Atomic Structure, Electron Configuration, Periodic Radii Trends, and Ionisation Energies

Atomic Structure and Fundamental Subatomic Particles

• All matter is composed of atoms, which represent the smallest parts of an element capable of participating in chemical reactions.

• The physical anatomy of an atom consists primarily of empty space surrounding a tiny, highly dense, centrally located nucleus.

• The nucleus contains the heavy nucleons: positively charged protons and neutral neutrons.

• Negatively charged electrons orbit the nucleus within discrete principal energy levels or quantum shells, creating a diffuse cloud of negative charge around the central core.

• The atom is maintained as a stable entity by the electrostatic attraction between the positively charged nucleus and the negatively charged electrons.

• The absolute masses and electrical charges of individual subatomic particles are exceptionally small; for convenience, chemists employ relative mass and relative charge scales based on comparisons among particles:

  • Proton: Relative mass = $1$; Relative charge = $+1$; Absolute charge = $+1.602 \times 10^{-19}\,\text{C}$.

  • Neutron: Relative mass = $1$; Relative charge = $0$; Absolute charge = $0\,\text{C}$.

  • Electron: Relative mass = $\frac{1}{1836}$ (almost negligible); Relative charge = $-1$; Absolute charge = $-1.602 \times 10^{-19}\,\text{C}$.

• Virtually the entire mass of an atom is concentrated within the nucleus because protons and neutrons are approximately $1836$ times heavier than electrons.

Behavior of Subatomic Particles in an Electric Field

• When beams of protons, neutrons, and electrons are passed at identical velocities through a uniform electric field between two oppositely charged plates, their physical trajectories diverge based on their charge-to-mass ($e/m$) ratios.

• Electrons: Deflect sharply and strongly toward the positively charged plate, confirming their negative charge. Because electrons have an exceptionally small mass ($\frac{1}{1836}$ relative mass), their acceleration is large, resulting in high curvature.

• Protons: Deflect gently toward the negatively charged plate, confirming their positive charge. Because protons are significantly heavier than electrons (mass ratio of approximately $1836:1$), they experience substantially less deflection along an identical flight path.

• Neutrons: Travel in a completely straight path without any deflection, confirming that they possess zero electrical charge and are entirely unaffected by electrostatic fields.

Atomic Notation and Subatomic Structure Determination

• Every chemical element and isotope is represented symbolically using standardized nuclear notation:

• Atomic Number ($Z$): Defined as the total number of protons located within the nucleus of an atom. The atomic number defines the chemical identity of an element. In an uncharged, neutral atom, the number of electrons is equal to the number of protons ($\text{Electrons} = Z$).

• Mass Number ($A$): Also termed nucleon number; defined as the total sum of protons and neutrons situated within the nucleus ($A = \text{protons} + \text{neutrons}$).

• Calculating Subatomic Composition:

  • $\text{Number of protons} = Z$

  • $\text{Number of neutrons} = A - Z$

  • $\text{Number of electrons (neutral atom)} = Z$

  • $\text{Number of electrons (positive ion / cation)} = Z - (\text{positive charge})$

  • $\text{Number of electrons (negative ion / anion)} = Z + (\text{magnitude of negative charge})$

• Worked Examples of Subatomic Structure Calculations:

  • Determination of Protons:

  • $\text{Mg}^{2+}$ ion: Atomic number $Z = 12$. Therefore, it possesses $12$ protons.

  • Carbon atom: Atomic number $Z = 6$. Therefore, it possesses $6$ protons.

  • Unknown atom of element $X$ with mass number $A = 63$ and $34$ neutrons: $\text{Protons} = A - \text{neutrons} = 63 - 34 = 29$. Element $X$ is copper ($\text{Cu}$, $Z = 29$).

  • Determination of Electrons:

  • $\text{Mg}^{2+}$ ion: Neutral magnesium has $12$ electrons; losing $2$ electrons to establish a $2+$ charge leaves $12 - 2 = 10$ electrons.

  • Carbon atom: Neutral atom with $Z = 6$ possesses $6$ orbiting electrons.

  • Neutral atom of element $X$ ($A = 63$, $34$ neutrons): Protons = $29$, meaning the neutral atom possesses $29$ electrons.

  • Determination of Neutrons:

  • $\text{Mg}^{2+}$ ion: $A = 24$, $Z = 12$. $\text{Neutrons} = 24 - 12 = 12$.

  • Carbon atom: $A = 12$, $Z = 6$. $\text{Neutrons} = 12 - 6 = 6$.

  • Neutral atom of element $X$: $A = 63$, $Z = 29$. $\text{Neutrons} = 63 - 29 = 34$.

Isotopes: Characteristics and Applications

• Definition: Isotopes are atoms of the same element that contain the same number of protons and electrons, but a different number of neutrons.

• Nomenclature: Written as the element name or chemical symbol followed by a hyphen and the mass number (e.g., carbon-12 and carbon-14, which possess $6$ and $8$ neutrons, respectively).

• Isotopic Symbols: Display the identical chemical symbol and atomic number $Z$, differing solely in nucleon number $A$ (e.g., chlorine-35, ${}^{35}_{17}\text{Cl}$, and chlorine-37, ${}^{37}_{17}\text{Cl}$).

• Isotopes of Hydrogen:

  • Protium (${}^1_1\text{H}$): $1$ proton, $0$ neutrons, $1$ electron.

  • Deuterium (${}^2_1\text{H}$): $1$ proton, $1$ neutron, $1$ electron.

  • Tritium (${}^3_1\text{H}$): $1$ proton, $2$ neutrons, $1$ electron.

• Chemical Properties of Isotopes:

  • Isotopes of a given element display identical chemical reactivity.

  • Chemical properties are determined solely by the number and arrangement of valence shell electrons.

  • Because all isotopes of an element share identical electron configurations, they form identical chemical bonds, react with identical elements, and demonstrate identical reaction mechanisms.

• Physical Properties of Isotopes:

  • Isotopes display slight variations in physical properties (such as density, boiling point, and melting point).

  • Neutrons contribute directly to nuclear mass without exerting charge or altering bonding dynamics; heavier isotopes therefore possess higher relative atomic masses and greater densities.

• Practical Applications of Isotopic Mass Discrepancies:

  • Mass Spectrometry: Enables qualitative identification and precise quantitative detection of isotopes separated by mass-to-charge ($m/z$) ratios.

  • Isotope Separation: Utilized in nuclear energy and isotope enrichment programs based on subtle physical diffusion or centrifugal velocity differences.

  • Medical Imaging & Diagnostics: Radioisotopes exploit nuclear instability and physical radiation decay signatures for targeted imaging and therapeutics.

Electronic Structure: Principal Quantum Shells and Sub-shells

• The specific arrangement of electrons inside an atom is designated as its electronic configuration.

• Electrons reside in discrete principal energy levels designated by the principal quantum number ($n$):

  • Lower values of $n$ correspond to shells located physically closer to the nucleus.

  • Higher values of $n$ denote quantum shells situated farther from the nucleus with progressively higher total energy.

• Maximum Electron Capacity per Principal Quantum Shell:

  • $n = 1$: up to $2$ electrons

  • $n = 2$: up to $8$ electrons

  • $n = 3$: up to $18$ electrons

  • $n = 4$: up to $32$ electrons

• Principal quantum shells are partitioned into sub-shells designated by the letters $s$, $p$, $d$, and $f$:

  • Elements possessing greater than $57$ electrons also incorporate an $f$ sub-shell.

  • Within any given principal quantum shell, the energy of the sub-shells increases in the strict order: $s < p < d < f$.

• Summary of Quantum Shell Architecture:

  • Shell $n = 1$: Possesses $s$ sub-shell ($1$ orbital); holds $2$ electrons per sub-shell; total $1$ orbital, maximum $2$ electrons per shell.

  • Shell $n = 2$: Possesses $s$ sub-shell ($1$ orbital, $2$ electrons) and $p$ sub-shell ($3$ orbitals, $6$ electrons); total $4$ orbitals, maximum $8$ electrons per shell.

  • Shell $n = 3$: Possesses $s$ sub-shell ($1$ orbital, $2$ electrons), $p$ sub-shell ($3$ orbitals, $6$ electrons), and $d$ sub-shell ($5$ orbitals, $10$ electrons); total $9$ orbitals, maximum $18$ electrons per shell.

  • Shell $n = 4$: Possesses $s$ sub-shell ($1$ orbital, $2$ electrons), $p$ sub-shell ($3$ orbitals, $6$ electrons), $d$ sub-shell ($5$ orbitals, $10$ electrons), and $f$ sub-shell ($7$ orbitals, $14$ electrons); total $16$ orbitals, maximum $32$ electrons per shell.

Atomic Orbitals: Geometry, Degeneracy, and Energy Overlap

• Definition of Atomic Orbital: A region of three-dimensional space situated at a specific energy level in which there is a high probability of finding up to a maximum of two electrons.

• Electrons are restricted to discrete, quantized energy states; they cannot exist at intermediate energies between orbitals.

• Degeneracy: Orbitals residing within the identical sub-shell in the ground state have identical energies and are defined as degenerate (e.g., $p_x$, $p_y$, and $p_z$ are mutually degenerate).

• Orbital Shapes:

  • $s$ Orbitals: Spherically symmetrical centered around the nucleus. The physical diameter and radius of $s$ orbitals expand as the principal quantum number increases ($1s < 2s < 3s$).

• $p$ Orbitals: Possess a directional, two-lobed dumbbell geometry. Every quantum shell from $n = 2$ upward possesses three distinct $p$ orbitals ($p_x$, $p_y$, and $p_z$) oriented mutually perpendicular ($90^\circ$) to one another along the Cartesian axes. The lobes elongate and expand with higher principal quantum numbers.

• $d$ and $f$ Orbitals: The $d$ sub-shell contains $5$ degenerate orbitals ($10$ electrons max), while the $f$ sub-shell contains $7$ degenerate orbitals ($14$ electrons max). The specific geometries of $d$ orbitals are not required at AS Level.

  • Sub-shell Energy Inversion and Overlap:

• Although principal quantum shells generally ascend in energy with increasing $n$, sub-shell energies overlap starting at $n = 3$.

• Specifically, the $4s$ sub-shell is lower in energy than the $3d$ sub-shell in neutral atoms.

• Consequently, the $4s$ sub-shell fills with electrons prior to the occupation of the $3d$ sub-shell.

Principles Governing Electronic Configuration

• Ground State: Represents the lowest energy, most thermodynamically stable electronic configuration of an isolated atom, realized by sequentially populating sub-shells from lowest energy ($1s$) upwards.

• Electron Spin and Magnetic Moment:

  • Electrons behave as localized spinning electrical charges rotating about their intrinsic axes in either a clockwise or anticlockwise sense.

  • This rotation induces a magnetic dipole, conventionally represented by upward-pointing ($\uparrow$) and downward-pointing ($\downarrow$) arrows.

• Pauli Exclusion Principle and Spin-Pair Repulsion:

  • Any individual atomic orbital can accommodate a maximum of two electrons, which must possess opposite (antiparallel) spins.

  • When two negatively charged electrons occupy the identical orbital volume, they experience mutual electrostatic repulsion termed spin-pair repulsion.

• Hund's Rule of Maximum Multiplicity:

  • When electrons enter degenerate orbitals (orbitals of identical energy within a sub-shell, such as $p_x$, $p_y$, $p_z$), they occupy separate orbitals singly with parallel spins before any pairing occurs, minimizing inter-electronic repulsion.

  • Pairing only takes place once every orbital in the sub-shell contains one electron; upon pairing, the second electron adopts an opposite spin.

• Orbital Box Notation:

  • Each orbital is represented by an individual box, arranged in ascending energetic order from left to right.

  • Opposite spins are shown as opposing vertical arrows ($\upharpoonleft\downharpoonright$ or $\uparrow\downarrow$).

  • Example - Titanium ($Z = 22$):

  • Titanium has $22$ electrons. Its configuration fills $1s$, $2s$, $2p$, $3s$, $3p$, $4s$, and partially occupies $3d$.

  • The box configuration is written as: $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2\,3d^2$.

  • The second $4s$ electron is not promoted to the $3d$ level because doing so would not yield an energetic advantage (it would not produce a full or half-full $d$ sub-shell).

• Free Radicals:

  • A free radical is an atom or molecular fragment bearing one or more unpaired electrons, conventionally designated with a bold dot (e.g., $\text{Cl}^\bullet$).

  • Free radicals are generated when a covalent bond breaks via homolytic fission, where each bonded atom retrieves one electron from the shared electron pair.

  • The chlorine free radical ($\text{Cl}^\bullet$) has the configuration $1s^2\,2s^2\,2p^6\,3s^2\,3p^5$; two $3p$ orbitals contain paired electrons while the third contains an unpaired electron.

Periodic Blocks and Determining Electronic Configurations

• Periodic Table Blocks: The Periodic Table is organized into discrete structural blocks based upon the identity of the sub-shell containing the highest-energy valence electron:

  • $s$-block: Groups 1 and 2 (valence electrons reside in an $s$ orbital).

  • $p$-block: Groups 13 to 18 (valence electrons reside in a $p$ orbital).

  • $d$-block: Transition metals (valence electrons reside in a $d$ orbital).

  • $f$-block: Lanthanoids and actinoids (valence electrons reside in an $f$ orbital).

• Configuration Formats:

  • Full Configuration: Explicitly lists every occupied sub-shell from $1s$ upward.

  • Shorthand Configuration: Replaces inner core electrons with the bracketed chemical symbol of the preceding noble gas (e.g., $[\text{Ar}]$ representing the $18$-electron core $1s^2\,2s^2\,2p^6\,3s^2\,3p^6$).

• Rules for Ion Formation:

  • Anions: Formed by adding electrons to the lowest available unoccupied outer sub-shell.

  • Cations: Formed by removing electrons from the outermost quantum shell.

  • Transition Metal Ion Rule: Although neutral transition metals fill the $4s$ sub-shell before $3d$, they always lose their outermost $4s$ electrons first when forming cations, before any $3d$ electrons are removed.

  • Neutral Iron ($\text{Fe}$, $Z = 26$): Full = $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^6\,4s^2$; Shorthand = $[\text{Ar}]\,3d^6\,4s^2$.

  • Iron(II) Ion ($\text{Fe}^{2+}$, $24$ electrons): Full = $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^6$; Shorthand = $[\text{Ar}]\,3d^6$.

• Exceptions to the Aufbau Principle (Chromium and Copper):

  • Chromium ($\text{Cr}$, $Z = 24$): Configuration is $[\text{Ar}]\,3d^5\,4s^1$ rather than the predicted $[\text{Ar}]\,3d^4\,4s^2$.

  • Copper ($\text{Cu}$, $Z = 29$): Configuration is $[\text{Ar}]\,3d^{10}\,4s^1$ rather than the predicted $[\text{Ar}]\,3d^9\,4s^2$.

  • Thermodynamic Rationale: Promoting one electron from the $4s$ orbital into the $3d$ sub-shell produces an exactly half-filled ($3d^5$) or fully filled ($3d^{10}$) sub-shell. These configurations confer added stability due to minimized inter-electron repulsion and enhanced exchange energy.

• Worked Examples of Electronic Configurations:

  • Potassium ($Z = 19$):

  • Total electrons = $19$

  • Full configuration: $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^1$

  • Shorthand configuration: $[\text{Ar}]\,4s^1$

  • Calcium ($Z = 20$):

  • Total electrons = $20$

  • Full configuration: $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2$

  • Shorthand configuration: $[\text{Ar}]\,4s^2$

  • Gallium ($Z = 31$):

  • Total electrons = $31$

  • Full configuration: $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^{10}\,4s^2\,4p^1$

  • Shorthand configuration: $[\text{Ar}]\,3d^{10}\,4s^2\,4p^1$

  • Calcium Ion ($\text{Ca}^{2+}$):

  • Total electrons = $18$ (losses of both $4s$ electrons)

  • Full configuration: $1s^2\,2s^2\,2p^6\,3s^2\,3p^6$

  • Shorthand configuration: $[\text{Ar}]$

Periodic Trends in Atomic and Ionic Radii

• Definition of Atomic Radius: Equal to half the distance between the centers of two identical nuclei bonded covalently in a homonuclear diatomic molecule ($\text{Atomic Radius} = \frac{d}{2}$).

• Periodic Trends in Atomic Radii:

  • Across a Period (Left to Right): Atomic radius decreases systematically.

  • Nuclear charge increases as protons are sequentially added to the nucleus.

  • Additional electrons enter the identical principal quantum shell, meaning inner-core electron shielding remains relatively constant.

  • The increased effective nuclear charge pulls the electron cloud closer to the nucleus.

  • Down a Group (Top to Bottom): Atomic radius increases systematically.

  • Each successive period introduces an entirely new principal quantum shell of electrons.

  • The increased number of inner shells provides greater electron shielding, which offsets and outweighs the increase in nuclear charge, weakening the net attraction and allowing the valence shell to expand outward.

  • Noble Gas to Alkali Metal Discontinuity: A sharp, dramatic expansion in atomic radius occurs between the noble gas terminating one period and the alkali metal initiating the next. The alkali metal places its lone valence electron into a new quantum shell, experiencing pronounced shielding.

• Trends in Ionic Radii:

  • Positive Ions (Cations): Always smaller than their parent neutral atoms.

  • Cations form when atoms shed valence electrons.

  • The remaining electrons experience an unchanged positive nuclear charge, increasing the effective nuclear pull per electron. The electron cloud is drawn inward.

  • Higher positive charges produce smaller ionic radii (e.g., $\text{Al}^{3+} < \text{Mg}^{2+} < \text{Na}^+$).

  • Negative Ions (Anions): Always larger than their parent neutral atoms.

  • Anions form when atoms capture additional electrons.

  • With nuclear charge constant, added electrons increase electron-electron repulsion and outer-shell shielding, expanding the electron cloud outward.

  • Higher negative charges produce larger ionic radii (e.g., $\text{O}^{2-} > \text{F}^-$).

• Quantitative Radii of Selected Elements and Their Ions (in picometres, $\text{pm}$):

  • Group 1:

  • Period 2: $\text{Li} = 134\,\text{pm}$; $\text{Li}^+ = 90\,\text{pm}$

  • Period 3: $\text{Na} = 154\,\text{pm}$; $\text{Na}^+ = 116\,\text{pm}$

  • Period 4: $\text{K} = 196\,\text{pm}$; $\text{K}^+ = 152\,\text{pm}$

  • Period 5: $\text{Rb} = 211\,\text{pm}$; $\text{Rb}^+ = 166\,\text{pm}$

  • Group 2:

  • Period 2: $\text{Be} = 90\,\text{pm}$; $\text{Be}^{2+} = 59\,\text{pm}$

  • Period 3: $\text{Mg} = 130\,\text{pm}$; $\text{Mg}^{2+} = 86\,\text{pm}$

  • Period 4: $\text{Ca} = 174\,\text{pm}$; $\text{Ca}^{2+} = 114\,\text{pm}$

  • Period 5: $\text{Sr} = 192\,\text{pm}$; $\text{Sr}^{2+} = 132\,\text{pm}$

  • Group 13:

  • Period 2: $\text{B} = 82\,\text{pm}$; $\text{B}^{3+} = 41\,\text{pm}$

  • Period 3: $\text{Al} = 118\,\text{pm}$; $\text{Al}^{3+} = 68\,\text{pm}$

  • Period 4: $\text{Ga} = 126\,\text{pm}$; $\text{Ga}^{3+} = 76\,\text{pm}$

  • Period 5: $\text{In} = 144\,\text{pm}$; $\text{In}^{3+} = 94\,\text{pm}$

  • Group 16:

  • Period 2: $\text{O} = 73\,\text{pm}$; $\text{O}^{2-} = 126\,\text{pm}$

  • Period 3: $\text{S} = 102\,\text{pm}$; $\text{S}^{2-} = 170\,\text{pm}$

  • Period 4: $\text{Se} = 116\,\text{pm}$; $\text{Se}^{2-} = 184\,\text{pm}$

  • Period 5: $\text{Te} = 135\,\text{pm}$; $\text{Te}^{2-} = 207\,\text{pm}$

  • Group 17:

  • Period 2: $\text{F} = 71\,\text{pm}$; $\text{F}^- = 119\,\text{pm}$

  • Period 3: $\text{Cl} = 99\,\text{pm}$; $\text{Cl}^- = 167\,\text{pm}$

  • Period 4: $\text{Br} = 114\,\text{pm}$; $\text{Br}^- = 182\,\text{pm}$

  • Period 5: $\text{I} = 133\,\text{pm}$; $\text{I}^- = 206\,\text{pm}$

Ionisation Energy: Definitions, Equations, and Influencing Factors

• Definition of Ionisation Energy (IE): The amount of energy required to remove one mole of electrons from one mole of gaseous atoms of an element to form one mole of gaseous ions under standard conditions ($298\,\text{K}$ and $101\,\text{kPa}$).

• Thermodynamic Nature: Ionisation energies are always endothermic processes characterized by positive values ($\Delta H > 0$), as energy must be supplied to overcome the electrostatic attraction between negative electrons and the positive nucleus.

• Units: Kilojoules per mole ($\text{kJ}\,\text{mol}^{-1}$).

• First Ionisation Energy ($\text{IE}_1$): The energy required to remove one mole of electrons from one mole of gaseous atoms of an element to form one mole of gaseous $1+$ ions.

  • General equation: $\text{X}\,(g) \rightarrow \text{X}^+\,(g) + e^-$

  • Specific example (Calcium): $\text{Ca}\,(g) \rightarrow \text{Ca}^+\,(g) + e^- \quad \text{IE}_1 = +590\,\text{kJ}\,\text{mol}^{-1}$

• Second Ionisation Energy ($\text{IE}_2$): The energy required to remove one mole of electrons from one mole of gaseous $1+$ ions to form one mole of gaseous $2+$ ions.

  • General equation: $\text{X}^+\,(g) \rightarrow \text{X}^{2+}\,(g) + e^-$

  • Specific example (Calcium): $\text{Ca}^+\,(g) \rightarrow \text{Ca}^{2+}\,(g) + e^- \quad \text{IE}_2 = +1145.4\,\text{kJ}\,\text{mol}^{-1}$ (tabulated also as $+1150\,\text{kJ}\,\text{mol}^{-1}$)

• Procedural Rules for Equations:

  • Ionisation processes proceed strictly one electron at a time. Formulating multi-electron simultaneous removals (e.g., $\text{Ca}\,(g) \rightarrow \text{Ca}^{2+}\,(g) + 2e^-$) is chemically inaccurate.

  • Gaseous state symbols ($g$) are mandatory in all definitions and balanced thermochemical equations.

• The Four Factors Dictating Ionisation Energy:

  • Nuclear Charge (Proton Number): Greater numbers of protons intensify positive electrostatic attraction toward orbiting electrons, requiring more energy for electron extraction (increases IE).

  • Distance from the Nucleus (Atomic Radius): Electrostatic force falls rapidly with increasing separation distance. Electrons situated farther away experience weaker attraction, facilitating removal (decreases IE).

  • Electron Shielding (Inner Shell Screening): Concentric shells of negative inner electrons repel valence electrons and screen them from the full positive nuclear charge, attenuating net pull (decreases IE).

  • Spin-Pair Repulsion: Two electrons forced to occupy the same spatial orbital experience inter-electronic repulsion due to identical negative charges, slightly destabilizing them and easing removal (decreases IE).

Periodicity and Anomalies in First Ionisation Energies

• First ionisation energy exhibits clear periodicity across the Periodic Table:

  • Group 1 alkali metals possess low first ionisation energies due to a single, well-shielded outer electron.

  • Group 18 noble gases possess exceptionally high first ionisation energies due to fully saturated shells and maximum effective nuclear charge.

• General Period Trend (Across a Period): First ionisation energy increases.

  • Nuclear charge increases with proton addition.

  • Atomic radius decreases across the period.

  • Shielding remains relatively constant because electrons enter the same quantum shell.

  • Net attraction increases, making outer electrons harder to remove.

• General Group Trend (Down a Group): First ionisation energy decreases.

  • Nuclear charge increases down the group.

  • Number of principal shells increases, enlarging atomic radius.

  • Inner-shell electron shielding multiplies significantly.

  • Increased shielding and distance outweigh the increased nuclear charge, weakening attraction and making outer electrons easier to extract.

• Summary of Trends:

  • Across a Period: Nuclear charge increases; number of shells remains constant; distance to outer electron decreases; shielding remains relatively constant; atomic radius decreases; outer electron is harder to remove (IE increases).

  • Down a Group: Nuclear charge increases; number of shells increases; distance to outer electron increases; shielding increases; atomic radius increases; outer electron is easier to remove (IE decreases).

• Discontinuities (Dips) Across Period 2:

  • Beryllium to Boron Drop:

  • Beryllium ($\text{IE}_1 = 900\,\text{kJ}\,\text{mol}^{-1}$): Electronic configuration = $1s^2\,2s^2$.

  • Boron ($\text{IE}_1 = 800\,\text{kJ}\,\text{mol}^{-1}$): Electronic configuration = $1s^2\,2s^2\,2p^1$.

  • The fifth electron in boron enters the $2p$ sub-shell, which is higher in energy, situated on average farther from the nucleus, and partially shielded by the internal $2s$ electrons. Consequently, less energy is needed to remove Boron's $2p^1$ electron than Beryllium's paired $2s$ electron.

  • Nitrogen to Oxygen Drop:

  • Nitrogen ($\text{IE}_1 = 1400\,\text{kJ}\,\text{mol}^{-1}$): Electronic configuration = $1s^2\,2s^2\,2p_x^1\,2p_y^1\,2p_z^1$.

  • Oxygen ($\text{IE}_1 = 1310\,\text{kJ}\,\text{mol}^{-1}$): Electronic configuration = $1s^2\,2s^2\,2p_x^2\,2p_y^1\,2p_z^1$.

  • In nitrogen, each $2p$ orbital contains one single electron with parallel spins. In oxygen, the $2p_x$ orbital contains two paired electrons. Mutual spin-pair repulsion within the shared $2p_x$ orbital destabilizes the paired electron, making it easier to remove than an electron from nitrogen's half-filled sub-shell.

• Discontinuities (Dips) Across Period 3:

  • Magnesium to Aluminium Drop: Aluminium's ($1s^2\,2s^2\,2p^6\,3s^2\,3p^1$) outermost electron enters the higher-energy, shielded $3p$ sub-shell, dropping its $\text{IE}_1$ below that of magnesium ($1s^2\,2s^2\,2p^6\,3s^2$).

  • Phosphorus to Sulfur Drop: Sulfur exhibits spin-pair repulsion in its paired $3p_x^2$ orbital, reducing its $\text{IE}_1$ relative to phosphorus.

Successive Ionisation Energies and Electronic Shell Deduction

• Successive ionisation energies for an element always increase monotonically ($\text{IE}_1 < \text{IE}_2 < \text{IE}_3 < \text{IE}_4 \dots$).

  • Each subsequent electron is extracted from an increasingly positive cation.

  • Total electron-electron repulsion decreases, and the remaining electrons experience reduced shielding.

  • The proton-to-electron ratio rises, drawing remaining electrons closer to the nucleus.

• Successive Ionisation Energies of Calcium:

  • First IE ($590\,\text{kJ}\,\text{mol}^{-1}$): Removal of $4s^1$ electron from $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2$.

  • Second IE ($1150\,\text{kJ}\,\text{mol}^{-1}$): Removal of remaining $4s$ electron from $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^1$; harder to remove due to higher net attraction and absence of spin-pair repulsion.

  • Third IE ($4940\,\text{kJ}\,\text{mol}^{-1}$): Sharp jump; the electron is taken from the inner $3p$ sub-shell of $1s^2\,2s^2\,2p^6\,3s^2\,3p^6$, which is significantly closer to the nucleus with less shielding.

  • Fourth IE ($6480\,\text{kJ}\,\text{mol}^{-1}$): Removal of second electron from the $3p$ sub-shell ($1s^2\,2s^2\,2p^6\,3s^2\,3p^5$).

• Interpreting Successive Ionisation Energy Graphs:

  • Large jumps signify that an electron is being removed from a completely new, inner principal quantum shell (closer to the nucleus, significantly less shielding).

  • Smaller intermediate jumps reflect shifts between sub-shells within the same principal quantum shell (such as transition from $p$ to $s$ sub-shell).

• Deducing Group Numbers and Electronic Structures:

  • Counting the number of electrons removed prior to the first major jump reveals the total number of valence electrons, establishing the main group position.

  • Sodium ($Z = 11$):

  • Successive IEs: 1st = $494\,\text{kJ}\,\text{mol}^{-1}$, 2nd = $4560\,\text{kJ}\,\text{mol}^{-1}$, 3rd = $6940\,\text{kJ}\,\text{mol}^{-1}$, 4th = $9540\,\text{kJ}\,\text{mol}^{-1}$.

  • The large jump between the 1st and 2nd IEs confirms $1$ valence electron ($3s^1$), placing sodium in Group 1.

  • Magnesium ($Z = 12$):

  • Successive IEs: 1st = $736\,\text{kJ}\,\text{mol}^{-1}$, 2nd = $1450\,\text{kJ}\,\text{mol}^{-1}$, 3rd = $7740\,\text{kJ}\,\text{mol}^{-1}$, 4th = $10500\,\text{kJ}\,\text{mol}^{-1}$.

  • The large jump between the 2nd and 3rd IEs confirms $2$ valence electrons ($3s^2$), placing magnesium in Group 2.

  • Aluminium ($Z = 13$):

  • Successive IEs: 1st = $577\,\text{kJ}\,\text{mol}^{-1}$, 2nd = $1820\,\text{kJ}\,\text{mol}^{-1}$, 3rd = $2740\,\text{kJ}\,\text{mol}^{-1}$, 4th = $11600\,\text{kJ}\,\text{mol}^{-1}$.

  • The large jump between the 3rd and 4th IEs confirms $3$ valence electrons ($3s^2\,3p^1$), placing aluminium in Group 13.

• Worked Example: Deducing Unknown Element Identity from Successive IEs:

  • Problem Statement: Deduce the electronic configuration of Element $Z$, a Period 3 element, given its successive ionisation energies:

  • 5th IE = $6542\,\text{kJ}\,\text{mol}^{-1}$

  • 6th IE = $9362\,\text{kJ}\,\text{mol}^{-1}$

  • 7th IE = $11018\,\text{kJ}\,\text{mol}^{-1}$

  • 8th IE = $33606\,\text{kJ}\,\text{mol}^{-1}$

  • Analysis:

  • A massive jump of $22588\,\text{kJ}\,\text{mol}^{-1}$ occurs between the 7th and 8th ionisation energies.

  • This proves that $7$ electrons occupy the outermost principal quantum shell before the 8th electron must be extracted from an inner, highly shielded quantum shell.

  • Element $Z$ possesses $7$ valence electrons and belongs to Group 17.

  • In Period 3, the Group 17 element is chlorine ($\text{Cl}$, $Z = 17$).

  • Full electronic configuration of Chlorine: $1s^2\,2s^2\,2p^6\,3s^2\,3p^5$.

Atomic Structure and the Subatomic Entourage

• Honey, let us talk about matter: literally everything in existence is built from atoms, which are the ultimate drama queens and the smallest units of an element capable of getting caught up in chemical reactions.

• If you peek inside an atom's private life, it is mostly complete emptiness surrounding an impossibly tiny, dense nucleus holding all the real weight dead in the center.

• Living in that nuclear VIP suite are the heavy nucleons: the unapologetically positive protons and the totally unbothered, zero-charge neutrons.

• Meanwhile, the negatively charged electrons are circling outside in discrete principal energy levels like clingy exes, spreading a diffuse cloud of negative vibes all around the core.

• The only reason this entire dysfunctional setup does not fall apart is pure electrostatic attraction between that positively charged nucleus and those negative electrons.

Drama in the Electric Field

• When you fire protons, neutrons, and electrons through a uniform electric field at identical velocities, their true colors come out based on their messy charge-to-mass ($e/m$) ratios.

• Electrons: Absolutely cannot play it cool. They veer sharply toward the positive plate because opposites attract, proving their negative charge. Because they weigh practically nothing ($\frac{1}{1836}$ relative mass), they experience massive acceleration and swerve with maximum curvature.

• Protons: Drift rather gracefully toward the negative plate, confirming their positive nature. But because they are roughly $1836$ times heavier than electrons, they barely budge compared to the electrons over the same distance.

• Neutrons: Total boundary queens—they walk right through in a dead-straight line without flinching, completely indifferent to electrostatic drama because they have zero charge.

Isotopes: Same Name, Secret Baggage

• The Scoop: Isotopes are atoms of the exact same element with the exact same count of protons and electrons, but someone brought extra baggage—a different number of neutrons.

• The Rebrand: They show up as the element name with their updated mass number tacked on, like carbon-12 versus carbon-14 (who clearly has $2$ extra neutrons worth of secrets).

• Isotopic Symbols: They flaunt the identical atomic number $Z$, but their nucleon number $A$ gives away who has packed on extra nuclear mass (think chlorine-35, ${}^{35}<em>{17}\text{Cl}$, versus chlorine-37, ${}^{37}</em>{17}\text{Cl}$).

• The Hydrogen Trio Exposed:

  • Protium (${}^1_1\text{H}$): The minimalist original with $1$ proton, $0$ neutrons, and $1$ electron.

  • Deuterium (${}^2_1\text{H}$): The middle child who brought along $1$ neutron for extra heft.

  • Tritium (${}^3_1\text{H}$): The heaviest one of all, burdened with $2$ extra neutrons.

• The True Tea on Their Behavior: Chemically, they are total clones—they react with the exact same partners because their outer valence electrons are identical. Physically, though? Different masses and different densities mean mass spectrometers expose them every single time.

Electronic Hierarchy: Quantum Shells and Sub-shells

• The seating arrangement of electrons is called their electronic configuration, and nobody is allowed to just sit wherever they want.

• Electrons are assigned strict principal quantum numbers ($n$):

  • Lower $n$ values are stuck sitting right under the nose of the controlling nucleus.

  • Higher $n$ values get to sit in higher-energy luxury further away.

• Strict Guest Capacities per Shell:

  • Shell $n = 1$: VIP booth for up to $2$ electrons only.

  • Shell $n = 2$: Caps out at $8$ electrons.

  • Shell $n = 3$: Holds up to $18$ electrons.

  • Shell $n = 4$: Expands to fit $32$ electrons before security cuts them off.

Atomic Orbitals: Geometry, Cliques, and the 4s Betrayal

• What an Orbital Really Is: A specific 3D region where there is a high probability of finding up to two electrons hanging out. Electrons are strictly banned from existing in the spaces between energy levels—they either make the cut or they do not.

• Degenerate Orbitals: Orbitals sharing the exact same sub-shell in the ground state have identical energy levels (like the $p<em>x$, $p</em>y$, and $p_z$ orbitals matching energy perfectly).

• Orbital Aesthetics:

  • $s$ Orbitals: Perfectly spherical and self-absorbed. As the principal quantum number increases, they expand into bigger spheres.

  • $p$ Orbitals: Classic dumbbell shape, flaunting two lobes oriented perpendicular to each other along the Cartesian $x$, $y$, and $z$ axes.

• The 4s Betrayal: At shell $n = 3$, the $4s$ sub-shell cuts right in front of the $3d$ sub-shell to fill up first because it is temporarily lower in energy. But the second transition metals ionise, they kick electrons out of $4s$ first! Talk about conditional loyalty.

• Roommate Rules:

  • Electrons hate sharing: they occupy degenerate orbitals singly with parallel spins first to keep their distance.

  • They only pair up when there are zero empty beds left, and when they do, they must adopt opposite spins to survive mutual spin-pair repulsion.

• Free Radicals: The unhinged chaos agents of chemistry with an unpaired electron—desperate, reactive, and ready to clash with the first molecule they encounter.

Periodic Radii Trends: The Squeeze and the Swell

• Atomic Radius Reality: Defined as half the internuclear distance between two identical bonded atoms ($\text{Atomic Radius} = \frac{d}{2}$).

• Across a Period (The Big Squeeze): As you go from left to right, atoms actually shrink. The nucleus adds more protons, building up major positive nuclear attraction while electrons are dumped into the exact same shell with zero extra shielding, hauling the entire electron cloud inward.

• Down a Group (The Glow-up): As you head down, atoms get noticeably bigger because whole new principal quantum shells are added. Inner shells shield outer electrons from the nucleus, so the outer electrons drift freely outward.

• Ionic Resizing Gossip:

  • Cations: Lose electrons and shrink in shame—the remaining electrons feel a stronger nuclear pull and zero competition.

  • Anions: Shove extra electrons in, explode in size, and expand because electron-electron repulsion forces everyone to back up.

Periodicity and Ionisation Energy Shenanigans

• First ionisation energy ($\text{IE}_1$) is the energy tax required to rip one mole of electrons away from one mole of gaseous atoms under standard conditions ($298\,\text{K}$, $101\,\text{kPa}$).

• The Baseline Trend:

  • Group 1 alkali metals let their single outer valence electron go for cheap.

  • Group 18 noble gases are locked down with full shells and massive nuclear pull—they refuse to let anyone leave without exorbitant energy payment.

• The Beryllium vs. Boron Scandal: You would expect boron's $\text{IE}_1$ to be higher than beryllium's, but boron's fifth electron is sitting in a higher-energy $2p$ sub-shell shielded by the $2s$ electrons, making it unexpectedly easy to steal.

• The Nitrogen vs. Oxygen Feud: Oxygen surprisingly has a lower $\text{IE}<em>1$ than nitrogen! Why? Oxygen forces two electrons to share a single $2p</em>x$ orbital. The mutual spin-pair repulsion gets so petty that popping one electron out is an absolute relief.

Successive Ionisation Energies: Exposing Inner Shells

• Taking one electron is easy compared to what comes next: successive ionisation energies always climb higher ($\text{IE}<em>1 < \text{IE}</em>2 < \text{IE}_3$). Once an atom becomes a positive ion, it grips remaining electrons tighter than ever.

• The Big Reveal: When you see a massive, astronomical leap between two successive ionisation energies, you just busted the atom—the easy electrons came from the valence shell, and that huge jump means you tried to rip an electron from a fully shielded, deep inner shell.

• Count how many electrons were snatched before that giant jump, and you have instantly exposed what group the element belongs to.