Chapter 4

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 a crucial part of understanding the fundamental concepts of chemistry. It lays the groundwork for more complex topics and provides a solid foundation for further learning. The chapter focuses on the periodic table, which is a tabular arrangement of elements, and the periodic trends that can be observed in the properties of elements.

In 1913, the English physicist Henry Moseley observed regularities in the characteristic X-ray spectra of elements. A plot of $\sqrt{\nu}$ (where $\nu$ is the frequency of X-rays emitted) against the atomic number ($Z$) gave a straight line, whereas a plot of $\sqrt{\nu}$ against atomic mass did not. This led to the formulation of the Modern Periodic Law, which states: "The physical and chemical properties of the elements are periodic functions of their atomic numbers."

The modern long-form periodic table is constructed on the basis of the quantum mechanical model of the atom and electronic configurations. It arranges elements in increasing order of their atomic numbers, naturally grouping elements with similar valence shell electronic configurations together into vertical columns.

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Learning Objectives

• Understand the periodic table and its significance: Grasp how atomic numbers form the fundamental basis of classification and how electronic structure dictates chemical identity.
• Learn about the periodic trends in physical and chemical properties: Master the underlying causes of variations in atomic radii, ionic radii, ionization enthalpy, electron gain enthalpy, electronegativity, valence states, and metallic/non-metallic character.
• Identify the blocks and groups in the periodic table: Distinguish clearly between the $s$, $p$, $d$, and $f$ blocks based on the differentiating electron's subshell, and understand group characteristics.
• Understand the concept of periodicity and its applications: Analyze how shielding effect, effective nuclear charge ($Z_{eff}$), and quantum mechanical shell filling give rise to periodic behavior and use this knowledge to predict chemical reactivity and compound stoichiometry.

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Historical Evolution of Periodic Classification

Before arriving at the modern periodic table, several scientists attempted to classify elements based on observed patterns in their physical and chemical properties:

1. Johann Wolfgang Döbereiner (Law of Triads, 1829)

Döbereiner arranged elements into groups of three called triads. In each triad, the atomic mass of the middle element was approximately equal to the arithmetic mean of the atomic masses of the other two elements.

• Example: Alkali Metal Triad ($\text{Li}=7, \text{Na}=23, \text{K}=39$). Mean of Li and K = $\frac{7 + 39}{2} = 23$ ($\text{Na}$).
• Limitation: Applicable only to a few elements known at the time; failed for broader classification.

2. John Alexander Newlands (Law of Octaves, 1865)

Newlands arranged elements in increasing order of atomic mass and noticed that every eighth element had properties similar to the first, analogous to musical octaves.

• Limitation: Valid only up to Calcium ($Z=20$). It assumed no lighter or heavier undiscovered elements would exist, and failed completely for heavier elements containing transition metals.

3. Dmitri Mendeleev & Lothar Meyer (1869)

Mendeleev proposed the Mendeleev's Periodic Law: "The properties of elements are periodic functions of their atomic masses." Lothar Meyer plotted atomic volumes against atomic weights, obtaining periodic curves showing similar elements occupying corresponding positions.

• Achievements of Mendeleev's Table:
  1. Systematic classification of all 63 known elements.
  2. Left gaps for undiscovered elements and accurately predicted their properties (e.g., Eka-Aluminium $\rightarrow$ Gallium; Eka-Silicon $\rightarrow$ Germanium).
  3. Corrected atomic masses of elements like Beryllium (revised from 13.5 to 9 based on valency).
• Anomalies/Limitations:
  1. Anomalous pairs of elements (e.g., Argon $A=39.9$ placed before Potassium $A=39.1$; Cobalt $A=58.9$ placed before Nickel $A=58.7$).
  2. Uncertain position of Hydrogen (resembles both Group 1 alkali metals and Group 17 halogens).
  3. Isotopes could not be assigned distinct positions despite differing atomic masses.

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Nomenclature of Elements with Atomic Numbers $Z > 100$

To avoid priority disputes among research groups proposing different names for newly synthesized transuranium elements, the IUPAC (International Union of Pure and Applied Chemistry) established a systematic nomenclature based directly on atomic numbers using numerical roots.

Systematic Roots

• $0 = \text{nil}$ (n)
• $1 = \text{un}$ (u)
• $2 = \text{bi}$ (b)
• $3 = \text{tri}$ (t)
• $4 = \text{quad}$ (q)
• $5 = \text{pent}$ (p)
• $6 = \text{hex}$ (h)
• $7 = \text{sept}$ (s)
• $8 = \text{oct}$ (o)
• $9 = \text{enn}$ (e)

The suffix -ium is added to the combined roots.

Atomic Number ($Z$)	Temporary Name	Symbol	Official IUPAC Name	Official Symbol
101	Unnilunium	Unu	Mendelevium	Md
102	Unnilbium	Unb	Nobelium	No
103	Unniltrium	Unt	Lawrencium	Lr
104	Unnilquadium	Unq	Rutherfordium	Rf
105	Unnilpentium	Unp	Dubnium	Db
106	Unnilhexium	Unh	Seaborgium	Sg
107	Unnilseptium	Uns	Bohrium	Bh
108	Unniloctium	Uno	Hassium	Hs
109	Unnilennium	Une	Meitnerium	Mt
110	Ununnilium	Uun	Darmstadtium	Ds
111	Unununium	Uuu	Roentgenium	Rg
112	Ununbium	Uub	Copernicium	Cn
113	Ununtrium	Uut	Nihonium	Nh
114	Ununquadium	Uuq	Flerovium	Fl
115	Ununpentium	Uup	Moscovium	Mc
116	Ununhexium	Uuh	Livermorium	Lv
117	Ununseptium	Uus	Tennessine	Ts
118	Ununoctium	Uuo	Oganesson	Og

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Important Concepts

Periodic Table

The periodic table is a tabular arrangement of elements, listed in order of increasing atomic number (number of protons in the nucleus). The elements are arranged in rows called periods and columns called groups. The periodic table is a powerful tool for predicting the properties of elements and their behavior.

The modern long form consists of 7 horizontal rows called Periods and 18 vertical columns called Groups.

• Periods: The principal quantum number $n$ of the outermost shell corresponds to the period number.
  • Period 1: $n=1$, contains 2 elements ($\text{H}, \text{He}$).
  • Period 2: $n=2$, contains 8 elements ($\text{Li}$ to $\text{Ne}$).
  • Period 3: $n=3$, contains 8 elements ($\text{Na}$ to $\text{Ar}$).
  • Period 4: $n=4$, contains 18 elements ($\text{K}$ to $\text{Kr}$, includes $3d$ transition series).
  • Period 5: $n=5$, contains 18 elements ($\text{Rb}$ to $\text{Xe}$, includes $4d$ transition series).
  • Period 6: $n=6$, contains 32 elements ($\text{Cs}$ to $\text{Rn}$, includes $4f$ Lanthanoids).
  • Period 7: $n=7$, contains 32 elements ($\text{Fr}$ to $\text{Og}$, includes $5f$ Actinoids).

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Blocks and Groups

The periodic table is divided into four blocks: s-block, p-block, d-block, and f-block, based on the type of atomic orbital that receives the last (differentiating) electron.

       +-------------------------------------------------------+
       |                  PERIODIC TABLE BLOCKS                |
       +-------------------------------------------------------+
       | s-Block |   d-Block (Transition)   |      p-Block     |
       | (Gr 1-2)|      (Groups 3-12)       |   (Groups 13-18)  |
       +---------+--------------------------+------------------+
                 |    f-Block (Inner-Trans) |
                 |  (Lanthanoids/Actinoids) |
                 +--------------------------+

1. s-Block Elements:
   • Located on the far left (Group 1: Alkali Metals, Group 2: Alkaline Earth Metals).
   • General electronic configuration: $ns^{1-2}$.
   • Highly reactive metals with low ionization energies, forming predominantly ionic $+1$ and $+2$ cations.
2. p-Block Elements:
   • Located on the right side (Groups 13 to 18).
   • General electronic configuration: $ns^2 np^{1-6}$.
   • Includes metals, metalloids, non-metals, and noble gases (Group 18, $ns^2 np^6$).
   • Representative Elements or Main Group Elements collectively refer to the $s$-block and $p$-block elements.
3. d-Block Elements (Transition Metals):
   • Located in the middle (Groups 3 to 12).
   • General electronic configuration: $(n-1)d^{1-10} ns^{1-2}$.
   • Characterized by variable oxidation states, formation of colored ions, paramagnetic behavior, and catalytic activity.
4. f-Block Elements (Inner Transition Metals):
   • Placed separately at the bottom to avoid excessive stretching of the table.
   • General electronic configuration: $(n-2)f^{1-14} (n-1)d^{0-1} ns^2$.
   • Consists of two series:
     • Lanthanoids ($4f$ subshell filling): Cerium ($Z=58$) to Lutetium ($Z=71$).
     • Actinoids ($5f$ subshell filling): Thorium ($Z=90$) to Lawrencium ($Z=103$). All actinoids are radioactive.

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Periodic Trends

Periodic trends refer to the patterns and relationships that can be observed in the properties of elements as we move across a period or down a group in the periodic table. These trends stem from changes in nuclear charge, screening effect, atomic size, and valence electron arrangements.

Across a Period (Left to Right):
  [Atomic Radius Decreases]  |  [Ionization Energy Increases]
  [Electronegativity Increases]  |  [Electron Affinity Increases]

Down a Group (Top to Bottom):
  [Atomic Radius Increases]  |  [Ionization Energy Decreases]
  [Electronegativity Decreases]  |  [Electron Affinity Decreases]

1. Atomic Radius

• Definition: The distance between the nucleus and the outermost shell containing electrons.
• Types:
  • Covalent Radius: Half the internuclear distance between two covalently bonded identical non-metallic single-bonded atoms ($\text{e.g.}, r_{cov} = \frac{d_{A-A}}{2}$).
  • Metallic Radius: Half the internuclear distance between two adjacent metal ions in a metallic crystal lattice.
  • Van der Waals Radius: Half the distance between two non-bonded nuclei of adjacent identical atoms in the solid state.
  • Relative Magnitude: $\text{Van der Waals Radius} > \text{Metallic Radius} > \text{Covalent Radius}$.
• Trend Across a Period: Decreases left to right because effective nuclear charge ($Z_{eff}$) increases as electrons are added to the same principal energy shell while protons increase, pulling the electron cloud closer to the nucleus.
• Trend Down a Group: Increases top to bottom because new principal energy levels ($n$) are added, increasing the distance from the nucleus despite an increase in $Z$.

2. Ionic Radius

• The effective distance from the nucleus of an ion up to which it exerts influence on its electron cloud.
• Cations are smaller than their parent neutral atoms ($r_{\text{cation}} < r_{\text{atom}}$) due to loss of electrons, increased $Z_{eff}$, and potential loss of an entire outer shell (e.g., $r(\text{Na}^+) = 95\text{ pm} < r(\text{Na}) = 186\text{ pm}$).
• Anions are larger than their parent neutral atoms ($r_{\text{anion}} > r_{\text{atom}}$) because adding electrons increases inter-electronic repulsions, expanding the electron cloud (e.g., $r(\text{F}^-) = 136\text{ pm} > r(\text{F}) = 64\text{ pm}$).
• Isoelectronic Species: Ions/atoms having the same number of electrons (e.g., $\text{N}^{3-}, \text{O}^{2-}, \text{F}^-, \text{Na}^+, \text{Mg}^{2+}, \text{Al}^{3+}$ all have 10 electrons).
  • Rule: Higher positive nuclear charge ($Z$) results in stronger electron pull and smaller ionic radius.
  • Size order: $\text{N}^{3-} > \text{O}^{2-} > \text{F}^- > \text{Na}^+ > \text{Mg}^{2+} > \text{Al}^{3+}$.

3. Ionization Energy / Ionization Enthalpy ($\Delta_i H$)

• Definition: The minimum energy required to remove the most loosely bound electron from an isolated gaseous neutral atom in its ground state: $\text{X}(g) + \Delta_i H \longrightarrow \text{X}^+(g) + e^-$
• Successive Ionization Enthalpies: $\Delta_i H_1 < \Delta_i H_2 < \Delta_i H_3$ because removing an electron from a positively charged cation requires overcoming significantly higher electrostatic forces.
• Factors Influencing $\Delta_i H$:
  1. Atomic Size: $\Delta_i H \propto \frac{1}{\text{Atomic Size}}$.
  2. Nuclear Charge: $\Delta_i H \propto Z_{eff}$.
  3. Shielding/Screening Effect: $\Delta_i H \propto \frac{1}{\text{Shielding Effect}}$.
  4. Penetration Effect: Power of subshells to penetrate closer to the nucleus: $s > p > d > f$.
  5. Electronic Configuration: Fully filled ($ns^2, np^6, d^{10}$) and half-filled ($np^3, d^5$) subshells possess extraordinary exchange energy and symmetry, making them exceptionally stable and raising $\Delta_i H$.
• Anomalies across Period 2:
  • Be vs B: $\Delta_i H_1(\text{Be}) = 899\text{ kJ/mol} > \Delta_i H_1(\text{B}) = 801\text{ kJ/mol}$. Be has a fully filled $2s^2$ shell with high penetration power, whereas B loses a $2p^1$ electron easily.
  • N vs O: $\Delta_i H_1(\text{N}) = 1402\text{ kJ/mol} > \Delta_i H_1(\text{O}) = 1314\text{ kJ/mol}$. Nitrogen has a stable half-filled $2p^3$ subshell, whereas Oxygen has $2p^4$, where removing one electron yields a stable half-filled $2p^3$ configuration.

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

• Definition: The enthalpy change occurring when an electron is added to a neutral isolated gaseous atom to convert it into a negative ion: $\text{X}(g) + e^- \longrightarrow \text{X}^-(g) \quad (\Delta_{eg}H)$
• Can be exothermic ($\Delta_{eg}H < 0$, release of energy, common for halogens) or endothermic ($\Delta_{eg}H > 0$, input of energy required, common for noble gases with stable octets).
• Trend Across a Period: Becomes more negative from left to right because $Z_{eff}$ increases and atomic radius decreases, making incoming electron addition more favorable.
• Trend Down a Group: Becomes less negative going down a group as atomic size increases.
• Anomalies:
  • Fluorine vs Chlorine: Chlorine has a more negative electron gain enthalpy than Fluorine ($\Delta_{eg}H(\text{Cl}) = -349\text{ kJ/mol}$, $\Delta_{eg}H(\text{F}) = -328\text{ kJ/mol}$). Fluorine's extremely small $2p$ subshell experiences intense electron-electron repulsions, resisting the incoming electron compared to Chlorine's roomier $3p$ orbital.
  • Oxygen vs Sulphur: Sulphur ($\Delta_{eg}H = -200\text{ kJ/mol}$) is more negative than Oxygen ($\Delta_{eg}H = -141\text{ kJ/mol}$) for identical reasons.

5. Electronegativity

• Definition: The relative tendency/ability of an atom in a chemical compound to attract the shared pair of covalent electrons toward itself. Unlike ionization enthalpy or electron gain enthalpy, electronegativity is not a measurable quantitative property of isolated atoms, but a dimensionless relative property in bonded states.
• Trend Across a Period: Increases from left to right across a period (Fluorine is the most electronegative element with Pauling value $4.0$).
• Trend Down a Group: Decreases down a group (Cs / Fr have lowest values $\approx 0.7$).

6. Periodic Trends in Chemical Properties & Reactivity

• Valency / Oxidation State: Valence electrons increase from 1 to 8 across a period. Valency with respect to hydrogen increases from 1 to 4 and then decreases to 1 ($\text{NaH}=1, \text{MgH}_2=2, \text{AlH}_3=3, \text{SiH}_4=4, \text{PH}_3=3, \text{H}_2\text{S}=2, \text{HCl}=1$).
• Acidic/Basic Nature of Oxides:
  • Elements on the left form strongly basic oxides ($\text{Na}_2\text{O}$).
  • Elements in the middle form amphoteric oxides ($\text{Al}_2\text{O}_3, \text{Ga}_2\text{O}_3$) or neutral oxides ($\text{CO}, \text{NO}, \text{N}_2\text{O}$).
  • Elements on the right form strongly acidic oxides ($\text{Cl}_2\text{O}_7, \text{SO}_3$).

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Periodicity

Periodicity refers to the repetition of physical and chemical properties and trends in the periodic table at regular numerical intervals ($2, 8, 8, 18, 18, 32$). This structural repetition occurs because elements in the same group share identical valence shell electronic configurations (e.g., all alkali metals possess $ns^1$).

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Advanced Concepts: Screening Constant ($\sigma$) and Slater's Rules

Valence shell electrons experience an attractive pull from the positively charged nucleus, counteracted by repulsions from inner core electrons. The core electrons act as a screen or shield, reducing the full nuclear charge ($Z$) to an Effective Nuclear Charge ($Z_{eff}$):

$Z_{eff} = Z - \sigma$

where $\sigma$ is the shielding (screening) constant.

Slater's Rules for Calculating Screening Constant ($\sigma$)

To calculate $\sigma$ for a given electron in an atom:

1. Write the electronic configuration grouped as follows: $(1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p)\dots$
2. Any electrons in groups to the right of the target electron contribute $0.00$ to $\sigma$.
3. For an electron residing in an $s$ or $p$ orbital:
   • Other electrons within the same $(ns, np)$ group contribute $0.35$ each (except $1s$, where the other electron contributes $0.30$).
   • Electrons in the $(n-1)$ shell contribute $0.85$ each.
   • Electrons in $(n-2)$ or deeper shells contribute $1.00$ each.
4. For an electron residing in a $d$ or $f$ orbital:
   • Electrons in the same $(nd)$ or $(nf)$ group contribute $0.35$ each.
   • All electrons in underlying groups (to the left) contribute $1.00$ each.

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Key Definitions

• Atomic radius: The distance between the nucleus and the outermost electron in an atom.
• Covalent Radius: Half of the distance between the nuclei of two similar atoms joined by a single covalent bond in a homonuclear diatomic molecule.
• Metallic Radius: Half of the internuclear distance separating two adjacent metal cations in a metallic lattice.
• Van der Waals Radius: Half of the distance between two non-bonded, adjacent, identical atoms belonging to two neighboring molecules in the solid state.
• Ionic Radius: The effective distance from the center of the nucleus of an ion up to the point where it exerts influence on its electron cloud.
• Isoelectronic Species: Atoms and ions that possess the exact same total number of electrons but differ in nuclear charge ($Z$).
• Electronegativity: The relative ability of an atom in a covalent bond to attract shared bonding electrons toward itself.
• Ionization energy (Ionization Enthalpy): The minimum energy required to remove the most loosely bound electron from an isolated gaseous atom in its ground state.
• Electron affinity (Electron Gain Enthalpy): The energy released (or change in enthalpy) when an electron is added to an isolated neutral gaseous atom to form a univalent negative ion.
• Screening Effect (Shielding Effect): The reduction in effective nuclear attraction on valence electrons caused by electrostatic repulsions from inner shell electrons.
• Diagonal Relationship: The similarity in chemical properties observed between certain diagonal pairs of adjacent period-2 and period-3 elements (e.g., $\text{Li} \sim \text{Mg}$, $\text{Be} \sim \text{Al}$, $\text{B} \sim \text{Si}$).

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Important Terms

Term	Meaning
Periodic table	A tabular arrangement of elements, listed in order of increasing atomic number.
Block	A division of the periodic table ($s, p, d, f$), based on the subshell being filled by the valence electron.
Group	A vertical column of elements in the periodic table, with similar outer electronic structure and properties.
Period	A horizontal row of elements in the periodic table, corresponding to filling a principal energy level ($n$).
Isoelectronic	Chemical species (atoms/ions) having identical total electron counts and electronic configurations.
Diagonal Relationship	Property resemblance between period 2 elements and diagonally opposite period 3 elements due to similar charge-to-size ratios.
Shielding Constant ($\sigma$)	A parameter quantifying the reduction in nuclear pull caused by intervening core electrons.
Penetration Effect	The proximity/probability density of an orbital's electrons near the nucleus ($s > p > d > f$).
Lanthanoid Contraction	The steady, gradual decrease in atomic/ionic radii across the Lanthanoid series ($4f$ filling) due to poor shielding by $4f$ electrons.
Amphoteric Oxide	An oxide that displays both acidic and basic character, reacting with both acids and bases ($\text{e.g.}, \text{Al}_2\text{O}_3, \text{ZnO}$).
Transuranium Elements	Synthetic radioelements with atomic numbers greater than Uranium ($Z > 92$).

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Important Formulas

1. Effective Nuclear Charge ($Z_{eff}$)

$Z_{eff} = Z - \sigma$

• $Z$ = Atomic Number (total nuclear charge / proton count)
• $\sigma$ = Screening constant evaluated via Slater's Rules

2. Pauling Electronegativity Difference

$\Delta X = |X_A - X_B| = 0.208 \times \sqrt{\Delta E} \quad (\text{if bond energies are in kcal/mol})$ $\Delta X = |X_A - X_B| = 0.102 \times \sqrt{\Delta E} \quad (\text{if bond energies are in kJ/mol})$ Where the resonance stabilization energy $\Delta E$ is given by: $\Delta E = E_{A-B} - \sqrt{E_{A-A} \times E_{B-B}}$

3. Mulliken Electronegativity Scale ($X_M$)

$X_M = \frac{IE + EA}{2} \quad (\text{where } IE \text{ and } EA \text{ are in electron-volts, eV})$ $X_M = \frac{IE + EA}{560} \quad (\text{where } IE \text{ and } EA \text{ are in kJ/mol})$

• Conversion to Pauling Scale: $X_P \approx \frac{X_M}{2.8}$

4. Allred-Rochow Electronegativity Scale ($X_{AR}$)

$X_{AR} = 0.359 \left( \frac{Z_{eff}}{r^2} \right) + 0.744$

• $r$ = covalent radius in Ångströms ($\text{\AA}$).

5. Relationship between Electron Gain Enthalpy and Electron Affinity

$\Delta_{eg}H = -EA - \frac{5}{2}RT$ At $T = 0\text{ K}$, $\Delta_{eg}H = -EA$.

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Diagrams (Description Only)

1. Long Form Periodic Table Structure Diagram:
   • Description: A rectangular grid organized into 7 horizontal rows (periods 1 to 7) and 18 vertical columns (groups 1 to 18). Groups 1 and 2 form the $s$-block on the far left; Groups 13 to 18 form the $p$-block on the far right; Groups 3 to 12 form the central $d$-block bridging $s$ and $p$. Two separate horizontal 14-element strips are rendered below the main table, representing the $f$-block (Lanthanoids $4f$ and Actinoids $5f$).
2. Summary of Periodic Trends Vector Diagram:
   • Description: A stylized periodic table outline with directional vectors along two main axes: Across a Period (Left to Right) and Down a Group (Top to Bottom).
   • Left to Right: Arrows point right showing Increasing Ionization Enthalpy, Increasing Electronegativity, Increasing Electron Gain Enthalpy, and Decreasing Atomic Radius.
   • Top to Bottom: Arrows point down showing Increasing Atomic Radius, Increasing Metallic Character, Decreasing Ionization Enthalpy, and Decreasing Electronegativity.
3. Shielding Effect and Effective Nuclear Charge Model:
   • Description: Concentric circular electron shells ($n=1, 2, 3$) surrounding a dense positive nucleus ($+Z$). Core electrons in inner shells $n=1$ and $n=2$ exert outward repulsive force vectors ($F_{repulsion}$) against the outer valence electron in shell $n=3$, partially canceling inward nuclear electrostatic attraction force vectors ($F_{attraction}$), yielding a net inward force corresponding to $Z_{eff}$.
4. Plot of First Ionization Enthalpy vs Atomic Number ($Z=1$ to $20$):
   • Description: Graph showing $\Delta_i H$ on the y-axis against $Z$ on the x-axis. Sharp peaks occur at noble gases ($\text{He, Ne, Ar}$), deep troughs occur at alkali metals ($\text{Li, Na, K}$). Local maxima occur at Be ($2s^2$) and N ($2p^3$), followed by drops at B ($2p^1$) and O ($2p^4$).

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Real-Life Applications

The periodic table has numerous real-life applications, including:

• Predicting the properties of elements and their behavior: Chemist/Engineers utilize periodic trends to estimate unknown boiling points, reactivities, and compound structures prior to laboratory synthesis.
• Identifying elements and their uses: Knowing group trends allows industrial selection of substitutes (e.g., substituting Platinum with Palladium in catalytic converters).
• Developing new materials and technologies:
  • Semiconductor Physics: Group 14 elements ($\text{Si, Ge}$) doped with Group 13 ($\text{B, Ga}$) or Group 15 ($\text{P, As}$) create p-type and n-type silicon chips powering modern microprocessors.
  • Battery Innovation: Lithium ($1s^2 2s^1$) possesses the highest oxidation potential and lowest mass density, making it ideal for high-density rechargeable Lithium-ion batteries.

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Key Points to Remember

• The periodic table is a tabular arrangement of elements, listed in order of increasing atomic number.
• Periodic trends refer to the patterns and relationships that can be observed in the properties of elements.
• The periodic table is divided into four blocks ($s, p, d, f$) and 18 groups.
• Periodicity refers to the repetition of properties and trends in the periodic table due to repeating valence shell electronic configurations.
• 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.
• Inert gas configurations, half-filled shells ($p^3, d^5$), and fully-filled shells ($s^2, p^6, d^{10}$) offer enhanced thermodynamic stability.

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Common Mistakes

• Confusing the periodic table with periodic trends: The periodic table is the physical structural grid arrangement, whereas periodic trends represent mathematical/physical patterns of properties across that grid.
• Not understanding the difference between blocks and groups: Blocks designate the subshell type ($s, p, d, f$) being filled by the valence electron, whereas Groups are vertical columns with identical valence electron counts.
• Not recognizing the repetition of properties and trends in the periodic table: Neglecting how quantum principal numbers ($n$) cause repeating chemical behaviors.
• Ignoring Exceptions in Ionization Enthalpy: Forgetting that Be has higher $\Delta_i H_1$ than B, and N has higher $\Delta_i H_1$ than O due to half-filled subshell stability and penetration effects.
• Assuming Fluorine has higher Electron Gain Enthalpy than Chlorine: Mistakenly picking Fluorine due to its high electronegativity, ignoring Fluorine's intense $2p$ inter-electronic repulsion.

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Quick Revision

• The periodic table is a tabular arrangement of elements.
• Periodic trends refer to the patterns and relationships in the properties of elements.
• The periodic table is divided into four blocks and 18 groups.
• Periodicity refers to the repetition of properties and trends.
• Atomic radius decreases as we move from left to right across a period.
• Electronegativity increases as we move from left to right across a period.
• Ionization energy increases as we move from left to right across a period.
• Electron affinity increases as we move from left to right across a period.
• The s-block elements are located on the left side of the periodic table.
• The p-block elements are located on the right side of the periodic table.
• The d-block elements are located in the middle of the periodic table.
• The f-block elements are located at the bottom of the periodic table.
• Cations are smaller than parent neutral atoms; anions are larger.
• For isoelectronic ions, greater positive charge $\Rightarrow$ smaller radius.
• Chlorine has the most negative electron gain enthalpy in the periodic table.
• Fluorine is the most electronegative element in the periodic table ($4.0$ on Pauling Scale).

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Deep-Dive Case Studies and Real-Life Applications

Case Study 1: Semiconductor Doping and Bandgap Engineering

In solid-state microelectronics, the periodic classification directly dictates how pure Silicon (Group 14, $3s^2 3p^2$) is engineered to construct $p-n$ junctions in microprocessors and solar cells.

• n-type Doping: Introducing Phosphorus (Group 15, $3s^2 3p^3$) into a Silicon lattice provides an extra unbonded valence electron, creating charge carriers (free electrons).
• p-type Doping: Introducing Boron (Group 13, $2s^2 2p^1$) into Silicon creates an electron deficiency or "hole" that acts as a positive charge carrier.
• Outcome: Understanding periodic group behaviors allows researchers to precisely tune semiconductor electrical conductivity across 10 orders of magnitude.

Case Study 2: Lanthanoid Contraction and Its Industrial Consequences

Across the $4f$ series (Lanthanoids, $Z=58$ to $71$), $4f$ orbitals fill progressively. Because $f$-orbitals have diffuse shapes, they exert extremely poor shielding on $5d$ and $6s$ electrons against the increasing nuclear charge ($Z$).

• Consequence: The atomic and ionic radii undergo a continuous, cumulative contraction (Lanthanoid Contraction).
• Industrial Impact: Second and third transition series elements in the same vertical group display nearly identical atomic radii:
  • Zirconium ($\text{Zr}$, Period 5, radius = $160\text{ pm}$) vs Hafnium ($\text{Hf}$, Period 6, radius = $159\text{ pm}$).
  • Separating $\text{Zr}$ and $\text{Hf}$ chemically is extraordinarily difficult, requiring complex liquid-liquid solvent extraction processes for nuclear reactor casing materials (where Zr is required due to low neutron absorption, while Hf absorbs neutrons heavily).

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Step-by-Step Problem Solving Strategies & Detailed Proofs

Strategy 1: Evaluating Effective Nuclear Charge ($Z_{eff}$) Using Slater's Rules

Problem: Calculate $Z_{eff}$ experienced by a $4s$ valence electron in a neutral Zinc atom ($Z=30$).

Step-by-Step Solution:

1. Write and group the electronic configuration: $\text{Zn } (Z=30): (1s^2) (2s^2, 2p^6) (3s^2, 3p^6) (3d^{10}) (4s^2)$
2. Identify target electron: We are testing one $4s$ electron in the $(4s)$ group.
3. Count remaining electrons in each group:
   • Same group $(4s)$: 1 remaining electron $\rightarrow 1 \times 0.35 = 0.35$
   • $(n-1)$ shell $(3d, 3s, 3p)$: $10 + 8 = 18$ electrons $\rightarrow 18 \times 0.85 = 15.30$
   • $(n-2)$ and deeper shells $(1s, 2s, 2p)$: $2 + 8 = 10$ electrons $\rightarrow 10 \times 1.00 = 10.00$
4. Sum contributions to find $\sigma$: $\sigma = 0.35 + 15.30 + 10.00 = 25.65$
5. Calculate $Z_{eff}$: $Z_{eff} = Z - \sigma = 30 - 25.65 = +4.35$

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Strategy 2: Determining Radii Ordering in Isoelectronic Series

Problem: Arrange $\text{Al}^{3+}, \text{Mg}^{2+}, \text{Na}^+, \text{F}^-, \text{O}^{2-}, \text{N}^{3-}$ in order of increasing ionic radius.

Step-by-Step Solution:

1. Verify electron counts for all species:
   • $\text{Al}^{3+}: 13 - 3 = 10 e^-$
   • $\text{Mg}^{2+}: 12 - 2 = 10 e^-$
   • $\text{Na}^+: 11 - 1 = 10 e^-$
   • $\text{F}^-: 9 + 1 = 10 e^-$
   • $\text{O}^{2-}: 8 + 2 = 10 e^-$
   • $\text{N}^{3-}: 7 + 3 = 10 e^-$
2. Identify Nuclear Charge ($Z$):
   • $\text{Al}^{3+} (Z=13), \text{Mg}^{2+} (Z=12), \text{Na}^+ (Z=11), \text{F}^- (Z=9), \text{O}^{2-} (Z=8), \text{N}^{3-} (Z=7)$
3. Apply Isoelectronic Rule: For species with equal electrons, $r \propto \frac{1}{Z}$.
4. Order by increasing radius (smallest to largest): $\text{Al}^{3+} < \text{Mg}^{2+} < \text{Na}^+ < \text{F}^- < \text{O}^{2-} < \text{N}^{3-}$

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Higher-Order Thinking Skills (HOTS) Questions

Q1: The first and second ionization enthalpies ($\text{kJ/mol}$) of three unknown elements X, Y, Z are given below:

• Element X: $\Delta_i H_1 = 520, \quad \Delta_i H_2 = 7300$
• Element Y: $\Delta_i H_1 = 419, \quad \Delta_i H_2 = 3051$
• Element Z: $\Delta_i H_1 = 900, \quad \Delta_i H_2 = 1760$

Which element is likely to be an alkali metal, and which is an alkaline earth metal? Explain.

Answer:

• Element X and Y exhibit massive jumps between $\Delta_i H_1$ and $\Delta_i H_2$ (a factor of over $7\times$ to $14\times$). Removing the second electron requires breaking into a stable noble gas core configuration. Thus, X and Y are Alkali Metals (Group 1). Since Element Y has a lower $\Delta_i H_1$ ($419\text{ kJ/mol}$) than X ($520\text{ kJ/mol}$), Y sits lower down Group 1 than X.
• Element Z exhibits a reasonable, moderate increase from $\Delta_i H_1$ ($900$) to $\Delta_i H_2$ ($1760$). This indicates the removal of two valence electrons from the same outermost shell ($ns^2$). Thus, Element Z is an Alkaline Earth Metal (Group 2).

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Q2: Why is the second electron gain enthalpy ($\Delta_{eg}H_2$) of Oxygen endothermic (positive), even though $\text{O}^{2-}$ attains a stable noble gas configuration ($\text{Ne}$)?

Answer: When a neutral Oxygen atom gains a single electron, the process is exothermic ($\Delta_{eg}H_1 = -141\text{ kJ/mol}$), forming the oxide anion $\text{O}^-(g)$. To convert $\text{O}^-(g)$ into $\text{O}^{2-}(g)$, a second electron must be added to an already negatively charged anion: $\text{O}^-(g) + e^- \longrightarrow \text{O}^{2-}(g) \quad (\Delta_{eg}H_2 = +780\text{ kJ/mol})$ Strong electrostatic repulsion occurs between the incoming electron and the negatively charged $\text{O}^-$ anion. To overcome this repulsion, energy must be absorbed. Consequently, $\Delta_{eg}H_2$ is strongly endothermic. (The lattice energy in solid ionic crystals subsequently stabilizes $\text{O}^{2-}$ species).

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Previous Year Questions (PYQs) with Detailed Solutions

PYQ 1: Define electronegativity. How does it differ from electron gain enthalpy? [CBSE Class 11]

Solution:

• Electronegativity: The relative tendency of an atom in a bonded molecule to attract the shared pair of covalent electrons toward itself.
  • It is a dimensionless relative property (measured on empirical scales like Pauling scale).
  • It applies to bonded atoms in a molecule.
• Electron Gain Enthalpy ($\Delta_{eg}H$): The quantitative measure of energy change (released or absorbed) when an isolated neutral gaseous atom accepts an extra electron to form a univalent anion.
  • It is a quantitatively measurable thermodynamic energy property expressed in $\text{kJ/mol}$ or $\text{eV/atom}$.
  • It applies strictly to isolated, non-bonded gaseous atoms.

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PYQ 2: Explain why the electron gain enthalpy of Chlorine is more negative than that of Fluorine. [NEET / CBSE Class 11]

Solution: Fluorine has a small atomic size with valence electrons in the compact $2p$ subshell ($n=2$). Adding an electron to Fluorine forces it into a restricted volume, producing high electron-electron repulsions that oppose the incoming electron.

Chlorine's valence electrons occupy the larger $3p$ subshell ($n=3$). The added electron experiences significantly weaker repulsive forces. Thus, adding an electron to Chlorine is thermodynamically more favorable, yielding a more negative electron gain enthalpy ($\Delta_{eg}H(\text{Cl}) = -349\text{ kJ/mol}$) than Fluorine ($\Delta_{eg}H(\text{F}) = -328\text{ kJ/mol}$).

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NCERT Textbook Questions & Detailed Answers

Q1: What is the basic theme of organisation of elements in the periodic table?

Answer: The basic theme of organizing elements in the periodic table is to classify elements with similar physical and chemical properties into groups based on their atomic numbers and electronic configurations. This periodic grouping simplifies the systematic study of the properties of elements and their compounds.

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Q2: Which important property did Mendeleev use to classify elements?

Answer: Mendeleev used atomic mass as the fundamental property to classify elements. He arranged elements in increasing order of atomic mass while ensuring that elements with similar chemical properties (especially formulas of their oxides and hydrides) were placed in the same vertical column.

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Q3: What is the basic difference between the Mendeleev’s Periodic Law and Modern Periodic Law?

Answer:

• Mendeleev's Periodic Law: States that physical and chemical properties of elements are periodic functions of their atomic masses.
• Modern Periodic Law: States that physical and chemical properties of elements are periodic functions of their atomic numbers ($Z$).

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Q4: On the basis of quantum numbers, justify that the sixth period of the periodic table should have 32 elements.

Answer: In the periodic table, a period begins with the filling of a new principal energy shell $n$. For the 6th period ($n=6$), electrons fill orbitals according to the Aufbau principle in order of increasing energy: $6s \longrightarrow 4f \longrightarrow 5d \longrightarrow 6p$ The orbital capacities are:

• One $6s$ orbital: holds $2$ electrons
• Seven $4f$ orbitals: hold $14$ electrons
• Five $5d$ orbitals: hold $10$ electrons
• Three $6p$ orbitals: hold $6$ electrons

Total electrons capacity $= 2 + 14 + 10 + 6 = 32\text{ electrons}$. Since each element corresponds to adding one differentiating electron, the 6th period contains 32 elements.

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Q5: Write the atomic number of the element present in the third period and 17th group of the periodic table.

Answer:

• Period = 3 implies outermost principal quantum number $n = 3$.
• Group = 17 corresponds to a halogen with valence shell configuration $ns^2 np^5 \rightarrow 3s^2 3p^5$.
• Complete electronic configuration: $1s^2 2s^2 2p^6 3s^2 3p^5$.
• Total electrons $= 2 + 2 + 6 + 2 + 5 = 17$.
• The element has an atomic number $Z = 17$ (Chlorine, $\text{Cl}$).

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Q6: Which element do you think would have been named by (a) Lawrence Berkeley Laboratory (b) Seaborg’s group?

Answer:

• (a) Lawrencium (Symbol $\text{Lr}$, $Z = 103$) and Californium (Symbol $\text{Cf}$, $Z = 98$) were named in honor of Lawrence Berkeley Laboratory and California.
• (b) Seaborgium (Symbol $\text{Sg}$, $Z = 106$) was named in honor of Glenn T. Seaborg and his research group.

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Q7: Why do elements in the same group have similar physical and chemical properties?

Answer: Elements present in the same group possess the same valence shell electronic configuration (same number of outer-shell electrons). Because chemical properties and reactivity depend primarily on the arrangement and count of valence electrons, elements within a group exhibit similar chemical behaviors and periodic trends.

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Q8: What does atomic radius and ionic radius mean to you?

Answer:

• Atomic Radius: The distance from the center of the nucleus to the outermost electron shell of a neutral isolated atom. Depending on bonding, it is measured as covalent radius, metallic radius, or van der Waals radius.
• Ionic Radius: The effective distance from the nucleus of an ion up to the point where it exerts electrostatic influence on its surrounding electron cloud.

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Q9: How do atomic radius vary in a period and in a group? How do you explain the variation?

Answer:

• Variation Across a Period (Left to Right): Atomic radius decreases.
  • Explanation: Electrons are added to the same main energy shell ($n$), while nuclear charge ($Z$) increases proton by proton. The effective nuclear charge ($Z_{eff}$) increases, pulling outer electrons closer to the nucleus.
• Variation Down a Group (Top to Bottom): Atomic radius increases.
  • Explanation: A new principal energy level ($n$) is added at each successive period, placing outer electrons progressively further from the nucleus and overcoming the increased nuclear charge.

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Q10: What do you understand by isoelectronic species? Name a species that will be isoelectronic with $\text{F}^-$.

Answer: Isoelectronic species are atoms, ions, or molecules that have the same total number of electrons.

• Fluoride ion ($\text{F}^-$) has $9 + 1 = 10\text{ electrons}$.
• Examples of species isoelectronic with $\text{F}^-$ (10 electrons):
  • Anions: $\text{N}^{3-}, \text{O}^{2-}$
  • Neutral atom: $\text{Ne}$
  • Cations: $\text{Na}^+, \text{Mg}^{2+}, \text{Al}^{3+}$

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Q11: Consider the following species: $\text{N}^{3-}, \text{O}^{2-}, \text{F}^-, \text{Na}^+, \text{Mg}^{2+}, \text{Al}^{3+}$. Arrange them in order of increasing ionic radii.

Answer: All given ions are isoelectronic containing 10 electrons. For an isoelectronic series, ionic size decreases as nuclear charge ($Z$) increases:

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

Increasing order of ionic radii: $\text{Al}^{3+} < \text{Mg}^{2+} < \text{Na}^+ < \text{F}^- < \text{O}^{2-} < \text{N}^{3-}$

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Q12: Explain why cation are smaller and anions are larger in radii than their parent atoms?

Answer:

• Cations: Formed by the loss of one or more valence electrons. This often results in the loss of an entire outer energy shell. Furthermore, the remaining electrons experience an increased effective nuclear charge ($Z_{eff}$) per electron, drawing them closer to the nucleus. Thus, $r_{\text{cation}} < r_{\text{parent atom}}$.
• Anions: Formed by adding one or more electrons to the neutral atom. The addition of electrons increases inter-electronic repulsions within the shell, causing the electron cloud to expand. Thus, $r_{\text{anion}} > r_{\text{parent atom}}$.

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Q13: 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': Ensures that individual atoms are completely separated from neighboring atoms, eliminating inter-atomic binding forces, metallic bonds, or lattice interactions that would alter measured energy values.
• 'Ground State': Ensures that the atom is in its lowest energy configuration. If the atom were excited, less energy would be required to remove or add an electron, leading to inconsistent measurement values.

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Q14: 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 $\text{J mol}^{-1}$.

Answer: Ionization enthalpy represents the energy required to move an electron from the ground state ($n=1$) to infinity ($n=\infty$): $\Delta E = E_{\infty} - E_1 = 0 - (-2.18 \times 10^{-18}\text{ J}) = +2.18 \times 10^{-18}\text{ J per atom}$

To calculate ionization enthalpy per mole ($\text{J mol}^{-1}$): $\Delta_i H = (2.18 \times 10^{-18}\text{ J/atom}) \times (6.022 \times 10^{23}\text{ atoms/mol})$ $\Delta_i H = 1.312 \times 10^6\text{ J mol}^{-1} = 1312\text{ kJ mol}^{-1}$

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Q15: 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 (i) Be has higher $\Delta_i H$ than B, (ii) O has lower $\Delta_i H$ than N and F.

Answer:

• (i) Be has higher $\Delta_i H$ than B:
  • Electronic configurations: $\text{Be} (Z=4) = 1s^2 2s^2$; $\text{B} (Z=5) = 1s^2 2s^2 2p^1$.
  • In Beryllium, the electron is removed from a fully filled, stable $2s$ subshell that penetrates closer to the nucleus. In Boron, the electron is removed from a higher energy $2p$ subshell that is less tightly held and easier to remove.
• (ii) O has lower $\Delta_i H$ than N and F:
  • Electronic configurations: $\text{N} (Z=7) = 1s^2 2s^2 2p_x^1 2p_y^1 2p_z^1$ (half-filled $2p^3$ subshell); $\text{O} (Z=8) = 1s^2 2s^2 2p_x^2 2p_y^1 2p_z^1$.
  • Nitrogen possesses extra stability due to a half-filled $2p^3$ configuration.
  • Oxygen has four $2p$ electrons, with paired electrons in one $2p_x$ orbital. The inter-electronic repulsion between electrons in the doubly occupied $2p_x$ orbital makes it easier to remove one electron to attain a half-filled stable $2p^3$ state. Oxygen's $\Delta_i H$ is lower than Fluorine's because Fluorine has a higher $Z_{eff}$.

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Q16: How would you explain the fact that the first ionization enthalpy of sodium is lower than that of magnesium but its second ionization enthalpy is higher than that of magnesium?

Answer:

• First Ionization Enthalpy ($\Delta_i H_1$):
  • $\text{Na} ([Ne] 3s^1) \longrightarrow \text{Na}^+ ([Ne]) + e^-$
  • $\text{Mg} ([Ne] 3s^2) \longrightarrow \text{Mg}^+ ([Ne] 3s^1) + e^-$
  • Na easily loses its single $3s^1$ electron to reach a stable noble gas configuration, while Mg loses one electron from a stable fully filled $3s^2$ subshell with higher $Z_{eff}$. Thus, $\Delta_i H_1(\text{Na}) < \Delta_i H_1(\text{Mg})$.
• Second Ionization Enthalpy ($\Delta_i H_2$):
  • $\text{Na}^+ ([Ne]) \longrightarrow \text{Na}^{2+} ([Ne] 2p^5) + e^-$
  • $\text{Mg}^+ ([Ne] 3s^1) \longrightarrow \text{Mg}^{2+} ([Ne]) + e^-$
  • Removing a second electron from $\text{Na}^+$ requires disrupting a highly stable $2p^6$ noble gas core configuration. For $\text{Mg}^+$, removing the second electron removes the remaining $3s^1$ electron to attain the stable noble gas configuration. Thus, $\Delta_i H_2(\text{Na}) \gg \Delta_i H_2(\text{Mg})$.

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Q17: What are the various factors due to which the ionization enthalpy of the main group elements tends to decrease down a group?

Answer: Ionization enthalpy decreases down a group due to the following factors:

1. Increase in Atomic Size: Additional principal quantum shells ($n$) are added going down the group, increasing the distance between the valence electron and the nucleus.
2. Increase in Shielding/Screening Effect: Additional inner electron shells shield the outer valence electrons from nuclear attraction, reducing the effective nuclear charge felt by outer electrons.
3. Dominance over Nuclear Charge: Although total nuclear charge increases down a group, the impact of increased shell size and inner shielding outweighs nuclear pull, making electron removal easier.

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Q18: The first ionization enthalpy values ($\Delta_i H_1$) of group 13 elements are: B (801), Al (577), Ga (579), In (558), Tl (589) kJ/mol. How would you explain this deviation from the general trend?

Answer: The irregular trend in Group 13 ionization enthalpies is explained by structural shielding anomalies:

• Al to Ga: Gallium ($\text{Ga}$) has $3d^{10}$ electrons in its inner core. $d$-orbitals provide poor shielding compared to $s$ and $p$ orbitals. As a result, the effective nuclear charge on Ga increases, causing its atomic size to contract and its $\Delta_i H_1$ to be slightly higher than Aluminium ($\text{Al}$).
• In to Tl: Thallium ($\text{Tl}$) contains $14$ inner $4f$ electrons. $f$-orbitals exhibit extremely poor shielding power (Lanthanoid Contraction). This weak shielding causes a strong nuclear pull on Tl's valence shell $6s^2 6p^1$ electrons, resulting in a jump in its $\Delta_i H_1$ relative to Indium ($\text{In}$).

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Q19: Which of the following pairs of elements would have a more negative electron gain enthalpy? (a) O or F (b) F or Cl.

Answer:

• (a) F has a more negative electron gain enthalpy than O:
  • Fluorine ($Z=9$) has a higher effective nuclear charge ($Z_{eff}$) and smaller atomic size than Oxygen ($Z=8$), attracting an extra electron more strongly.
• (b) Cl has a more negative electron gain enthalpy than F:
  • Fluorine's $2p$ subshell is extremely small and compact, producing high inter-electronic repulsion when an extra electron is added. Chlorine's outer $3p$ orbital is larger and accommodates the incoming electron with much less repulsion, yielding a more negative $\Delta_{eg}H$.

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Q20: Would you expect the second electron gain enthalpy of O as positive, more negative or less negative than the first? Justify your answer.

Answer: The second electron gain enthalpy ($\Delta_{eg}H_2$) of Oxygen is positive (endothermic).

• The first electron gain forms a monovalent anion: $\text{O}(g) + e^- \longrightarrow \text{O}^-(g) \quad (\Delta_{eg}H_1 = -141\text{ kJ/mol})$
• Adding a second electron to form $\text{O}^{2-}$ requires adding a negative charge to an already negatively charged ion ($\text{O}^-$): $\text{O}^-(g) + e^- \longrightarrow \text{O}^{2-}(g) \quad (\Delta_{eg}H_2 = +780\text{ kJ/mol})$
• Strong electrostatic repulsion between the negative ion and the incoming electron must be overcome by supplying energy, making $\Delta_{eg}H_2$ positive.

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Chapter Summary

The periodic table is a powerful tool for predicting the properties of elements and their behavior. It is a tabular arrangement of elements, listed in order of increasing atomic number. The periodic table is divided into four blocks ($s, p, d, f$) and 18 groups, each with a unique set of properties. Periodic trends refer to the patterns and relationships that can be observed in the properties of elements, governed by variations in $Z_{eff}$, principal quantum shells ($n$), screening effects, and atomic geometry. The repetition of properties and trends in the periodic table is known as periodicity. Understanding the periodic table and its trends is essential for predicting the properties of elements and their behavior.