Comprehensive Notes on Mendeleev and Modern Periodic Classification

Mendeleev's Periodic Classification

• Mendeleev's Periodic Law states that the physical and chemical properties of the elements, as well as the formulae and properties of their compounds, are the periodic functions of their atomic weights (atomic masses).
• Key inferences drawn from Mendeleev's Periodic Law:
  • The physical and chemical properties of the elements depend directly upon their atomic masses.
  • The dependence of physical and chemical properties of elements upon their atomic masses is periodic, meaning that if elements are arranged in increasing order of atomic masses, elements with similar properties recur after regular intervals.
• Mendeleev's Original Periodic Table:
  • Arranged approximately $65$ elements known at the time horizontally in ten series in order of increasing atomic weights.
  • Divided these series into seven horizontal rows (periods) and eight vertical columns (groups).
  • Mendeleev attempted to place elements with similar properties in the same group, occasionally ignoring the strict order of atomic masses to maintain property-based grouping.
  • Gaps were intentionally left in the table for unknown elements, and their physical and chemical properties were predicted based on other elements in the same group.
  • Anecdote: Mendeleev reported that the idea for organizing elements into groups came to him in a dream where he saw all elements fall into place; he recorded his observation immediately upon waking.

Structural Features of Modified Mendeleev's Periodic Table

• Modified Structure Overview:
  • Numbers in bold to the left of element symbols represent atomic numbers ($Z$).
  • Numbers written below element symbols refer to atomic masses.
• Horizontal Series:
  • All known elements are arranged in ten horizontal columns called series.
  • Atomic masses increase in a regular fashion within each series.
• Vertical Groups:
  • Contains nine vertical columns called groups, numbered VIII and zero.
  • Except for group VIII and group zero, all other groups are subdivided into two sub-groups designated as A and B (e.g., IA, IB, IIA, IIB).
  • Group VIII consists of three sets, each containing three elements (total of $9$ elements).
  • Group zero contains noble gases, which were undiscovered at the time of Mendeleev's original table.
  • Elements within a group exhibit similar properties with regular gradation.
• Periods:
  • The ten horizontal series are arranged in seven horizontal columns termed periods, numbered from I to VII.
  • First period: Contains $2$ elements (consists of the 1st series).
  • Second period: Contains $8$ elements (consists of the 2nd series); designated as a short period.
  • Third period: Contains $8$ elements (consists of the 3rd series); designated as a short period.
  • Fourth period: Contains $18$ elements (consists of 4th and 5th series); designated as a long period.
  • Fifth period: Contains $18$ elements (consists of 6th and 7th series); designated as a long period.
  • Sixth period: Contains $32$ elements (consists of 8th and 9th series); designated as a long period.
  • Seventh period: Incomplete period containing $19$ elements belonging to the 10th series.
  • Elements in a period exhibit a gradual change in properties from left to right.

Contributions of Mendeleev's Periodic Table

• Systematic Study of Chemistry:
  • Categorized elements systematically for the first time, making the study of elements and their compounds simpler.
  • Knowing group properties enables the prediction of properties for all elements and compounds within that group.
• Discovery of New Elements:
  • Predicted properties of undiscovered elements and left corresponding gaps.
  • Named undiscovered elements using the prefix eka- based on preceding elements: Ekaaluminium (later discovered as Gallium) and Ekasilicon (later discovered by Winkler in 1886 as Germanium).
  • Detailed Comparison between Ekasilicon ($1871$ prediction) and Germanium ($1886$ discovery):
  • Atomic mass: Predicted $72$; Determined as $72.6$.
  • Density: Predicted $5.5\,g\,cm^{-3}$; Determined as $5.36\,g\,cm^{-3}$.
  • Melting point: Predicted High; Determined as $1231\,K$.
  • Valency: Predicted $4$; Determined as $4$.
  • Action of alkalies: Predicted No action; Determined as No reaction with $\text{NaOH}$.
  • Action of acids: Predicted Slightly attacked by acids; Determined as Not attacked by $\text{HCl}$, reacts with hot concentrated $\text{HNO}_3$.
  • Oxide formula: Predicted $MO_2$; Determined as $GeO_2$.
  • Chloride formula: Predicted $MCl_4$; Determined as $GeCl_4$.
• Correction of Atomic Masses:
  • Helped correct doubtful atomic masses based on periodic positioning.
  • Beryllium atomic mass correction: Previously determined as $14.8$ using Dulong and Petit's law. Mendeleev established Beryllium as bivalent with an equivalent mass of $4.5$. Corrected atomic mass = $\text{equivalent mass} \times \text{valency} = 4.5 \times 2 = 9$.

Defects of Mendeleev's Periodic Table

• Position of Hydrogen: Hydrogen resembles both group IA alkali metals and group VIIA halogens, but was placed only in group IA.
• Position of Isotopes: Isotopes possess different atomic masses but identical chemical properties. Placing them according to atomic weight requires separate positions, which creates an anomaly.
• Position of Lanthanoids and Actinoids: Lanthanoids (14 elements following Lanthanum, $Z = 58$ to $71$) and Actinoids (14 elements following Actinium, $Z = 90$ to $103$) are placed together in group III, violating periodic law.
• Variable Valency: Shows only one characteristic valency per element, whereas many elements exhibit multiple valencies.
• Anomalous Pairs of Elements: Several pairs violate the order of increasing atomic mass:
  • Argon (atomic mass $39.9$) is placed before Potassium (atomic mass $39.1$).
  • Tellurium (atomic mass $127.61$) is placed before Iodine (atomic mass $126.91$).
  • Strict adherence to atomic weight would place Potassium in group zero and Argon in group IA.
• Similar Elements Placed in Different Groups: Elements with similar chemical properties are separated, such as Silver ($Ag$) and Thallium ($Tl$), Barium ($Ba$) and Lead ($Pb$), Copper ($Cu$) and Mercury ($Hg$).
• Dissimilar Elements Placed in the Same Group: Elements in sub-groups A and B exhibit completely different physical and chemical properties despite being placed in the same main group.
• Eighth Group Anomalies: Full of anomalies; except Osmium ($Os$), no element in group VIII exhibits the group octavalency.

Modern Periodic Law and Long Form Periodic Table

• Modern Periodic Law:
  • Established by Moseley, who showed that atomic number ($Z$), rather than atomic mass, is the most fundamental property determining physical and chemical behavior.
  • Statement: "The physical and chemical properties of the elements are the periodic functions of their atomic numbers."
  • Implication: Arranging elements in order of increasing atomic number results in a periodic recurrence of similar physical and chemical properties at regular intervals.
• Structure of the Long Form (Extended Form) Periodic Table:
  • Periods (7 horizontal rows):
  • Period 1: Contains $2$ elements ($H, He$); short period.
  • Period 2: Contains $8$ elements ($Li$ to $Ne$); short period.
  • Period 3: Contains $8$ elements ($Na$ to $Ar$); short period.
  • Period 4: Contains $18$ elements ($K$ to $Kr$); long period.
  • Period 5: Contains $18$ elements ($Rb$ to $Xe$); long period.
  • Period 6: Contains $32$ elements ($Cs$ to $Rn$), including 14 lanthanides placed separately at the bottom; long period.
  • Period 7: Contains $32$ elements ($Fr$ to $Og$), including 14 actinides placed separately at the bottom.
  • Groups (18 vertical columns):
  • Numbered 1 to 18 according to IUPAC recommendations ($1984$).
  • Replaces sub-groups A and B.

Electronic Configuration and Period Formation

• Relationship between Quantum Shells and Periods:
  • Principal quantum number ($n$) of the valence shell corresponds to the period number.
  • A period begins with the filling of a new principal energy shell and ends when the shell orbitals are completely filled according to the Bohr-Bury scheme.
• Detailed Orbital Filling per Period:
  • First Period ($n = 1$): Fills $1s$ orbital (max $2$ electrons). Contains $2$ elements: $H\,(1s^1)$ and $He\,(1s^2)$. K shell is completed at $He$
  • Second Period ($n = 2$): Fills $2s$ and $2p$ orbitals (4 orbitals total, max $8$ electrons). Contains $8$ elements ($Li$ to $Ne$). L shell completed at $Ne$.
  • Third Period ($n = 3$): Fills $3s$ and $3p$ orbitals (4 orbitals total, max $8$ electrons). The $3d$ orbitals are higher in energy than $4s$, so they remain unfilled. Contains $8$ elements ($Na\,[Ne]3s^1$ to $Ar\,[Ne]3s^2 3p^6$).
  • Fourth Period ($n = 4$): Fills $4s$, $3d$, and $4p$ orbitals in order. Contains $18$ elements: $K\,(4s^1)$, $Ca\,(4s^2)$, $Sc\,(3d^1 4s^2)$ to $Zn\,(3d^{10} 4s^2)$, and $Ga\,(3d^{10} 4s^2 4p^1)$ to $Kr\,(3d^{10} 4s^2 4p^6)$.
  • Fifth Period ($n = 5$): Fills $5s$, $4d$, and $5p$ orbitals in order. Contains $18$ elements: $Rb\,(5s^1)$, $Sr\,(5s^2)$, $Y\,(4d^1 5s^2)$ to $Cd\,(4d^{10} 5s^2)$, and $In\,(4d^{10} 5s^2 5p^1)$ to $Xe\,(4d^{10} 5s^2 5p^6)$.
  • Sixth Period ($n = 6$): Fills $6s$, $5d$ (1 electron in $La$), $4f$, remainder of $5d$, and $6p$ orbitals in order. Contains $32$ elements: $Cs\,(6s^1)$, $Ba\,(6s^2)$, $La\,([Xe]5d^1 6s^2)$, Lanthanoids $Ce\,(4f^1 5d^1 6s^2)$ to $Lu\,(4f^{14} 5d^1 6s^2)$, $Hg\,(4f^{14} 5d^{10} 6s^2)$, and $Tl\,(4f^{14} 5d^{10} 6s^2 6p^1)$ to $Rn\,(4f^{14} 5d^{10} 6s^2 6p^6)$.
  • Seventh Period ($n = 7$): Fills $7s$, $6d$ (1 electron in $Ac$), $5f$, remainder of $6d$, and $7p$ orbitals. Contains $32$ elements: $Fr\,(7s^1)$, $Ra\,(7s^2)$, $Ac\,(6d^1 7s^2)$, Actinoids $Th\,(\text{theoretical: } 5f^1 6d^1 7s^2;\text{ observed: } 5f^0 6d^2 7s^2)$ to $Lr\,(5f^{14} 6d^1 7s^2)$, up to $Og\,(7p^6)$.
• Orbitals Filled and Capacity Summary:
  • First Period: Orbitals filled = $1s$; Electrons accommodated = $2$; Total elements = $2$.
  • Second Period: Orbitals filled = $2s, 2p$; Electrons accommodated = $2 + 6 = 8$; Total elements = $8$.
  • Third Period: Orbitals filled = $3s, 3p$; Electrons accommodated = $2 + 6 = 8$; Total elements = $8$.
  • Fourth Period: Orbitals filled = $4s, 3d, 4p$; Electrons accommodated = $2 + 10 + 6 = 18$; Total elements = $18$.
  • Fifth Period: Orbitals filled = $5s, 4d, 5p$; Electrons accommodated = $2 + 10 + 6 = 18$; Total elements = $18$.
  • Sixth Period: Orbitals filled = $6s, 5d, 4f, 5d, 6p$; Electrons accommodated = $2 + 1 + 14 + 9 + 6 = 32$; Total elements = $32$.
  • Seventh Period: Orbitals filled = $7s, 6d, 5f, 6d, 7p$; Electrons accommodated = $2 + 1 + 14 + 9 + 6 = 32$; Total elements = $32$.

IUPAC Nomenclature for Elements with $Z > 100$

• System Context: Elements with atomic numbers $Z > 100$ are synthesized via artificial transmutation, are highly unstable, and are produced in minute quantities. To avoid priority disputes (e.g., element $104$ named Rutherfordium by American scientists and Kurchatovium by Soviet scientists), systematic IUPAC rules were created.
• Nomenclature Rules:
  • Names are constructed directly from atomic number digits using specific roots:
  • Digit $0$: Root = nil; Abbreviation = n
  • Digit $1$: Root = un; Abbreviation = u
  • Digit $2$: Root = bi; Abbreviation = b
  • Digit $3$: Root = tri; Abbreviation = t
  • Digit $4$: Root = quad; Abbreviation = q
  • Digit $5$: Root = pent; Abbreviation = p
  • Digit $6$: Root = hex; Abbreviation = h
  • Digit $7$: Root = sept; Abbreviation = s
  • Digit $8$: Root = oct; Abbreviation = o
  • Digit $9$: Root = enn; Abbreviation = e
  • Roots are written in sequence according to the digits of the atomic number and terminated with the suffix -ium.
  • Spelling modifications:
  • If enn appears before nil, the second n of enn is dropped (e.g., en-nil).
  • If bi or tri appears before -ium, the final i is dropped (e.g., b-ium, tr-ium).
  • Element symbols consist of the combined single-letter abbreviations of the roots.
• Systematic Names and IUPAC Official Names for $Z > 100$:
  • $Z = 101$: Systematic Name = Unnilunium; Symbol = Unu; Official Name = Mendelevium; Official Symbol = Md
  • $Z = 102$: Systematic Name = Unnilbium; Symbol = Unb; Official Name = Nobelium; Official Symbol = No
  • $Z = 103$: Systematic Name = Unniltrium; Symbol = Unt; Official Name = Lawrencium; Official Symbol = Lr
  • $Z = 104$: Systematic Name = Unnilquadium; Symbol = Unq; Official Name = Rutherfordium; Official Symbol = Rf
  • $Z = 105$: Systematic Name = Unnilpentium; Symbol = Unp; Official Name = Dubnium; Official Symbol = Db
  • $Z = 106$: Systematic Name = Unnilhexium; Symbol = Unh; Official Name = Seaborgium; Official Symbol = Sg
  • $Z = 107$: Systematic Name = Unnilseptium; Symbol = Uns; Official Name = Bohrium; Official Symbol = Bh
  • $Z = 108$: Systematic Name = Unniloctium; Symbol = Uno; Official Name = Hassium; Official Symbol = Hs
  • $Z = 109$: Systematic Name = Unnilennium; Symbol = Une; Official Name = Meitnerium; Official Symbol = Mt
  • $Z = 110$: Systematic Name = Ununnillium; Symbol = Uun; Official Name = Darmstadtium; Official Symbol = Ds
  • $Z = 111$: Systematic Name = Unununium; Symbol = Uuu; Official Name = Roentgenium; Official Symbol = Rg
  • $Z = 112$: Systematic Name = Ununbium; Symbol = Uub; Official Name = Copernicium; Official Symbol = Cn
  • $Z = 113$: Systematic Name = Ununtrium; Symbol = Uut; Official Name = Nihonium; Official Symbol = Nh
  • $Z = 114$: Systematic Name = Ununquadium; Symbol = Uuq; Official Name = Flerovium; Official Symbol = Fl
  • $Z = 115$: Systematic Name = Ununpentium; Symbol = Uup; Official Name = Moscovium; Official Symbol = Mc
  • $Z = 116$: Systematic Name = Ununhexium; Symbol = Uuh; Official Name = Livermorium; Official Symbol = Lv
  • $Z = 117$: Systematic Name = Ununseptium; Symbol = Uus; Official Name = Tennessine; Official Symbol = Ts
  • $Z = 118$: Systematic Name = Ununoctium; Symbol = Uuo; Official Name = Oganesson; Official Symbol = Og

Division of Periodic Table into Blocks

• Classification based on subshell filling:
  • s-Block: Outer electronic configuration = $ns^{1-2}$. Includes Groups 1 and 2.
  • p-Block: Outer electronic configuration = $ns^2 np^{1-6}$. Includes Groups 13 to 18.
  • d-Block: Outer electronic configuration = $(n-1)d^{1-10} ns^{1-2}$. Includes Groups 3 to 12.
  • f-Block: Outer electronic configuration = $(n-2)f^{1-14} (n-1)d^{0-1} ns^2$. Includes Lanthanoids and Actinoids.
• Merits of the Long Form Periodic Table:
  • Based on atomic number, a fundamental property of elements.
  • Position directly correlates with electronic configuration.
  • Groups elements into distinct physical blocks ($s, p, d, f$).
  • Justifies placing isotopes in the same position due to identical atomic numbers.
  • Eliminates group VIII anomalies by splitting it into distinct groups 8, 9, and 10.
  • Separates dissimilar elements previously lumped into sub-groups A and B.
• Defects of the Long Form Periodic Table:
  • Hydrogen position remains poorly defined (resembles group 1 alkali metals and group 17 halogens).
  • Helium ($1s^2$) is placed in p-block (Group 18) despite lacking an $ns^2 np^6$ configuration.
  • Lanthanoids and Actinoids are not incorporated into the main body of the periodic table.
• Methods for Predicting Period, Block, and Group:
  • Differentiating Electron: The electron occupying the final position while writing the electronic configuration of an atom.
  • Period: Determined by the principal quantum number ($n$) of the valence shell.
  • Block: Determined by the subshell entered by the differentiating electron (Helium is an exception).
  • Group Determination Rules:
  • For s-block elements: $\text{Group number} = \text{number of valence electrons}$.
  • For p-block elements: $\text{Group number} = 10 + \text{number of valence electrons}$.
  • For d-block elements: $\text{Group number} = 2 + \text{number of } (n-1)d \text{ electrons}$.
  • Worked Examples:
  • Magnesium ($Mg, Z = 12$): Configuration $1s^2 2s^2 2p^6 3s^2$. Differentiating electron in $3s$; Valence $n = 3$; Valence electrons = $2$. Block = s-block; Period = Third; Group = 2.
  • Vanadium ($V, Z = 23$): Configuration $1s^2 2s^2 2p^6 3s^2 3p^6 3d^3 4s^2$. Differentiating electron in $3d$; Valence $n = 4$; $(n-1)d$ electrons = $3$. Block = d-block; Period = Fourth; Group = $2 + 3 = 5$.
  • Antimony ($Sb, Z = 51$): Configuration $1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 5s^2 5p^3$. Differentiating electron in $5p$; Valence $n = 5$; Valence electrons = $2 + 3 = 5$. Block = p-block; Period = Fifth; Group = 10 + 5 = 15$.\n * Radon (Rn, Z = 86$): Configuration$1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 4f^{14} 5s^2 5p^6 5d^{10} 6s^2 6p^6$. Differentiating electron in$6p$; Valence$n = 6$; Valence electrons =$2 + 6 = 8$. Block = p-block; Period = Sixth; Group =$10 + 8 = 18$.

Detailed Categories of Elements

• Noble Gases:
  • Group 18 (zero group in old scheme) elements at the extreme right of each period: $He\,(Z=2)$, $Ne\,(Z=10)$, $Ar\,(Z=18)$, $Kr\,(Z=36)$, $Xe\,(Z=54)$, $Rn\,(Z=86)$.
  • Outer shell configuration = $ns^2 np^6$ (except Helium, which is $1s^2$).
  • Possess fully filled outer and inner shells according to Bohr-Bury scheme, leading to high chemical stability and negligible tendency to gain or lose electrons under normal conditions.
  • Helium application: Required in hospitals for MRI machines to cool superconducting magnets to $-269^\circ\text{C}$, as Helium has the lowest boiling point of any element.
• Representative or Normal Elements (s- and p-block elements):
  • s-Block Elements (Group 1 Alkali Metals and Group 2 Alkaline Earth Metals):
  • Group 1 Configuration: $ns^1$ (e.g., $H: 1s^1$, $Li: 1s^2 2s^1$, $Na: 1s^2 2s^2 2p^6 3s^1$, $K: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^1$).
  • Group 2 Configuration: $ns^2$ (e.g., $Be: 1s^2 2s^2$, $Mg: 1s^2 2s^2 2p^6 3s^2$, $Ca: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2$, $Sr: 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 5s^2$).
  • Characteristics: White or greyish-white metallic luster; soft, malleable, ductile, good conductors of heat/electricity; highly electropositive with low ionization energies; form ionic compounds; non-variable valency ($+1$ for Group 1, $+2$ for Group 2); strong reducing agents.
  • p-Block Elements (Groups 13, 14, 15, 16, 17, 18):
  • Configurations range from $ns^2 np^1$ to $ns^2 np^6$ (e.g., $B: 1s^2 2s^2 2p^1$, $C: 1s^2 2s^2 2p^2$, $N: 1s^2 2s^2 2p^3$, $O: 1s^2 2s^2 2p^4$, $F: 1s^2 2s^2 2p^5$, $Ne: 1s^2 2s^2 2p^6$).
  • Characteristics: Contains non-metals, metalloids, and metals; low electropositive character with higher electronegativity and ionization energy; form predominantly covalent compounds; exhibit variable valency/oxidation states.
• Transition Elements (d-Block Elements):
  • Groups 3 to 12 elements with differentiating electrons entering $(n-1)d$ subshells. General configuration = $(n-1)d^{1-10} ns^{1-2}$.
  • Transition Series Breakdown:
  • First Transition Series (3d series, $Z = 21$ to $30$): Filling of $3d$ subshell. First member $Sc\,(1s^2 2s^2 2p^6 3s^2 3p^6 3d^1 4s^2)$; Last member $Zn\,(1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2)$.
  • Second Transition Series (4d series, $Z = 39$ to $48$): Filling of $4d$ subshell. First member $Y\,(1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^1 5s^2)$; Last member $Cd\,(1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 5s^2)$.
  • Third Transition Series (5d series, $Z = 57, 72$ to $80$): Filling of $5d$ subshell. First member $La\,(1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 5s^2 5p^6 5d^1 6s^2)$; Last member $Hg\,(1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 4f^{14} 5s^2 5p^6 5d^{10} 6s^2)$.
  • Fourth Transition Series (6d series): Incomplete, involves filling of $6d$ subshell.
  • Characteristics: High melting and boiling point metals; variable valency and multiple oxidation states; form coloured and paramagnetic ions containing unpaired electrons; exhibit catalytic properties; form coordination/complex compounds and alloys.
  • Medical role: Cobalt is an essential structural component of Vitamin $B_{12}$, required for red blood cell formation and nervous system function.
• Inner Transition Elements (f-Block Elements):
  • Elements where differentiating electrons enter the $(n-2)f$ antepenultimate subshell. General configuration = (n-2)f^{1-14} (n-1)d^{0-1} ns^2$.\n * Series Division:\n * Lanthanoid Series: 14 elements from Cerium (Ce, Z = 58$) to Lutetium ($Lu, Z = 71$). Configuration =$4f^{1-14} 5d^{0-1} 6s^2. Also called rare earth elements.\n * Ce\,(Z=58): 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 4f^1 5s^2 5p^6 5d^1 6s^2\n * Lu\,(Z=71): 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 4f^{14} 5s^2 5p^6 5d^1 6s^2\n * Actinoid Series: 14 elements from Thorium (Th, Z = 90$) to Lawrencium ($Lr, Z = 103$). Configuration =$5f^{1-14} 6d^{0-1} 7s^2.\n * Pa\,(Z=91): 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 4f^{14} 5s^2 5p^6 5d^{10} 5f^2 6s^2 6p^6 6d^1 7s^2\n * Characteristics: High density, high melting/boiling point metals; variable valencies; coloured and paramagnetic ions; radioactive nature; form complex compounds.\n\n# Periodic Trends in Atomic and Ionic Radii\n\n* Cause of Periodicity: Recurrence of similar valence shell electronic configurations at regular intervals when elements are arranged by increasing atomic numbers. Example: Halogens (F, Cl, Br, I, At$) all share an$ns^2 np^5 valence shell configuration.\n* Atomic Radius Definitions:\n * Distance from nucleus center to the point where outer electron density is effectively zero.\n * Metallic / Crystal Radius: Half the internuclear distance between two adjacent metal atoms in a crystal lattice. Sodium internuclear distance = 3.72\,\text{\AA}$; Metallic radius =$\frac{3.72}{2} = 1.86\,\text{\AA}.\n * Covalent Radius: Half the distance between nuclei of two identical atoms joined by a single covalent bond. Oxygen (O_2$) internuclear distance =$1.32\,\text{\AA}$; Covalent radius =$\frac{1.32}{2} = 0.66\,\text{\AA}$. Additive property example:$H = 0.37\,\text{\AA}$,$Cl = 0.99\,\text{\AA}$; Internuclear distance in$HCl = 0.37 + 0.99 = 1.36\,\text{\AA}.\n * van der Waals' Radius: Half the internuclear distance between two non-bonded atoms of adjacent molecules at closest approach. Hydrogen closest approach = 2.4\,\text{\AA}$; van der Waals' radius =$\frac{2.4}{2} = 1.2\,\text{\AA}.\n * Radius Size Comparison: \text{Covalent Radius} < \text{Metallic Radius} < \text{van der Waals' Radius}.\n* Variations in Atomic Radii:\n * Period Trend: Decreases left to right. Principal energy shell remains constant, while increasing nuclear charge pulls the electron cloud closer.\n * Second Period Values: Li\,(1.23\,\text{\AA})$,$Be\,(0.90\,\text{\AA})$,$B\,(0.80\,\text{\AA})$,$C\,(0.77\,\text{\AA})$,$N\,(0.75\,\text{\AA})$,$O\,(0.74\,\text{\AA})$,$F\,(0.72\,\text{\AA})$. Neon ($Ne = 1.31\,\text{\AA}$) is an exception because$1.31\,\text{\AA} represents its non-bonded van der Waals' radius.\n * Group Trend: Increases top to bottom down a group. Addition of new quantum shells outweighs the effect of increased nuclear charge.\n * Group 1 Values: H\,(0.37\,\text{\AA})$,$Li\,(1.23\,\text{\AA})$,$Na\,(1.57\,\text{\AA})$,$K\,(2.02\,\text{\AA})$,$Rb\,(2.16\,\text{\AA})$,$Cs\,(2.35\,\text{\AA}).\n* Ionic Radii:\n * Cation Radii: Always smaller than parent atomic radii. Loss of valence electrons increases effective nuclear charge per remaining electron. Valence shell removal may also occur.\n * Na\,(1.57\,\text{\AA}) \rightarrow Na^+\,(0.95\,\text{\AA}) + e^-\n * Mg\,(1.36\,\text{\AA}) \rightarrow Mg^{2+}\,(0.65\,\text{\AA}) + 2e^-\n * Anion Radii: Always larger than parent atomic radii. Addition of valence electrons decreases effective nuclear charge and increases inter-electronic repulsion, expanding the electron cloud.\n * Cl\,(0.99\,\text{\AA}) + e^- \rightarrow Cl^-\,(1.81\,\text{\AA})\n * Comparative Atomic vs Ionic Radii Summary Data:\n * Cations: Li\,(1.23\,\text{\AA}) / Li^+\,(0.60\,\text{\AA})$;$Na\,(1.57\,\text{\AA}) / Na^+\,(0.95\,\text{\AA})$;$K\,(2.02\,\text{\AA}) / K^+\,(1.33\,\text{\AA})$;$Mg\,(1.36\,\text{\AA}) / Mg^{2+}\,(0.65\,\text{\AA})$;$Ca\,(1.40\,\text{\AA}) / Ca^{2+}\,(0.99\,\text{\AA})$;$Al\,(1.25\,\text{\AA}) / Al^{3+}\,(0.50\,\text{\AA})$;$Fe\,(1.26\,\text{\AA}) / Fe^{2+}\,(0.76\,\text{\AA}).\n * Anions: F\,(0.72\,\text{\AA}) / F^-\,(1.36\,\text{\AA})$;$Cl\,(0.99\,\text{\AA}) / Cl^-\,(1.81\,\text{\AA})$;$Br\,(1.14\,\text{\AA}) / Br^-\,(1.95\,\text{\AA})$;$I\,(1.33\,\text{\AA}) / I^-\,(2.16\,\text{\AA})$;$O\,(0.73\,\text{\AA}) / O^{2-}\,(1.40\,\text{\AA})$;$S\,(1.02\,\text{\AA}) / S^{2-}\,(1.84\,\text{\AA})$;$N\,(0.75\,\text{\AA}) / N^{3-}\,(1.71\,\text{\AA}).\n* Isoelectronic Ions:\n * Ions with identical electron counts but differing nuclear charges (Z).\n * Size is inversely proportional to \frac{Z}{e}$ratio (Nuclear Charge / Number of Electrons). Smaller$\frac{Z}{e} value indicates larger ionic radius.\n * Isoelectronic 10-Electron Series Data:\n * N^{3-}$:$Z = 7$;$e = 10$;$\frac{Z}{e} = 0.7$; Ionic Radius =$1.71\,\text{\AA}\n * O^{2-}$:$Z = 8$;$e = 10$;$\frac{Z}{e} = 0.8$; Ionic Radius =$1.40\,\text{\AA}\n * F^-$:$Z = 9$;$e = 10$;$\frac{Z}{e} = 0.9$; Ionic Radius =$1.36\,\text{\AA}\n * Ne$:$Z = 10$;$e = 10$;$\frac{Z}{e} = 1.0$; Radius =$1.12\,\text{\AA}\n * Na^+$:$Z = 11$;$e = 10$;$\frac{Z}{e} = 1.1$; Ionic Radius =$0.95\,\text{\AA}\n * Mg^{2+}$:$Z = 12$;$e = 10$;$\frac{Z}{e} = 1.2$; Ionic Radius =$0.65\,\text{\AA}\n * Al^{3+}$:$Z = 13$;$e = 10$;$\frac{Z}{e} = 1.3$; Ionic Radius =$0.50\,\text{\AA}\n * Isoelectronic Examples:\n * Isoelectronic with Ne$(10 electrons):$N^{3-}, O^{2-}, F^-, Na^+, Mg^{2+}, Al^{3+}.\n * Isoelectronic with Cl^-$(18 electrons):$S^{2-}, Cl^-, Ar, K^+, Ca^{2+}, Sc^{3+}.\n * Isoelectronic with H^-$(2 electrons):$He, Li^+, Be^{2+}.\n * Isoelectronic with Rb^+$(36 electrons):$Kr, Sr^{2+}, Y^{3+}.\n\n# Periodic Trends in Valency\n\n* Definition: Expressed as combining capacity relative to Hydrogen, Chlorine, or double the Oxygen atom count.\n* Period Trend: Across a period, valency with respect to Hydrogen and Chlorine increases from 1$to$4$, then decreases to$0.\n* Valency Data Across Second and Third Periods:\n * Second Period Hydrides & Valency wrt H:\n * LiH (Valency = 1)\n * BeH_2 (Valency = 2)\n * BH_3 (Valency = 3)\n * CH_4 (Valency = 4)\n * NH_3 (Valency = 3)\n * H_2O (Valency = 2)\n * HF (Valency = 1)\n * Second Period Chlorides & Valency wrt Cl:\n * LiCl (Valency = 1)\n * BeCl_2 (Valency = 2)\n * BCl_3 (Valency = 3)\n * CCl_4 (Valency = 4)\n * NCl_3 (Valency = 3)\n * Cl_2O (Valency = 2)\n * FCl (Valency = 1)\n * Third Period Hydrides & Valency wrt H:\n * NaH (Valency = 1)\n * MgH_2 (Valency = 2)\n * AlH_3 (Valency = 3)\n * SiH_4 (Valency = 4)\n * PH_3 (Valency = 3)\n * H_2S (Valency = 2)\n * HCl (Valency = 1)\n\n# Ionisation Enthalpy (Ionisation Energy)\n\n* Definition: Amount of energy required to remove the most loosely bound electron from an isolated gaseous atom to form a unipositive gaseous ion.\n * Reaction Equation: M(g) + \text{Energy}(\Delta_i H \text{ or } \text{IE}) \rightarrow M^+(g) + e^-\n * Units: Expressed in kJ\,mol^{-1}$or electron volts ($eV$).$1\,eV = 1.6021 \times 10^{-19}\,J = 1.6021 \times 10^{-22}\,kJ.\n* Successive Ionisation Energies:\n * Second (\text{IE}2$) and Third ($\text{IE}_3) Ionisation Energies require removing electrons from positively charged cations, which possess smaller ionic radii and higher effective nuclear charges.\n * Universal Order: \text{IE}_3 > \text{IE}_2 > \text{IE}_1\n* Ionisation Energy Values (\text{IE}_1, \text{IE}_2, \text{IE}_3$in$kJ\,mol^{-1}):\n * H\,(1s^1)$:$\text{IE}_1 = 1312.0\n * He\,(1s^2)$:$\text{IE}_1 = 2372.6$,$\text{IE}_2 = 5246.7\n * Li\,(1s^2 2s^1)$:$\text{IE}_1 = 520.3$,$\text{IE}_2 = 7297$,$\text{IE}_3 = 11810\n * Be\,(1s^2 2s^2)$:$\text{IE}_1 = 899.5$,$\text{IE}_2 = 1757$,$\text{IE}_3 = 14850\n * B\,(1s^2 2s^2 2p^1)$:$\text{IE}_1 = 800.6$,$\text{IE}_2 = 2427$,$\text{IE}_3 = 3650\n * C\,(1s^2 2s^2 2p^2)$:$\text{IE}_1 = 1086.4$,$\text{IE}_2 = 2352$,$\text{IE}_3 = 4619\n * N\,(1s^2 2s^2 2p^3)$:$\text{IE}_1 = 1402$,$\text{IE}_2 = 2860$,$\text{IE}_3 = 4577\n * O\,(1s^2 2s^2 2p^4)$:$\text{IE}_1 = 1314$,$\text{IE}_2 = 3389$,$\text{IE}_3 = 5301\n * F\,(1s^2 2s^2 2p^5)$:$\text{IE}_1 = 1681$,$\text{IE}_2 = 3366$,$\text{IE}_3 = 6066\n * Ne\,(1s^2 2s^2 2p^6)$:$\text{IE}_1 = 2080$,$\text{IE}_2 = 3963$,$\text{IE}_3 = 6192\n* Factors Influencing Ionisation Energy:\n * Size of the atom: Larger atomic size reduces electrostatic attraction between nucleus and valence electron, decreasing \text{IE}.\n * Nuclear charge: Higher nuclear charge increases nuclear attraction, increasing \text{IE}.\n * Screening Effect / Shielding Effect: Inner shell electrons shield outer valence electrons from the full nuclear charge. Effective nuclear charge is defined by Z^* = Z - S$(where$Z$is actual nuclear charge and$S$is the screening constant). Greater inner electron counts increase screening, lowering$\text{IE}.\n * Penetration Effect of Electrons: Penetration power for the same principal quantum shell (n$) follows the order$s > p > d > f$. Higher penetration places electrons closer to the nucleus, raising$\text{IE}$in the order$s > p > d > f.\n * Electronic Configuration: Fully filled (ns^2$,$ns^2 np^6$) and half-filled ($ns^2 np^3) subshells possess enhanced extra stability, requiring higher energy to remove an electron.\n\n# Electron Gain Enthalpy\n\n* Definition: Enthalpy change occurring when an electron is added to an isolated gaseous neutral atom to form a mono-negative gaseous ion.\n* Successive Electron Gain Enthalpies:\n * First electron gain enthalpy (\Delta{eg} H_1) is typically negative (exothermic process).\n * Second electron gain enthalpy (\Delta_{eg} H_2) is always positive (endothermic process) due to strong electrostatic repulsion between the added electron and the mono-negative ion.\n * Oxygen Examples:\n * O(g) + e^- \rightarrow O^-(g); \Delta_{eg} H_1 = -141.0\,kJ\n * O^-(g) + e^- \rightarrow O^{2-}(g); \Delta_{eg} H_2 = +780.0\,kJ\n * Sulphur Examples:\n * S(g) + e^- \rightarrow S^-(g); \Delta_{eg} H_1 = -200.4\,kJ\n * S^-(g) + e^- \rightarrow S^{2-}(g); \Delta_{eg} H_2 = -590\,kJ (stated positive process in text)\n* Influencing Factors:\n * Nuclear charge: Higher nuclear charge yields more negative electron gain enthalpies.\n * Atomic size: Larger atomic size decreases attraction on incoming electrons, yielding less negative electron gain enthalpies.\n * Electronic configuration: Stable filled or half-filled shells exhibit little attraction for extra electrons, yielding large positive values.\n* Periodic Trends:\n * Period Trend: Becomes progressively more negative left to right across a period due to decreasing size and increasing nuclear charge.\n * Group Trend: Becomes less negative moving down a group due to increased atomic size.\n* Notable Specific Trends:\n * Halogens possess the most negative electron gain enthalpies in their respective periods.\n * Chlorine (Cl$) has a more negative electron gain enthalpy than Fluorine ($F$). Fluorine's small size causes intense inter-electronic repulsion in its compact$2p$subshell compared to Chlorine's spacious$3p subshell.\n * Noble gases and Group 2 elements exhibit large positive electron gain enthalpies due to filled stable configurations.\n * Nitrogen possesses a positive electron gain enthalpy due to its stable half-filled 2p^3 shell.\n* Calculation Example: Conversion of 10^6$(one million) Oxygen atoms into$O^- ions:\n * 6.022 \times 10^{23}\text{ atoms release } 141\,kJ\n * \text{Energy released} = \frac{141}{6.022 \times 10^{23}} \times 10^6 = 2.34 \times 10^{-16}\,kJ\n\n# Electronegativity\n\n* Definition: The structural property or tendency of an atom in a covalent bond to pull the shared pair of electrons toward itself.\n* Factors Influencing Electronegativity:\n * Effective Nuclear Charge: Higher Z^* yields higher electronegativity.\n * Atomic Size: Smaller atomic size yields higher electronegativity.\n * Oxidation State: Higher oxidation state increases electronegativity (e.g., \text{Fe}^{3+} > \text{Fe}^{2+}).\n * State of Hybridisation: Higher s-character in hybrid orbitals increases electronegativity due to orbital proximity to nucleus:\n * sp^3$hybridisation ($25\%$s-character): Electronegativity =$2.48\n * sp^2$hybridisation ($33.3\%$s-character): Electronegativity =$2.75\n * sp$hybridisation ($50\%$s-character): Electronegativity =$3.29\n* Periodic Trends:\n * Period Trend: Increases left to right across a period (Group 1 alkali metals are least electronegative/electropositive; Group 17 halogens are most electronegative).\n * Group Trend: Decreases down a group due to increasing atomic size.\n* Specific Comparative Exceptions & Notes:\n * Electronegativities of Cesium (Cs$) and Francium ($Fr$) are equal; the addition of a shell from$Cs$to$Fr$is balanced by an increase of$+32 in nuclear charge.\n * Fluorine (F$) is the most electronegative element ($F > Cl$), although Chlorine ($Cl$) has a higher electron affinity ($Cl > F).\n * Group 13 (IIIA) shows an irregular electronegativity trend going down the group due to transition contraction: Electronegativity of Gallium (Ga$) > Electronegativity of Aluminium ($Al$$).