their atomic weights." Mendeleev left deliberate gaps for undiscovered elements (e.g., Eka-Aluminum, which later became Gallium, and Eka-Silicon, which became Germanium) and correctly predicted their properties.
   • Limitations: Anomalous pairs (e.g., Ar before K, Co before Ni), position of Hydrogen, position of isotopes, and grouping of chemically dissimilar elements.
5. Henry Moseley (1913) - Modern Periodic Law: By analyzing characteristic X-ray spectra emitted by metals, Moseley discovered a linear relationship between the square root of frequency ($\sqrt{\nu}$) of X-rays and the atomic number ($Z$): $\sqrt{\nu} = a(Z - b)$ This proved that atomic number ($Z$), rather than atomic weight, is the fundamental property of an element.

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Learning Objectives

• To understand the periodic table and its historical significance in systematizing chemical concepts.
• To learn about the four different electronic blocks ($s$, $p$, $d$, and $f$) in the periodic table and their general characteristics.
• To understand the concept of periods and groups in the periodic table and master the IUPAC nomenclature for elements with atomic number $Z > 100$.
• To master the physical and chemical periodicity, including quantitative trends in atomic and ionic radii, effective nuclear charge ($Z_{\text{eff}}$), ionization enthalpy ($\Delta_i H$), electron gain enthalpy ($\Delta_{\text{eg}} H$), electronegativity ($\chi$), valency, and diagonal relationships.
• To apply periodic trends to predict chemical reactivity, nature of oxides, and non-metallic versus metallic behavior.

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Important Concepts

Periodic Table & Modern Periodic Law

The modern periodic table (long form of the periodic table) is a tabular arrangement of elements, organized based on their atomic number (number of protons in the nucleus), electron configuration, and recurring chemical properties. The elements are arranged in a way that elements with similar properties and electron configurations are placed in the same group or family.

The underlying basis of periodicity is the repetitive pattern of valence shell electron configurations at regular intervals of atomic numbers (2, 8, 8, 18, 18, 32).

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Blocks in the Periodic Table

The periodic table is divided into four distinct blocks based on the subshell being progressively filled by the differentiating electron:

                      MODERN PERIODIC TABLE BLOCKS
   ┌───────────────────┬───────────────────┬───────────────────┬───────────────────┐
   │      s-block      │      p-block      │      d-block      │      f-block      │
   ├───────────────────┼───────────────────┼───────────────────┼───────────────────┤
   │ Groups 1 & 2      │ Groups 13 to 18   │ Groups 3 to 12    │ Inner-transition   │
   │ Outer: ns¹⁻²      │ Outer: ns² np¹⁻⁶  │ Outer: (n-1)d¹⁻¹⁰ │ Outer: (n-2)f¹⁻¹⁴ │
   │                   │                   │        ns¹⁻²      │   (n-1)d⁰⁻¹ ns²   │
   └───────────────────┴───────────────────┴───────────────────┴───────────────────┘

1. s-block Elements

• Definition: Elements in the first two groups (1 and 2) of the periodic table, which have their outermost electrons in the $s$-orbital.
• General Outer Electronic Configuration: $ns^{1-2}$ (Group 1: $ns^1$ - Alkali metals; Group 2: $ns^2$ - Alkaline earth metals).
• Key Characteristics:
  • Soft metals with low melting and boiling points.
  • Highly electropositive with low ionization enthalpies.
  • Readily form ionic compounds by losing valence electrons (oxidation state +1 for Group 1, +2 for Group 2).
  • Act as strong reducing agents and impart characteristic colors to a flame due to low excitation energy of outer electrons.

2. p-block Elements

• Definition: Elements in groups 13 to 18 of the periodic table, which have their outermost electrons in the $p$-orbital.
• General Outer Electronic Configuration: $ns^2 np^{1-6}$ ($n = 2\text{--}7$).
• Key Characteristics:
  • Together with the $s$-block elements, they are known as Main Group or Representative Elements.
  • Includes metals, metalloids, and non-metals.
  • Group 18 elements ($ns^2 np^6$) are known as Noble Gases or Inert Gases, possessing a stable octet (or duplet for He) configuration with high positive or zero electron gain enthalpy.
  • Electronegativity and non-metallic character increase across the block from left to right.

3. d-block Elements

• Definition: Elements in groups 3 to 12 of the periodic table, which have their outermost electrons entering the inner $(n-1)d$-orbital.
• General Outer Electronic Configuration: $(n-1)d^{1-10} ns^{1-2}$.
• Key Characteristics:
  • Commonly referred to as Transition Elements because their properties lie transitionally between the highly electropositive $s$-block metals and electronegative $p$-block non-metals.
  • All are metals exhibiting variable oxidation states (due to small energy difference between $(n-1)d$ and $ns$ orbitals).
  • Form colored ions, paramagnetic complexes, and act as industrial catalysts (e.g., Fe in Haber's process, V₂O₅ in Contact process).

4. f-block Elements

• Definition: Elements in the two rows at the bottom of the periodic table, which have their outermost electrons filling the anti-penultimate $(n-2)f$-orbitals.
• General Outer Electronic Configuration: $(n-2)f^{1-14} (n-1)d^{0-1} ns^2$.
• Key Characteristics:
  • Consists of two series of 14 elements each:
    • Lanthanides ($4f$-series): Cerium ($Z = 58$) to Lutetium ($Z = 71$).
    • Actinides ($5f$-series): Thorium ($Z = 90$) to Lawrencium ($Z = 103$).
  • Also known as Inner Transition Elements.
  • Actinides are predominantly radioactive, and those beyond Uranium ($Z > 92$) are synthetic, known as Transuranium Elements.

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Periods and Groups

Periods

A horizontal row of elements in the periodic table, which have the same principal quantum number ($n$) for their outermost electron shell.

• The period number corresponds to the highest principal quantum number ($n$) of the elements in that row.
• 1st Period: $n = 1$ (2 elements: H, He) - Shortest period.
• 2nd & 3rd Periods: $n = 2, 3$ (8 elements each) - Short periods.
• 4th & 5th Periods: $n = 4, 5$ (18 elements each) - Long periods.
• 6th Period: $n = 6$ (32 elements, includes 14 Lanthanides) - Longest period.
• 7th Period: $n = 7$ (32 elements, includes 14 Actinides) - Incomplete in early tables, now complete.

Groups

A vertical column of elements in the periodic table, which have identical valence shell electron configurations and similar chemical properties.

• According to modern IUPAC notation, groups are numbered 1 through 18.
• Elements within a group exhibit similar chemical reactivity due to identical outer configuration (e.g., Group 17 Halogens all have $ns^2 np^5$).

Nomenclature of Elements with $Z > 100$

To avoid naming disputes among discovering nations, IUPAC systematic roots derived from atomic numbers are used until discovery is officially recognized:

Digit	Root	Abbreviation
0	nil	n
1	un	u
2	bi	b
3	tri	t
4	quad	q
5	pent	p
6	hex	h
7	sept	s
8	oct	o
9	enn	e

Example: Element with $Z = 120 \rightarrow$ Un-bi-nil-ium (Symbol: Ubn).

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Trends in Physical and Chemical Properties

               PERIODIC TRENDS AT A GLANCE
               
             Increasing Ionization Enthalpy
             Increasing Electronegativity
             Increasing Electron Gain Enthalpy (more negative)
             Decreasing Atomic Radius
   ───────────────────────────────────────────────────────►
  ┌────────────────────────────────────────────────────────┐
  │                                                        │
  │                     PERIODIC TABLE                     │  │ Increasing
  │                                                        │  │ Atomic Radius
  └────────────────────────────────────────────────────────┘  │ Decreasing
  ───────────────────────────────────────────────────────►    │ Electronegativity
             Decreasing Metallic Character                    ▼

1. Effective Nuclear Charge ($Z_{\text{eff}}$) and Shielding Effect

• The net positive charge experienced by an electron in a multi-electron atom.
• Inner shell electrons screen outer valence electrons from the full nuclear attraction ($Z$). $Z_{\text{eff}} = Z - \sigma$ where $Z$ is the atomic number and $\sigma$ is the shielding or screening constant.
• Shielding Power Order: $s > p > d > f$. Poor shielding by $d$ and $f$ electrons results in a sharper increase in $Z_{\text{eff}}$, causing phenomena like the Lanthanide Contraction.

2. Atomic Radius

The distance from the center of the nucleus to the outermost shell containing electrons. Because atomic boundaries are fuzzy, atomic radius is defined by operational metrics:

• Covalent Radius: Half of the internuclear distance between two identical non-metallic atoms bonded by a single covalent bond ($r_{\text{cov}} = \frac{1}{2} d_{\text{A-A}}$).
• Metallic Radius: Half of the internuclear distance between two adjacent metal cations in a metallic lattice.
• Van der Waals Radius: Half of the distance between two non-bonded adjacent atoms belonging to neighboring molecules in the solid state.
• Relative Order of Magnitudes: $r_{\text{vanderWaals}} > r_{\text{metallic}} > r_{\text{covalent}}$

Periodic Trend:

• Across a Period: The atomic radius decreases from left to right across a period. This is because nuclear charge ($Z$) increases while electrons are added to the same energy shell, increasing $Z_{\text{eff}}$ and pulling valence electrons closer to the nucleus.
• Down a Group: The atomic radius increases down a group. This occurs because new principal energy levels ($n$) are added successively, dominant over the increase in nuclear charge, expanding the electron cloud.

Ionic Radii & Isoelectronic Species:

• Cation Radius: A cation is smaller than its parent atom ($r_{\text{cation}} < r_{\text{atom}}$) because of loss of valence electrons, increased $Z_{\text{eff}}$, and reduced inter-electronic repulsion.
• Anion Radius: An anion is larger than its parent atom ($r_{\text{anion}} > r_{\text{atom}}$) due to electron addition, increased inter-electronic repulsion, and decreased $Z_{\text{eff}}$.
• Isoelectronic Species: Atoms and ions having the same number of total electrons (e.g., $\text{N}^{3-}, \text{O}^{2-}, \text{F}^-, \text{Na}^+, \text{Mg}^{2+}, \text{Al}^{3+}$ all have 10 electrons).
  • Rule: For isoelectronic species, as the nuclear charge ($Z$) increases, ionic radius decreases. $\text{Ionic Size: } \text{N}^{3-} > \text{O}^{2-} > \text{F}^- > \text{Na}^+ > \text{Mg}^{2+} > \text{Al}^{3+}$

3. Ionization Enthalpy ($\Delta_i H$)

The minimum amount of energy required to remove the most loosely bound electron from an isolated gaseous atom in its ground state: $\text{X}_{(g)} + \Delta_i H \longrightarrow \text{X}^+_{(g)} + e^-$

• Unit: $\text{kJ mol}^{-1}$ or $\text{eV/atom}$.
• Successive Ionization Enthalpies: Removal of subsequent electrons requires progressively higher energy due to increasing positive charge on the ion: $\Delta_i H_1 < \Delta_i H_2 < \Delta_i H_3$

Factors Affecting Ionization Enthalpy:

1. Atomic Size: Inverse relation ($\Delta_i H \propto \frac{1}{\text{Atomic Size}}$).
2. Effective Nuclear Charge: Direct relation ($\Delta_i H \propto Z_{\text{eff}}$).
3. Screening Effect: Inverse relation ($\Delta_i H \propto \frac{1}{\text{Shielding}}$).
4. Penetration Effect: Subshells closer to nucleus require more energy ($s > p > d > f$).
5. Electronic Stability: Completely filled or half-filled subshells exhibit enhanced stability and abnormally high $\Delta_i H$.

Periodic Trend & Anomalies:

• Across a Period: Increases left to right due to increasing $Z_{\text{eff}}$ and decreasing size.
  • Anomaly 1 (Be vs B): $\Delta_i H_1(\text{Be}) > \Delta_i H_1(\text{B})$. Beryllium ($1s^2 2s^2$) has a fully-filled $2s$ subshell, whereas Boron ($1s^2 2s^2 2p^1$) has a single easily removable $2p$ electron. Furthermore, $2s$ electrons penetrate closer to the nucleus than $2p$.
  • Anomaly 2 (N vs O): $\Delta_i H_1(\text{N}) > \Delta_i H_1(\text{O})$. Nitrogen ($1s^2 2s^2 2p_x^1 2p_y^1 2p_z^1$) has an extra stable half-filled $2p$ subshell compared to Oxygen ($1s^2 2s^2 2p_x^2 2p_y^1 2p_z^1$), which experiences inter-electron repulsion in the doubly-occupied $2p_x$ orbital.
• Down a Group: Decreases down a group due to increased atomic size and dominant screening effect.

4. Electron Gain Enthalpy ($\Delta_{\text{eg}} H$)

The enthalpy change accompanying the process where an electron is added to a neutral isolated gaseous atom to form a negative ion (anion): $\text{X}_{(g)} + e^- \longrightarrow \text{X}^-_{(g)} \quad (\Delta_{\text{eg}} H)$

• Can be exothermic ($\Delta_{\text{eg}} H < 0$, release of energy for species seeking electrons, e.g., Halogens) or endothermic ($\Delta_{\text{eg}} H > 0$, requiring energy to force electron insertion, e.g., Noble Gases, Alkaline Earth metals).

Periodic Trend & Anomalies:

• Across a Period: Becomes progressively more negative from left to right as $Z_{\text{eff}}$ increases and atomic size shrinks.
• Down a Group: Becomes less negative down a group as atomic size increases.
  • Anomaly 1 (Chlorine vs Fluorine): Chlorine has a more negative electron gain enthalpy than Fluorine ($\Delta_{\text{eg}} H(\text{Cl}) = -349 \text{ kJ mol}^{-1}$, $\Delta_{\text{eg}} H(\text{F}) = -328 \text{ kJ mol}^{-1}$). Due to the extremely compact size of the $2p$ orbital in Fluorine, adding an electron induces high inter-electronic repulsions. Chlorine’s $3p$ orbital is larger, accommodating the incoming electron with less repulsion.
  • Anomaly 2 (Oxygen vs Sulfur): Sulfur has a more negative $\Delta_{\text{eg}} H$ than Oxygen for the same reason ($2p$ vs $3p$ orbital density).

5. Electronegativity ($\chi$)

A qualitative measure of the ability of an atom in a chemical compound to attract shared pairs of electrons towards itself.

• Unlike ionization enthalpy or electron gain enthalpy, electronegativity is not a measurable thermodynamic property; it is a dimensionless relative property.

Scales of Electronegativity:

1. Pauling Scale: Based on bond dissociation energies. Fluorine is assigned an arbitrary value of 4.0 (most electronegative element).
2. Mulliken-Jaffe Scale: Averages first ionization enthalpy and electron gain enthalpy: $\chi_{\text{Mulliken}} = \frac{\Delta_i H + \Delta_{\text{eg}} H}{2} \quad (\text{values in eV})$ $\chi_{\text{Pauling}} \approx \frac{\chi_{\text{Mulliken}}}{2.8}$

Periodic Trend:

• Across a Period: Increases from left to right due to increased $Z_{\text{eff}}$ and smaller size.
• Down a Group: Decreases down a group due to larger atomic size and weaker nuclear hold on valence electrons.

6. Periodic Trends in Chemical Reactivity & Valency

• Valency: The combining capacity of an element.
  • For $s$-block and representative elements: Valency equals the number of valence electrons (for Groups 1, 2, 13, 14) or $(8 - \text{number of valence electrons})$ (for Groups 15, 16, 17, 18).
  • Across a period, valency increases with respect to hydrogen/oxygen from 1 to 4 and then decreases to 0.
• Anomalous Properties of Second-Period Elements: Elements of the second period (Li, Be, B, C, N, O, F) differ significantly from their heavier group congeners due to:
  1. Small atomic and ionic size.
  2. High electronegativity and high charge-to-radius ratio.
  3. Non-availability of vacant $d$-orbitals (covalency strictly capped at 4).
  4. Strong capacity to form $p\pi-p\pi$ multiple bonds (e.g., $\text{C}=\text{C}$, $\text{N}\equiv\text{N}$).
• Diagonal Relationship: Certain elements of the 2nd period show striking chemical resemblance to elements placed diagonally across in the 3rd period:
  • Lithium (Li) $\longleftrightarrow$ Magnesium (Mg)
  • Beryllium (Be) $\longleftrightarrow$ Aluminum (Al)
  • Boron (B) $\longleftrightarrow$ Silicon (Si) Cause: Similar ionic radii and similar charge-to-radius ratio ($\frac{\text{ionic charge}}{\text{ionic radius}}$), leading to similar polarising powers.

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Key Definitions

• Atomic Number ($Z$): The number of protons present in the nucleus of an isolated atom, uniquely identifying a chemical element.
• Electron Configuration: The arrangement of electrons within atomic orbitals following Pauli's Exclusion Principle, Hund's Rule of Maximum Multiplicity, and the Aufbau Principle.
• Block: A division of the periodic table based on the type of subshell orbital ($s, p, d, f$) occupied by the differentiating (outermost) electron.
• Period: A horizontal row of elements in the periodic table sharing the same principal quantum number ($n$).
• Group: A vertical column of elements in the periodic table possessing analogous valence-shell configurations and matching chemical properties.
• Effective Nuclear Charge ($Z_{\text{eff}}$): The net attractive positive force exerted by the nucleus on a given electron after accounting for electron-electron shielding.
• Ionization Enthalpy ($\Delta_i H$): The enthalpy change required to completely remove one mole of electrons from one mole of isolated neutral gaseous atoms in their ground state.
• Electron Gain Enthalpy ($\Delta_{\text{eg}} H$): The enthalpy change occurring when an electron is added to a neutral isolated gaseous atom to form a gaseous anion.
• Electronegativity ($\chi$): The tendency of an atom bound in a covalent molecule to draw shared bonding electron pairs toward itself.
• Diagonal Relationship: The chemical similarity observed between lighter elements of period 2 and diagonally adjacent elements of period 3 due to similar ionic size and polarizing power.

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Important Terms

Term	Meaning & Detailed Electronic Significance
s-block	Elements in the first two groups (1 and 2) having valence configurations $ns^1$ or $ns^2$. Highly electropositive.
p-block	Elements in groups 13 to 18 possessing configurations $ns^2 np^{1-6}$. Includes non-metals, metalloids, and post-transition metals.
d-block	Elements in groups 3 to 12 with filling inner $(n-1)d$ orbitals ($(n-1)d^{1-10} ns^{1-2}$). Known as transition metals.
f-block	Lanthanides and Actinides occupying separate rows with configuration $(n-2)f^{1-14} (n-1)d^{0-1} ns^2$. Inner transition elements.
Isoelectronic Species	Atoms/ions sharing the same total electron count but possessing different atomic numbers $Z$ (e.g., $\text{O}^{2-}, \text{F}^-, \text{Na}^+$).
Lanthanide Contraction	The steady decrease in atomic/ionic radii across the $4f$ series due to poor shielding by $4f$ electrons, making $5d$ elements identical in size to $4d$ elements.
Screening Effect	The shielding of outer valence electrons from nuclear attraction by inner core electrons.
Amphoteric Oxide	Oxides that react with both acids and bases to yield salt and water (e.g., $\text{Al}_2\text{O}_3$, $\text{ZnO}$, $\text{BeO}$).

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Important Formulas

1. Effective Nuclear Charge (Slater’s Rule formulation)

$Z_{\text{eff}} = Z - \sigma$ Where:

• $Z = \text{Actual Atomic Number (Proton Count)}$
• $\sigma = \text{Shielding / Screening Constant}$

2. Pauling Electronegativity Difference

$|\chi_{\text{A}} - \chi_{\text{B}}| = 0.102 \times \sqrt{\Delta}$ $\Delta = E_{\text{d}}(\text{A-B}) - \sqrt{E_{\text{d}}(\text{A-A}) \times E_{\text{d}}(\text{B-B})}$ Where:

• $E_{\text{d}}(\text{A-B})$ is the bond dissociation energy of molecule $\text{A-B}$ in $\text{kJ/mol}$.
• $\chi_{\text{A}}$ and $\chi_{\text{B}}$ are electronegativities of constituent atoms.

3. Mulliken Electronegativity Scale

$\chi_{\text{Mulliken}} = \frac{\Delta_i H + \Delta_{\text{eg}} H}{2} \quad (\text{energies expressed in eV})$

4. Conversion between Pauling and Mulliken Scales

$\chi_{\text{Pauling}} = \frac{\chi_{\text{Mulliken}}}{2.8} = \frac{\Delta_i H + \Delta_{\text{eg}} H}{5.6} \quad (\text{in eV})$ $\chi_{\text{Pauling}} = \frac{\Delta_i H + \Delta_{\text{eg}} H}{540} \quad (\text{in kJ mol}^{-1})$

5. Periodicity of Oxides (Acidic/Basic Character Ratio)

$\text{Non-metal oxide} + \text{H}_2\text{O} \longrightarrow \text{Acidic solution} \quad (\text{e.g., } \text{SO}_3 + \text{H}_2\text{O} \rightarrow \text{H}_2\text{SO}_4)$ $\text{Metal oxide} + \text{H}_2\text{O} \longrightarrow \text{Basic solution} \quad (\text{e.g., } \text{Na}_2\text{O} + \text{H}_2\text{O} \rightarrow 2\text{NaOH})$

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Diagrams (Description Only)

1. Ionization Enthalpy vs. Atomic Number ($Z$) Plot:

   • Description: A jagged line plot showing $Z$ on the x-axis ($Z = 1$ to $20$) and First Ionization Enthalpy ($\Delta_i H_1$) on the y-axis.
   • Key Features: Sharp local maxima occur at noble gases ($\text{He, Ne, Ar}$) due to complete octets. Local minima occur at alkali metals ($\text{Li, Na, K}$) due to single loosely-held $s^1$ outer electrons. Sharp drops occur between Group 2 and Group 13 ($\text{Be} \rightarrow \text{B}$) and small dips between Group 15 and Group 16 ($\text{N} \rightarrow \text{O}$).

2. Atomic Radius Across Period 2 Plot:

   • Description: A smooth descending curve from Lithium ($\text{Li}$) to Fluorine ($\text{F}$), followed by a sharp uptick at Neon ($\text{Ne}$).
   • Key Features: Demonstrates continuous shrinking of metallic/covalent radius due to increasing $Z_{\text{eff}}$. Neon spikes sharply upward because noble gas radius is measured as a non-bonded Van der Waals radius, which is intrinsically larger than covalent radii.

3. Slater’s Shielding Model Schematic:

   • Description: Concentric circular electron shells around a central positive nucleus. Inner shell electrons ($\text{n}-1, \text{n}-2$) act as a physical "negative electrostatic shield" or umbrella, reducing the net attractive pull experienced by the outermost valence electron in the $n$-shell.

4. Lothar Meyer’s Atomic Volume Curve:

   • Description: A plot of Atomic Volume ($\text{cm}^3/\text{mol}$) against Atomic Mass.
   • Key Features: Strongly electropositive alkali metals ($\text{Li, Na, K, Rb, Cs}$) occupy the peaks. Alkaline earth metals ($\text{Be, Mg, Ca, Sr, Ba}$) occupy descending slopes. Halogens ($\text{F, Cl, Br, I}$) occupy ascending slopes, and transition metals lie in the broad troughs.

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Real-Life Applications & Deep-Dive Case Studies

Real-Life Applications

The periodic table has numerous real-life applications, such as:

• Chemical Industry: The periodic table is used to predict the reactivity, stoichometry, and behavior of elements and their compounds in industrial synthesis.
• Materials Science: The periodic table is used to design and develop new materials with specific properties, such as superconductors, shape-memory alloys, and catalysts.
• Environmental Science: The periodic table is used to understand the environmental mobility, toxicity, and bioaccumulation of heavy metals (like $\text{Hg, Pb, Cd}$) and to develop strategies for pollution remediation.

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Deep-Dive Case Studies

Case Study 1: Lanthanide Contraction and the Separation of Zirconium ($\text{Zr}$) and Hafnium ($\text{Hf}$)

In aerospace engineering and nuclear reactor design, element separation is critical. Zirconium ($\text{Zr}$, Period 5, Group 4) and Hafnium ($\text{Hf}$, Period 6, Group 4) reside in the same group. Standard periodic trends suggest $\text{Hf}$ should be substantially larger than $\text{Zr}$.

However, between $\text{Zr}$ ($Z=40$) and $\text{Hf}$ ($Z=72$), 14 Lanthanide elements ($Z=58\text{--}71$) intervene, filling the $4f$ subshell. Because $4f$ orbitals have extremely diffuse spatial shapes, they shield nuclear charge poorly ($\sigma_{\text{4f}}$ is very low).

Consequently, as $Z$ increases by 14 units, the effective nuclear charge pulling the valence shell in $\text{Hf}$ increases dramatically, pulling its orbitals inward. This effect—Lanthanide Contraction—cancels out the expected size expansion from adding the $n=6$ shell.

Result:

• Radius of $\text{Zr}^{4+} = 0.72 \text{ Å}$
• Radius of $\text{Hf}^{4+} = 0.71 \text{ Å}$

Because their ionic radii, electronegativity, and outer electronic configurations are virtually identical, $\text{Zr}$ and $\text{Hf}$ possess nearly indistinguishable chemical properties. They co-occur in nature in zircon minerals, and separating nuclear-grade $\text{Zr}$ (which absorbs few neutrons) from $\text{Hf}$ (which is an aggressive neutron absorber used in control rods) requires complex, multi-stage liquid-liquid solvent extractions.

       LANTHANIDE CONTRACTION EFFECT ON ATOMIC RADII
       
  Period 4:  Titanium (Ti)      r = 132 pm
                   │  (+32 pm due to extra shell)
                   ▼
  Period 5:  Zirconium (Zr)    r = 160 pm
                   │  (LANTHANIDE CONTRACTION CANCELS EXPANSION)
                   ▼
  Period 6:  Hafnium (Hf)      r = 159 pm  (Nearly identical to Zr!)

Case Study 2: Semiconductor Bandgap Engineering (Group 13-15 Compounds)

Silicon ($Z=14$, Group 14) is the classic material of modern microelectronics, possessing a bandgap of $1.1 \text{ eV}$. However, optoelectronic devices like modern telecommunication lasers and LEDs require customized electronic bandgaps.

By combining elements from Group 13 ($\text{Ga, In}$) with elements from Group 15 ($\text{N, As, P}$), scientists construct binary compound semiconductors (e.g., Gallium Arsenide $\text{GaAs}$, Indium Phosphide $\text{InP}$, Gallium Nitride $\text{GaN}$) that average out to the 4 valence-electron configuration of Group 14.

Using periodic trends:

• Down Group 15 ($\text{N} \rightarrow \text{P} \rightarrow \text{As}$), interatomic bond length increases, bond energy decreases, and the energy bandgap drops.
• $\text{GaN}$ (small size, high electronegativity difference) yields a wide bandgap ($3.4 \text{ eV}$), emitting high-energy blue/UV photon emissions.
• $\text{GaAs}$ yields a smaller bandgap ($1.42 \text{ eV}$), emitting infrared light suited for high-speed fiber-optic transmissions.

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Step-by-Step Problem Solving Strategies & Detailed Proofs

Strategy 1: Determining Period, Group, and Block of an Element from Atomic Number ($Z$)

1. Step 1: Write the complete electronic configuration using the Aufbau principle.
2. Step 2: The Period Number equals the highest principal quantum number ($n$) present in the configuration.
3. Step 3: Identify the Block by looking at which subshell receives the last (differentiating) electron:
   • If last electron enters $s$-subshell $\rightarrow$ s-block.
   • If last electron enters $p$-subshell $\rightarrow$ p-block.
   • If last electron enters $(n-1)d$-subshell $\rightarrow$ d-block.
   • If last electron enters $(n-2)f$-subshell $\rightarrow$ f-block.
4. Step 4: Compute the Group Number:
   • For s-block: Group Number = Number of valence $s$-electrons.
   • For p-block: Group Number = $12 + \text{Number of valence } p\text{-electrons}$ (or $10 + \text{total valence electrons}$).
   • For d-block: Group Number = $(\text{Number of } (n-1)d \text{ electrons}) + (\text{Number of } ns \text{ electrons})$.
   • For f-block: Group Number is always Group 3.

Worked Example:

Problem: Identify the block, period, and group for an element with atomic number $Z = 35$.

1. Configuration: $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^5$.
2. Highest principal quantum number ($n$) = 4 $\rightarrow$ Period 4.
3. The differentiating electron enters the $4p$ subshell $\rightarrow$ p-block.
4. Number of $p$-electrons in valence shell = 5. Group Number = $12 + 5 = 17$ (Halogens).
5. Identity: Bromine ($\text{Br}$).

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Strategy 2: Calculating Shielding Constant ($\sigma$) and $Z_{\text{eff}}$ using Slater's Rules

To calculate $\sigma$ for a valence electron in an $n s$ or $n p$ orbital:

1. Write configuration grouped as: $(1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) \dots$
2. Electrons in groups higher than the target electron contribute $0$ to $\sigma$.
3. Other electrons in the same $(ns, np)$ group contribute $0.35$ each ($0.30$ if calculating for $1s$).
4. Electrons in the $(n-1)$ shell contribute $0.85$ each.
5. Electrons in $(n-2)$ or deeper shells contribute $1.00$ each.

Worked Example:

Problem: Calculate $Z_{\text{eff}}$ for a $4s$ electron in Zinc ($\text{Zn}, Z = 30$).

1. Configuration: $(1s^2) (2s^2, 2p^6) (3s^2, 3p^6) (3d^{10}) (4s^2)$.
2. Target electron is in $4s$.
3. Remaining $4s$ electrons = $1 \times 0.35 = 0.35$.
4. Electrons in $(n-1)$ level (i.e., $3s, 3p, 3d$ containing $2+6+10 = 18$ electrons) = $18 \times 0.85 = 15.30$.
5. Electrons in $(n-2)$ and deeper levels (i.e., $1s, 2s, 2p$ containing $2+2+6 = 10$ electrons) = $10 \times 1.00 = 10.00$.
6. Total Shielding Constant ($\sigma$): $\sigma = 0.35 + 15.30 + 10.00 = 25.65$
7. Effective Nuclear Charge ($Z_{\text{eff}}$): $Z_{\text{eff}} = Z - \sigma = 30 - 25.65 = 4.35$

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Higher-Order Thinking Skills (HOTS) Questions

Question 1

The first ($\Delta_i H_1$) and second ($\Delta_i H_2$) ionization enthalpies of three elements A, B, and C are given below (in $\text{kJ mol}^{-1}$):

Element	$\Delta_i H_1$	$\Delta_i H_2$
A	520	7300
B	900	1760
C	2080	3960

Identify which of these elements is likely to be: (i) a reactive alkali metal, (ii) a noble gas, and (iii) an alkaline earth metal. Justify your answer.

Answer:

• (i) Element A is a reactive alkali metal. Reasoning: It has a low $\Delta_i H_1$ ($520 \text{ kJ mol}^{-1}$), indicating an easily removable valence electron. However, its $\Delta_i H_2$ jumps drastically to $7300 \text{ kJ mol}^{-1}$ (more than a 14-fold increase). This indicates that removing the second electron requires breaking a stable noble-gas inner-shell electron octet, characteristic of Group 1 metals.
• (ii) Element C is a noble gas. Reasoning: It exhibits an extremely high first ionization enthalpy $\Delta_i H_1$ ($2080 \text{ kJ mol}^{-1}$), demonstrating a fully-filled stable electronic configuration that strongly resists losing electrons.
• (iii) Element B is an alkaline earth metal. Reasoning: It has a moderately low $\Delta_i H_1$ ($900 \text{ kJ mol}^{-1}$) and a reasonable $\Delta_i H_2$ ($1760 \text{ kJ mol}^{-1}$). The ratio $\Delta_i H_2 / \Delta_i H_1 \approx 2$, indicating that both electrons reside in the outermost shell ($ns^2$). Removing two electrons yields a stable inert configuration (Group 2 behavior).

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Question 2

Explain why $\text{Na}^+$ has a smaller radius than $\text{F}^-$, even though both are isoelectronic and possess 10 electrons.

Answer: Both $\text{Na}^+$ and $\text{F}^-$ share the electronic configuration $1s^2 2s^2 2p^6$ (10 electrons). However, they differ in nuclear charge:

• For Sodium ion ($\text{Na}^+$): $Z = 11$ (11 protons attracting 10 electrons).
• For Fluoride ion ($\text{F}^-$): $Z = 9$ (9 protons attracting 10 electrons).

The Effective Nuclear Charge ($Z_{\text{eff}}$) acting on the outer electrons in $\text{Na}^+$ is significantly higher than in $\text{F}^-$: $\left(\frac{Z}{e}\right)_{\text{Na}^+} = \frac{11}{10} = 1.1 \quad \text{vs} \quad \left(\frac{Z}{e}\right)_{\text{F}^-} = \frac{9}{10} = 0.9$ Because $\text{Na}^+$ has a greater proton-to-electron ratio, its nucleus pulls the surrounding electron cloud inward with greater electrostatic force, resulting in a smaller ionic radius ($\text{Na}^+ = 102 \text{ pm}$ vs $\text{F}^- = 133 \text{ pm}$).

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Question 3

Why is the electron gain enthalpy of noble gases positive, whereas that of halogens is highly negative?

Answer:

• Halogens ($ns^2 np^5$): Need just one electron to complete a octet structure ($ns^2 np^6$). Due to high effective nuclear charge and small size, the incoming electron experiences strong nuclear attraction. Energy is released when the electron is added, making $\Delta_{\text{eg}} H$ highly negative (exothermic).
• Noble Gases ($ns^2 np^6$): Already possess completely filled valence subshells (stable octet/duplet). An incoming electron must enter the next higher principal energy level ($(n+1)s$), where it is heavily shielded by core electrons and experiences minimal net nuclear attraction. Forcing an electron into this high-energy state requires work to be done on the system, making $\Delta_{\text{eg}} H$ positive (endothermic).

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Key Points to Remember

• The periodic table is a tabular arrangement of elements, organized based on their atomic number, electron configuration, and recurring chemical properties.
• The elements are arranged in a way that elements with similar properties and electron configurations are placed in the same group or family.
• The periodic table is divided into four blocks: $s$-block, $p$-block, $d$-block, and $f$-block.
• The trends in physical and chemical properties of elements can be predicted using the periodic table.
• Atomic radius decreases across a period and increases down a group.
• Ionization Enthalpy and Electronegativity generally increase across a period and decrease down a group.
• Electron Gain Enthalpy becomes more negative across a period and less negative down a group, with notable exceptions (e.g., $\text{Cl} > \text{F}$, $\text{S} > \text{O}$).
• Lanthanide contraction causes $4d$ and $5d$ transition series elements in the same group to have nearly identical atomic/ionic radii (e.g., $\text{Zr} \approx \text{Hf}$).
• Second period elements show anomalous behavior compared to lower group members due to small size, high electronegativity, and absence of vacant $d$-orbitals.

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Common Mistakes

• Confusing Period and Group: Students often confuse the terms "period" (horizontal row) and "group" (vertical column) in the periodic table.
• Neglecting Block Placement: Students often forget to consider the block of an element when predicting its properties and variable oxidation states.
• Fluorine vs. Chlorine Electron Gain Enthalpy: Incorrectly assuming Fluorine has a more negative electron gain enthalpy than Chlorine. Fluorine's small size leads to inter-electronic repulsions, making Chlorine's $\Delta_{\text{eg}} H$ more negative.
• Ignoring Noble Gas Radii Nature: Comparing noble gas radii directly with covalent radii of halogens without realizing noble gas radii are Van der Waals radii (which are inherently larger).
• Applying Ionization Trends Blindly: Forgetting subshell stability exceptions (e.g., Be vs. B, where Be > B due to full $s$-shell; N vs. O, where N > O due to half-filled $p$-shell).

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Quick Revision

• Periodic Law: Properties of elements are periodic functions of their atomic numbers ($Z$).
• Block Configurations:
  • $s$-block: $ns^{1-2}$
  • $p$-block: $ns^2 np^{1-6}$
  • $d$-block: $(n-1)d^{1-10} ns^{1-2}$
  • $f$-block: $(n-2)f^{1-14} (n-1)d^{0-1} ns^2$
• Atomic Radius: Decreases from left to right across a period; increases down a group.
• Ionization Enthalpy ($\Delta_i H$): Increases across a period; decreases down a group. (Exceptions: $\text{Be} > \text{B}$ and $\text{N} > \text{O}$).
• Electron Gain Enthalpy ($\Delta_{\text{eg}} H$): Becomes more negative across a period; less negative down a group. (Exception: $\text{Cl} > \text{F}$ and $\text{S} > \text{O}$).
• Electronegativity ($\chi$): Increases across a period; decreases down a group. Fluorine is the most electronegative element ($\chi = 4.0$).
• Valency: Increases from 1 to 4 across a period (with respect to oxygen up to 7), then drops to 0.
• Diagonal Relationships: $\text{Li-Mg}$, $\text{Be-Al}$, $\text{B-Si}$ share similar ionic potential ($\frac{z}{r}$).

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Chapter Summary

The periodic table is a tabular arrangement of elements, organized based on their atomic number, electron configuration, and recurring chemical properties. The elements are arranged in a way that elements with similar properties and electron configurations are placed in the same group or family. The periodic table is divided into four blocks: $s$-block, $p$-block, $d$-block, and $f$-block.

Periodic trends such as atomic/ionic radius, ionization enthalpy, electron gain enthalpy, and electronegativity vary predictably across periods and down groups due to changes in effective nuclear charge ($Z_{\text{eff}}$) and principal quantum shells ($n$). Understanding the periodic table is essential for predicting the chemical reactivity, bonding capabilities, and general behavior of elements and their compounds.

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Previous Year Questions (PYQs) with Solutions

Question 1 (JEE Main / CBSE)

The element with atomic number $Z = 114$ was discovered recently. To which group, period, and block does it belong, and what is its electronic configuration?

Solution:

1. Atomic number $Z = 114$.
2. The nearest preceding noble gas is Radon ($\text{Rn}, Z = 86$).
3. Complete configuration: $[\text{Rn}] \, 5f^{14} \, 6d^{10} \, 7s^2 \, 7p^2$
4. Highest principal quantum number ($n$) = 7 $\rightarrow$ Period = 7.
5. The differentiating (last) electron enters the $7p$ subshell $\rightarrow$ Block = p-block.
6. Group Number = $12 + \text{number of } p\text{-electrons} = 12 + 2 = 14$ (Carbon Family / Tetragens).
7. IUPAC Name: Ununquadium (Uuq), now officially named Flerovium (Fl).

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Question 2 (NEET)

Among the elements $\text{B}, \text{Al}, \text{C},$ and $\text{Si}$, arrange them in increasing order of:

1. First Ionization Enthalpy
2. Non-metallic Character

Solution: Position in Periodic Table:

• Period 2: Boron ($\text{B}$, Group 13), Carbon ($\text{C}$, Group 14)
• Period 3: Aluminum ($\text{Al}$, Group 13), Silicon ($\text{Si}$, Group 14)

1. First Ionization Enthalpy:

   • Across a period, $\Delta_i H_1$ increases ($\text{C} > \text{B}$ and $\text{Si} > \text{Al}$).
   • Down a group, $\Delta_i H_1$ decreases ($\text{B} > \text{Al}$ and $\text{C} > \text{Si}$).
   • Combining these trends: $\text{Al} < \text{Si} < \text{B} < \text{C}$.

2. Non-metallic Character:

   • Non-metallic character increases across a period and decreases down a group.
   • Therefore, $\text{Al}$ is the most metallic, and $\text{C}$ is the most non-metallic.
   • Correct Order: $\text{Al} < \text{Si} < \text{B} < \text{C}$.

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Question 3 (CBSE Board)

What is the basic difference in approach between Mendeleev’s Periodic Law and the Modern Periodic Law?

Solution:

• Mendeleev’s Periodic Law considers atomic mass (atomic weight) as the fundamental property governing an element's physical and chemical traits. It states: "Properties of elements are periodic functions of their atomic weights."
• Modern Periodic Law considers atomic number ($Z$) (or nuclear charge/electronic configuration) as the fundamental property. It states: "Properties of elements are periodic functions of their atomic numbers."

This distinction solved historical anomalies in Mendeleev's table, such as inverted pairs ($\text{Ar}$ before $\text{K}$, $\text{Co}$ before $\text{Ni}$) and the placement of isotopes.

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NCERT Textbook Questions & Detailed Answers

Q1. What is the basic theme of organization of elements in the periodic table?

Answer: The basic theme of organization of elements in the periodic table is to classify all known chemical elements in a systematic manner according to their atomic numbers and electronic configurations. This classification brings elements with similar physical and chemical properties into the same vertical column (group), enabling scientists to predict the properties of elements and their compounds based on periodic trends rather than studying each element individually.

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Q2. Which important property did Moseley use to study the periodic system? What did he conclude?

Answer: Henry Moseley studied the characteristic X-ray emission spectra of a large number of elements by bombarding metal targets with high-energy electrons.

He plotted the square root of the frequency ($\sqrt{\nu}$) of emitted X-rays against the atomic number ($Z$) and obtained a straight line, according to the relation: $\sqrt{\nu} = a(Z - b)$ where $a$ and $b$ are constants.

Conclusion: Moseley concluded that the atomic number ($Z$) (number of protons in the nucleus) is a more fundamental property of an element than its atomic weight. This led to the revision of Mendeleev's Periodic Law into the Modern Periodic Law.

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Q3. Consider the following species: $\text{N}^{3-}, \text{O}^{2-}, \text{F}^-, \text{Na}^+, \text{Mg}^{2+}, \text{Al}^{3+}$.

(a) What is common in them? (b) Arrange them in order of increasing ionic radii.

Answer: (a) All these species are isoelectronic; each contains a total of 10 electrons ($1s^2 2s^2 2p^6$).

(b) For isoelectronic species, ionic size decreases as the nuclear charge ($Z$) increases. The nuclear charges ($Z$) are:

• $\text{N}^{3-} (Z = 7)$
• $\text{O}^{2-} (Z = 8)$
• $\text{F}^- (Z = 9)$
• $\text{Na}^+ (Z = 11)$
• $\text{Mg}^{2+} (Z = 12)$
• $\text{Al}^{3+} (Z = 13)$

Order of Increasing Ionic Radii: $\text{Al}^{3+} < \text{Mg}^{2+} < \text{Na}^+ < \text{F}^- < \text{O}^{2-} < \text{N}^{3-}$

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Q4. What do you understand by exothermic and endothermic electron gain enthalpy? Explain with examples.

Answer:

• Exothermic Electron Gain Enthalpy ($\Delta_{\text{eg}} H < 0$): When an electron is added to a neutral isolated gaseous atom and energy is released, the process is exothermic. This happens when the incoming electron experiences a net electrostatic attraction from the nucleus. Example: Halogens have high negative electron gain enthalpies because adding an electron achieves a stable noble gas octet: $\text{Cl}_{(g)} + e^- \longrightarrow \text{Cl}^-_{(g)} \quad (\Delta_{\text{eg}} H = -349 \text{ kJ mol}^{-1})$

• Endothermic Electron Gain Enthalpy ($\Delta_{\text{eg}} H > 0$): When an atom resists electron addition (e.g., due to a stable full subshell), energy must be supplied to force the electron into the atom. Example: Noble gases have positive electron gain enthalpies because the added electron must enter an empty higher energy shell: $\text{Ne}_{(g)} + e^- \longrightarrow \text{Ne}^-_{(g)} \quad (\Delta_{\text{eg}} H = +116 \text{ kJ mol}^{-1})$

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Q5. How do atomic radius and electronegativity vary across a period from left to right and down a group in the Periodic Table? Explain why.

Answer:

1. Atomic Radius:

   • Across a Period (Left to Right): Decreases. As nuclear charge ($Z$) increases across a period, electrons enter the same principal energy shell ($n$). The shielding effect remains nearly constant while $Z_{\text{eff}}$ increases, pulling the outer electrons closer to the nucleus.
   • Down a Group (Top to Bottom): Increases. A new energy level ($n$) is added at each step down a group. The increase in atomic size due to additional principal shells outweighs the pull of the increasing nuclear charge.

2. Electronegativity:

   • Across a Period (Left to Right): Increases. The decrease in atomic radius combined with the increase in effective nuclear charge enables the nucleus to attract shared bonding electron pairs more strongly.
   • Down a Group (Top to Bottom): Decreases. Increasing atomic radius and additional inner screening shells weaken the electrostatic attraction between the nucleus and shared bonding electrons.

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Q6. What is the significance of the terms — 'isolated gaseous atom' and 'ground state' while defining ionization enthalpy and electron gain enthalpy?

Answer:

• Isolated Gaseous Atom: In solid or liquid phases, individual atoms interact with surrounding neighboring atoms through interatomic forces, hydrogen bonds, or metallic networks. To measure the intrinsic property of a single atom without external influences, the sample must be separated into single atoms in the gaseous phase where interatomic interactions are negligible.
• Ground State: An atom can exist in various excited electronic energy states upon absorbing energy. Since ionization enthalpy and electron gain enthalpy represent absolute baseline properties, measurements must be standardized to the state of lowest energy—the ground state.

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Q7. Energy of an electron in the ground state of the hydrogen atom is $-2.18 \times 10^{-18} \text{ J}$. Calculate the ionization enthalpy of atomic hydrogen in terms of $\text{J mol}^{-1}$.

Answer: Ionization enthalpy represents the energy required to remove an electron completely from the ground state ($n = 1$) to infinity ($n = \infty$).

1. Energy required for one atom ($E$): $\Delta E = E_{\infty} - E_1 = 0 - (-2.18 \times 10^{-18} \text{ J}) = 2.18 \times 10^{-18} \text{ J/atom}$

2. Ionization enthalpy per mole ($\Delta_i H$): Multiply by Avogadro's number ($N_A = 6.022 \times 10^{23} \text{ mol}^{-1}$): $\Delta_i H = (2.18 \times 10^{-18} \text{ J/atom}) \times (6.022 \times 10^{23} \text{ atoms/mol})$ $\Delta_i H = 1.312 \times 10^6 \text{ J mol}^{-1} = 1312 \text{ kJ mol}^{-1}$

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Q8. Among the second period elements, the actual ionization enthalpies are in the order: $\text{Li} < \text{B} < \text{Be} < \text{C} < \text{O} < \text{N} < \text{F} < \text{Ne}$. Explain why:

1. $\text{Be}$ has higher $\Delta_i H$ than $\text{B}$
2. $\text{O}$ has lower $\Delta_i H$ than $\text{N}$

Answer:

1. $\text{Be}$ vs $\text{B}$:

   • Electronic configurations: $\text{Be} \, (Z=4): 1s^2 2s^2$; $\text{B} \, (Z=5): 1s^2 2s^2 2p^1$.
   • Beryllium has a completely filled $2s$ subshell, which is inherently stable. Removing an electron from Beryllium requires removing a $2s$ electron.
   • For Boron, the electron to be removed is in a $2p$ subshell, which is higher in energy, penetrates less toward the nucleus, and is shielded by the inner $2s^2$ electrons. Thus, $\Delta_i H_1(\text{Be}) > \Delta_i H_1(\text{B})$.

2. $\text{O}$ vs $\text{N}$:

   • Electronic configurations: $\text{N} \, (Z=7): 1s^2 2s^2 2p_x^1 2p_y^1 2p_z^1$; $\text{O} \, (Z=8): 1s^2 2s^2 2p_x^2 2p_y^1 2p_z^1$.
   • Nitrogen has a extra-stable half-filled $2p$ subshell with three unpaired electrons occupying distinct orbitals.
   • Oxygen has four $2p$ electrons, with one orbital containing a doubly-occupied electron pair. The electron-electron repulsion within this doubly-occupied $2p_x$ orbital makes it easier to remove one electron to reach the stable half-filled $2p^3$ configuration. Therefore, $\Delta_i H_1(\text{O}) < \Delta_i H_1(\text{N})$.

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Q9. How would you explain the fact that the first ionization enthalpy of Sodium ($\text{Na}$) is lower than that of Magnesium ($\text{Mg}$), but its second ionization enthalpy is higher than that of Magnesium?

Answer:

• First Ionization Enthalpy ($\Delta_i H_1$):

  • Configurations: $\text{Na} \, (Z=11): [\text{Ne}] \, 3s^1$; $\text{Mg} \, (Z=12): [\text{Ne}] \, 3s^2$.
  • Sodium easily loses its single $3s^1$ electron to achieve the stable inert Neon configuration ($[\text{Ne}]$). Magnesium has a higher effective nuclear charge and a stable, filled $3s^2$ subshell. Thus, $\Delta_i H_1(\text{Na}) < \Delta_i H_1(\text{Mg})$.

• Second Ionization Enthalpy ($\Delta_i H_2$):

  • Configurations of monovalent cations: $\text{Na}^+: [\text{Ne}] = 1s^2 2s^2 2p^6$; $\text{Mg}^+: [\text{Ne}] \, 3s^1$.
  • Removing a second electron from $\text{Na}^+$ requires disrupting a stable closed-shell noble gas octet ($n=2$ level), which demands a large amount of energy.
  • For $\text{Mg}^+$, removing the second electron removes the remaining $3s^1$ electron to yield a noble gas octet, which is thermodynamically favorable. Thus, $\Delta_i H_2(\text{Na}) \gg \Delta_i H_2(\text{Mg})$.

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Q10. What are the major differences between metals and non-metals in terms of their physical and chemical properties based on periodic trends?

Answer:

Property	Metals (Left/Bottom of Periodic Table)	Non-Metals (Top/Right of Periodic Table)
Position & Subshell	Mostly $s, d, f$ blocks and lower $p$-block.	Exclusively located in upper right of $p$-block.
Ionization Enthalpy	Low $\Delta_i H$; readily lose electrons to form cations.	High $\Delta_i H$; resist losing electrons.
Electron Gain Enthalpy	Less negative or slightly positive.	Highly negative $\Delta_{\text{eg}} H$; readily accept electrons.
Electronegativity	Low electronegativity (Electropositive).	High electronegativity (Electronegative).
Nature of Oxides	Form basic oxides (e.g., $\text{Na}_2\text{O}, \text{CaO}$).	Form acidic oxides (e.g., $\text{SO}_3, \text{CO}_2, \text{N}_2\text{O}_5$).
Bonding Behavior	Form ionic bonds with non-metals.	Form covalent bonds with other non-metals.
Physical Traits	Malleable, ductile, metallic luster, good electrical/thermal conductors.	Brittle, dull non-conductors (except graphite).