Comprehensive Study Notes on Electronic Structure, Orbitals, and Periodic Trends

Electron Microscopy Principles and Practical Considerations

• Operational requirements for electron microscopy:
  • Low-pressure vacuum environment: The interior of an electron microscope must be maintained at an extremely low pressure so that virtually no air is present, preventing electron beams from colliding with and scattering off gas molecules.
  • Surface dryness: Specimens examined under an electron microscope must possess completely dry surfaces to prevent water vaporization in the high-vacuum chamber, which would disrupt the vacuum and distort imaging.
  • High-resolution observation: Looking at substances in enhanced microscopic detail allows the direct observation of sub-cellular, crystalline, and nanoscale structures that are undetectable using optical microscopy.

Principal Energy Levels and Simple Electronic Configurations

• Core concepts of atomic energy levels:
  • Outside the atomic nucleus, electrons reside in specific energy levels designated as principal quantum shells, represented by the principal quantum number symbol $n$.
  • Principal quantum shells are indexed by whole numbers according to their radial distance from the nucleus: the lowest energy level, $n = 1$, is closest to the nucleus, followed by $n = 2$, $n = 3$, $n = 4$, and continuing outward.
  • Distance-energy relationship: Electrons occupying quantum shells located farther from the nucleus possess higher average energy and experience weaker electrostatic attraction to the positively charged nucleus.
• Key definitions:
  • Energy levels: The defined average amount of energy characteristic of each electron within an atom. Each principal energy level (symbol $n$) corresponds to an electron shell situated at a specific distance from the nucleus, and these principal levels are subdivided into sub-levels designated as $s$, $p$, $d$, and $f$.
  • Electronic configuration: The formal structural representation of the spatial arrangement of electrons within an atom, specifying the principal quantum shells, sub-shells, and total electron population (for example, $1s^2\,2s^2\,2p^3$), or represented visually using orbital box diagrams.
• Maximum electron occupancy per principal quantum shell:
  • Shell 1 ($n = 1$): Accommodates up to a maximum of $2$ electrons.
  • Shell 2 ($n = 2$): Accommodates up to a maximum of $8$ electrons.
  • Shell 3 ($n = 3$): Accommodates up to a maximum of $18$ electrons.
  • Shell 4 ($n = 4$): Accommodates up to a maximum of $32$ electrons.
• Simple electronic configurations of the first 11 elements in the Periodic Table:
  • Hydrogen ($H$, $Z = 1$): $n = 1: 1$
  • Helium ($He$, $Z = 2$): $n = 1: 2$
  • Lithium ($Li$, $Z = 3$): $n = 1: 2$, $n = 2: 1$ (shorthand notation: $2, 1$)
  • Beryllium ($Be$, $Z = 4$): $n = 1: 2$, $n = 2: 2$
  • Boron ($B$, $Z = 5$): $n = 1: 2$, $n = 2: 3$
  • Carbon ($C$, $Z = 6$): $n = 1: 2$, $n = 2: 4$
  • Nitrogen ($N$, $Z = 7$): $n = 1: 2$, $n = 2: 5$
  • Oxygen ($O$, $Z = 8$): $n = 1: 2$, $n = 2: 6$
  • Fluorine ($F$, $Z = 9$): $n = 1: 2$, $n = 2: 7$
  • Neon ($Ne$, $Z = 10$): $n = 1: 2$, $n = 2: 8$ (shorthand notation: $2, 8$)
  • Sodium ($Na$, $Z = 11$): $n = 1: 2$, $n = 2: 8$, $n = 3: 1$
• Additional shorthand electronic structures:
  • Chlorine ($Cl$, $Z = 17$): Shorthand structure is represented as $2, 8, 7$.

Factors Influencing Ionisation Energy

• Four fundamental physical factors modulate the magnitude of atomic ionisation energy:
  • Size of the nuclear charge: As the atomic number (total proton count) increases, the net positive charge of the nucleus increases. A larger positive nuclear charge exerts a stronger electrostatic force of attraction on the surrounding electrons, necessitating greater energy input to dislodge an electron. Consequently, ionisation energy generally increases with increasing proton number.
  • Distance of outer electrons from the nucleus: Electrostatic attraction between positive and negative charges falls off steeply as the physical separation between them increases. Outer-shell electrons situated further from the nucleus experience markedly weaker nuclear attraction compared to inner-shell electrons. Consequently, ionisation energy decreases as the distance between the outermost shell and the nucleus increases.
  • Shielding effect of inner electrons: All electrons bear negative charges and mutually repel. Negatively charged electrons residing in completely filled inner shells repel outer-shell electrons, screening them from experiencing the full electrostatic force of the nuclear charge. Increased shielding reduces net nuclear attraction, causing ionisation energy to decline as the number of intervening full shells increases.
  • Spin-pair repulsion: Electrons localized within the same atomic orbital repel one another more intensely than electrons positioned in separate orbitals within the same sub-shell. This localized mutual repulsion destabilizes the electron pair, reducing the energy needed to extract one of the paired electrons, which lowers the first ionisation energy.
• Key definition:
  • Shielding: The capacity of inner-shell electrons to screen or reduce the effective positive nuclear charge felt by electrons in outer shells.

Interpreting Successive Ionisation Energies

• Logarithmic representation:
  • Successive ionisation energies vary over several orders of magnitude; therefore, plotting the logarithm to the base 10 ($\log_{10}$) of successive ionisation energies against the number of electrons removed allows wide ranges of values to be analyzed on a single graph.
• Electronic deductions from successive ionisation energies of Sodium ($Na$, $Z = 11$):
  • Removal of 1st electron: Possesses a comparatively low ionisation energy value, indicating that it is easily removed, situated far from the nucleus in shell $n = 3$, and heavily shielded by inner electron shells.
  • Removal of 2nd electron: Displays an abrupt, massive numerical jump compared to the first ionisation energy. This reveals that the second electron is located much closer to the nucleus in an inner shell ($n = 2$). The large jump between the 1st and 2nd values confirms that sodium possesses exactly one outer valence electron.
  • Removal of 2nd through 9th electrons: Exhibits a continuous, gradual increase across all eight electron removals, confirming that these eight electrons occupy the same principal quantum shell ($n = 2$).
  • Removal of 10th and 11th electrons: Features an enormous surge in ionisation energy, demonstrating that these two electrons reside in the innermost shell ($n = 1$) directly adjacent to the nucleus. They experience massive, unshielded electrostatic attraction.
  • The configuration deduced from these steps corresponds directly to $2$ inner electrons, $8$ intermediate electrons, and $1$ outer valence electron.
• Practical analytical applications of successive ionisation energy data:
  • Deducing or verifying the simple electronic configuration of elements.
  • Establishing the number of valence electrons located in the outermost shell.
  • Pinpointing the precise Group classification of an unknown element within the Periodic Table.
• Worked Example 1 — Identifying an element from successive ionisation energies:
  • Given data for element $X$ (successive ionisation energies in $\text{kJ}\,\text{mol}^{-1}$):
  • 1st: $1000\,\text{kJ}\,\text{mol}^{-1}$
  • 2nd: $2260\,\text{kJ}\,\text{mol}^{-1}$
  • 3rd: $3390\,\text{kJ}\,\text{mol}^{-1}$
  • 4th: $4540\,\text{kJ}\,\text{mol}^{-1}$
  • 5th: $7010\,\text{kJ}\,\text{mol}^{-1}$
  • 6th: $8500\,\text{kJ}\,\text{mol}^{-1}$
  • 7th: $27100\,\text{kJ}\,\text{mol}^{-1}$
  • 8th: $31670\,\text{kJ}\,\text{mol}^{-1}$
  • 9th: $36580\,\text{kJ}\,\text{mol}^{-1}$
  • 10th: $43140\,\text{kJ}\,\text{mol}^{-1}$
  • Step 1: Locate the primary discontinuous jump in ionisation energy. The massive increase occurs between the removal of the 6th electron ($8500\,\text{kJ}\,\text{mol}^{-1}$) and the 7th electron ($27100\,\text{kJ}\,\text{mol}^{-1}$).
  • Step 2: Identify the lower electron index preceding this jump, which corresponds to the number of easily removed outer valence electrons. Here, this value is $6$.
  • Step 3: Correlate the number of valence electrons to the group number. An element containing $6$ outer valence electrons belongs to Group 16 of the Periodic Table.

Quantum Sub-Shells and Atomic Orbitals

• Nature and hierarchy of quantum sub-shells:
  • Definition: Sub-shells (subsidiary quantum shells) are defined sub-regions within principal quantum shells where electrons reside in specific spatial domains possessing discrete amounts of energy, designated by the letters $s$, $p$, $d$, and $f$.
  • Sub-shell breakdown across principal quantum shells:
  • Shell $n = 1$: Comprises one sub-shell ($1s$), holding a maximum of $2$ electrons.
  • Shell $n = 2$: Comprises two sub-shells ($2s$, $2p$), holding a maximum of $8$ electrons ($2$ in $s$, $6$ in $p$).
  • Shell $n = 3$: Comprises three sub-shells ($3s$, $3p$, $3d$), holding a maximum of $18$ electrons ($2$ in $s$, $6$ in $p$, $10$ in $d$).
  • Shell $n = 4$: Comprises four sub-shells ($4s$, $4d$, $4d$, $4f$), accommodating $f$ sub-shells in elements containing more than $57$ electrons.
  • Energy progression within any given shell follows the strict ascending hierarchy: $s < p < d < f$.
• Spectroscopic nomenclature:
  • High-speed electron bombardment of gaseous atoms under reduced pressure produces emission spectra visible as sharp, discrete spectral lines via a spectroscope.
  • Historical origins of sub-shell letter designations:
  • $s$ denotes 'sharp'
  • $p$ denotes 'principal'
  • $d$ denotes 'diffuse'
• Atomic orbitals and spatial probability:
  • Definition: An atomic orbital is a three-dimensional region of space situated outside the nucleus within which there is a high probability of locating an electron, capable of housing a maximum of two electrons.
  • Orbital capacity by sub-shell:
  • $s$ sub-shell: Contains $1$ orbital (maximum occupancy: $2$ electrons).
  • $p$ sub-shell: Contains $3$ orbitals (maximum occupancy: $6$ electrons).
  • $d$ sub-shell: Contains $5$ orbitals (maximum occupancy: $10$ electrons).
• Three-dimensional shapes of atomic orbitals:
  • $s$ orbitals: Perfectly spherical in shape, centered on the atomic nucleus. A $2s$ orbital is identical in spherical symmetry to a $1s$ orbital, but is larger in radius and higher in energy.
  • $p$ orbitals: Hourglass- or dumbbell-shaped, featuring two symmetrical lobes oriented along mutually perpendicular axes. The three degenerate $2p$ orbitals are designated $2p_x$, $2p_y$, and $2p_z$, aligned respectively along the Cartesian $x$, $y$, and $z$ axes. They are equal in energy to each other. The $3p$ orbitals exhibit analogous geometries but possess higher energy levels.
  • $d$ orbitals: Geometrically more complex. In 1925, Louis de Broglie posited that electrons display wave properties, establishing the modern concept of electron probability clouds. A prominent example is the $d_{z^2}$ orbital, which exhibits a modified dumbbell orientation alongside an equatorial ring or doughnut encircling its central waist.
• Aufbau principle and orbital filling order:
  • Ground-state stability dictates that electrons occupy the available sub-shells of lowest relative energy first.
  • Energy level crossover: After the $3p$ sub-shell fills at argon, the energy progression deviates from a simple principal-shell sequence. The $4s$ sub-shell is lower in energy than the $3d$ sub-shell. As a result, the $4s$ sub-shell fills before the $3d$ sub-shell starts filling.
  • Filling sequence up to shell $n = 4$: $1s \rightarrow 2s \rightarrow 2p \rightarrow 3s \rightarrow 3p \rightarrow 4s \rightarrow 3d \rightarrow 4p \rightarrow 4d \rightarrow 4f$.

Detailed Electronic Configurations and Periodic Table Blocks

• Notation conventions:
  • In standard $1s^2$ notation, the leading integer indicates the principal quantum number ($n$), the letter designates the sub-shell type ($s, p, d$), and the superscript denotes the total electron count residing in that sub-shell.
• Detailed ground-state configurations for elements 1 to 18:
  • Hydrogen ($H$, $Z = 1$): $1s^1$
  • Helium ($He$, $Z = 2$): $1s^2$
  • Lithium ($Li$, $Z = 3$): $1s^2\,2s^1$
  • Beryllium ($Be$, $Z = 4$): $1s^2\,2s^2$
  • Boron ($B$, $Z = 5$): $1s^2\,2s^2\,2p^1$
  • Carbon ($C$, $Z = 6$): $1s^2\,2s^2\,2p^2$
  • Nitrogen ($N$, $Z = 7$): $1s^2\,2s^2\,2p^3$
  • Oxygen ($O$, $Z = 8$): $1s^2\,2s^2\,2p^4$
  • Fluorine ($F$, $Z = 9$): $1s^2\,2s^2\,2p^5$
  • Neon ($Ne$, $Z = 10$): $1s^2\,2s^2\,2p^6$
  • Sodium ($Na$, $Z = 11$): $1s^2\,2s^2\,2p^6\,3s^1$
  • Magnesium ($Mg$, $Z = 12$): $1s^2\,2s^2\,2p^6\,3s^2$
  • Aluminium ($Al$, $Z = 13$): $1s^2\,2s^2\,2p^6\,3s^2\,3p^1$
  • Silicon ($Si$, $Z = 14$): $1s^2\,2s^2\,2p^6\,3s^2\,3p^2$
  • Phosphorus ($P$, $Z = 15$): $1s^2\,2s^2\,2p^6\,3s^2\,3p^3$
  • Sulfur ($S$, $Z = 16$): $1s^2\,2s^2\,2p^6\,3s^2\,3p^4$
  • Chlorine ($Cl$, $Z = 17$): $1s^2\,2s^2\,2p^6\,3s^2\,3p^5$
  • Argon ($Ar$, $Z = 18$): $1s^2\,2s^2\,2p^6\,3s^2\,3p^6$
• Noble gas core shorthand:
  • The core structure of argon, $1s^2\,2s^2\,2p^6\,3s^2\,3p^6$, is routinely abbreviated as $[\text{Ar}]$ when detailing configurations of elements from $Z = 19$ onward.
• Electronic configurations of elements 19 through 36:
  • Potassium ($K$, $Z = 19$): $[\text{Ar}]\,4s^1$
  • Calcium ($Ca$, $Z = 20$): $[\text{Ar}]\,4s^2$
  • Scandium ($Sc$, $Z = 21$): $[\text{Ar}]\,3d^1\,4s^2$ (the first element to incorporate an electron into the $3d$ sub-shell)
  • Chromium ($Cr$, $Z = 24$): $[\text{Ar}]\,3d^5\,4s^1$ (anomalous configuration; favored over the anticipated $[\text{Ar}]\,3d^4\,4s^2$ due to the energetic stability of a half-filled $3d$ sub-shell)
  • Manganese ($Mn$, $Z = 25$): $[\text{Ar}]\,3d^5\,4s^2$
  • Copper ($Cu$, $Z = 29$): $[\text{Ar}]\,3d^{10}\,4s^1$ (anomalous configuration; favored over the anticipated $[\text{Ar}]\,3d^9\,4s^2$ due to the energetic stability of a completely filled $3d$ sub-shell)
  • Zinc ($Zn$, $Z = 30$): $[\text{Ar}]\,3d^{10}\,4s^2$
  • Gallium ($Ga$, $Z = 31$): $[\text{Ar}]\,3d^{10}\,4s^2\,4p^1$
  • Bromine ($Br$, $Z = 35$): $[\text{Ar}]\,3d^{10}\,4s^2\,4p^5$
  • Krypton ($Kr$, $Z = 36$): $[\text{Ar}]\,3d^{10}\,4s^2\,4p^6$
• Structural blocks of the Periodic Table:
  • s-block: Comprises Groups 1 and 2, where the highest-energy valence electrons reside in an outer $s$ sub-shell.
  • p-block: Comprises Groups 13 through 18 (excluding Helium), where outer valence electrons enter a $p$ sub-shell.
  • d-block: Elements in which successive electrons are added into underlying $d$ sub-shells, corresponding primarily to the transition elements.

Orbital Box Diagrams, Electron Spin, and Free Radicals

• Rules for constructing orbital box diagrams:
  • Individual atomic orbitals are drawn as discrete boxes, arranged vertically in order of increasing energy from base to top.
  • Individual electrons are depicted as vertical arrows pointing upward or downward, representing the intrinsic property of electron 'spin' (conceptualized as clockwise or counter-clockwise rotation about an internal axis).
  • When an orbital houses two electrons, their spins must be paired in opposite orientations, depicted as antiparallel arrows ($\u21c5$).
• Hund's rule and spin-pair repulsion:
  • Key definition: Spin-pair repulsion describes the electrostatic repulsion experienced by two electrons sharing the same spatial orbital due to their identical negative charges. Aligning paired spins in opposite directions minimizes this repulsion, but repulsion between electrons within the same orbital remains greater than repulsion between electrons occupying separate orbitals.
  • Minimization behavior: Electrons systematically occupy empty degenerate orbitals within a sub-shell singly with parallel spins before undergoing pairing. Pairing only initiates once every orbital within that sub-shell contains at least one electron.
  • Exemplified sub-shell occupations:
  • Carbon ($1s^2\,2s^2\,2p^2$): Features two unpaired electrons possessing identical parallel spins housed in two distinct $2p$ orbitals, leaving the third $2p$ orbital vacant.
  • Nitrogen ($1s^2\,2s^2\,2p^3$): Contains three unpaired electrons with parallel spins singly occupying all three $2p$ orbitals.
  • Oxygen ($1s^2\,2s^2\,2p^4$): Accommodates four $2p$ electrons; one $2p$ orbital contains a spin-paired electron couple ($\u21c5$), while the remaining two orbitals each hold a single unpaired electron.
• Free radicals and chemical species:
  • Chemical species: A comprehensive term encompassing any distinct chemical entity, such as individual atoms, ions, molecules, free radicals, or isolated electrons.
  • Free radical definition: Any chemical species containing one or more unpaired electrons.
  • Examples:
  • Chlorine free radical ($\text{Cl}^\bullet$): Electronic configuration $1s^2\,2s^2\,2p^6\,3s^2\,3p^5$, containing two paired $3p$ orbitals and one orbital holding a lone unpaired electron, denoted with a dot.
  • Methyl free radical ($\text{H}_3\text{C}^\bullet$): A polyatomic molecular fragment centered on a carbon atom bearing a single unpaired electron.

Electronic Configuration of Ions

• Cation and anion configurations:
  • Positive ions (cations): Formed when neutral atoms lose electrons. For example, a sodium atom ($Z = 11$) loses one electron to produce $\text{Na}^+$, giving a $10$-electron configuration of $1s^2\,2s^2\,2p^6$, isoelectronic with neon.
  • Negative ions (anions): Formed when neutral atoms gain electrons. For example, a sulfur atom ($Z = 16$) gains two electrons to form $\text{S}^{2-}$, yielding an $18$-electron configuration of $1s^2\,2s^2\,2p^6\,3s^2\,3p^6$, isoelectronic with argon.
• Transition metal cation formation rules:
  • In transition metals (d-block elements), the $4s$ sub-shell fills before the $3d$ sub-shell during atomic construction. However, upon ionisation, electrons occupying the outer $4s$ sub-shell are lost first before any $3d$ electrons are removed.
  • Titanium ionisation:
  • Neutral atom (Ti): $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^2\,4s^2$
  • Divalent cation ($\text{Ti}^{2+}$): $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^2$
  • Chromium ionisation:
  • Neutral atom (Cr): $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^5\,4s^1$
  • Trivalent cation ($\text{Cr}^{3+}$): Loses the lone $4s^1$ electron and two $3d$ electrons, yielding $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^3$
• Worked Example 2 — Configuration of the $\text{Fe}^{3+}$ ion:
  • Step 1: Establish the total electron count of a neutral iron atom ($Z = 26$), which possesses $26$ electrons.
  • Step 2: Formulate the neutral iron atomic configuration by filling orbitals in order of increasing energy ($4s$ before $3d$): $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2\,3d^6$.
  • Step 3: Remove three electrons sequentially to construct the $3+$ oxidation state:
  • Dislodge the two outermost $4s$ electrons first: $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2\,3d^6 \rightarrow 1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^6$
  • Remove one electron from the outer $3d$ sub-shell: $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^6 \rightarrow 1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^5$
  • Final configuration for $\text{Fe}^{3+}$: $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^5$.

Periodic Patterns in Atomic and Ionic Radii

• Covalent atomic radius:
  • Key definition: The covalent atomic radius is defined as half the internuclear distance between two covalently bonded atoms of identical elemental identity.
• Periodic trends in atomic radius:
  • Down a group: Atomic radius increases progressively. With each successive period, an additional principal electron shell is added, situated further from the nucleus. Although nuclear charge simultaneously increases down the group, the shielding effect from extra inner electron shells counterbalances and outweighs the increased nuclear charge, yielding an expanded overall electron cloud.
  • Across a period: Atomic radius decreases steadily from left to right. Each successive element possesses an additional proton, increasing the positive nuclear charge by $+1$. The corresponding additional electron enters the same outer principal quantum shell, meaning internal electron shielding remains essentially constant. Consequently, the intensified nuclear pull draws the valence electron shell closer to the nucleus.
• Periodic trends in ionic radius:
  • Down a group: Ionic radius increases down any group for ions possessing equivalent charge states (such as Group 2 forming $2+$ ions, or Group 17 forming $-1$ ions). Each step down the group introduces an additional quantum shell, where greater inner shielding outcompetes the increased nuclear charge.
  • Across a period (Groups 1 to 14): Ionic radius exhibits a continuous decrease. The increasing positive nuclear charge exerts an progressively stronger attractive force on isoelectronic or similarly structured electron configurations, contracting the ionic radius.
• Comparative size of atoms versus ions:
  • Metal cations: Stable metal cations are consistently smaller than their parent neutral atoms. The formation of a cation entails the complete shedding of the outermost valence shell electrons, which diminishes electron-electron repulsion and leaves the remaining electrons bound under a higher effective nuclear charge per electron.
  • Non-metal anions: Stable non-metal anions are consistently larger than their parent neutral atoms. Anions are formed through the acquisition of extra electrons to achieve a completed valence shell, which increases mutual electron-electron repulsion and slightly diminishes the net electrostatic attraction exerted by the nucleus across the valence shell.

Questions & Practice Exercises

• Question 1 — Writing simple principal quantum configurations:
  • Sulfur ($S$, $Z = 16$): Simple shell structure is $2, 8, 6$.
  • Magnesium ($Mg$, $Z = 12$): Simple shell structure is $2, 8, 2$.
  • Fluorine ($F$, $Z = 9$): Simple shell structure is $2, 7$.
  • Potassium ($K$, $Z = 19$): Simple shell structure is $2, 8, 8, 1$.
  • Carbon ($C$, $Z = 6$): Simple shell structure is $2, 4$.
• Question 2 — Successive ionisation energies of Boron ($B$, $Z = 5$):
  • Given ionisation energies in $\text{kJ}\,\text{mol}^{-1}$: 1st = $799$, 2nd = $2420$, 3rd = $3660$, 4th = $25000$, 5th = $32800$.
  • Part i: Explanation of the large jump between the 3rd and 4th ionisation energies:
  • The 4th electron is removed from the innermost principal quantum shell ($n = 1$), which is situated much closer to the nucleus and experiences zero inner-shell shielding, unlike the first three electrons which are removed from the outer shell ($n = 2$).
  • Part ii: Confirmation of electronic structure $2, 3$:
  • The first three electrons are removed with comparatively modest energy inputs, reflecting three valence electrons residing in the outer $n = 2$ shell. The dramatic surge between the 3rd and 4th ionisation energies confirms the boundary between principal quantum shells, leaving two tightly held inner electrons in the $n = 1$ shell.
  • Part iii: Prediction for aluminium ($Al$, $Z = 13$):
  • A plot of $\log_{10}(\text{ionisation energy})$ versus electron removal index displays three valence electrons removed with gradual increases ($n = 3$), followed by a large jump between the 3rd and 4th removals ($n = 2$), an eight-electron plateau spanning the 4th through 11th removals, a second steep jump between the 11th and 12th removals ($n = 1$), and a final high-energy plateau for the 12th and 13th removals.
• Question 3 — Deducing group identity and logarithmic curve:
  • Given first six ionisation energies: $1090$, $2350$, $4610$, $6220$, $37800$, and $47300\,\text{kJ}\,\text{mol}^{-1}$.
  • Part a: Group assignment and explanation:
  • The element belongs to Group 14. The significant discontinuity occurs between the 4th ($6220\,\text{kJ}\,\text{mol}^{-1}$) and 5th ($37800\,\text{kJ}\,\text{mol}^{-1}$) ionisation energies, demonstrating the presence of four outer valence electrons.
  • Part b: Logarithmic curve for a Group 2 element:
  • A graph of $\log_{10}(\text{ionisation energy})$ over the first four removals displays a gentle incline between electron 1 and electron 2, followed by a steep discontinuous jump between electron 2 and electron 3 (signaling the transition from valence shell into an inner full shell), followed by a minor increase between electron 3 and electron 4.
• Question 4 — Shell sub-levels and capacities:
  • Part a: Orbital types in the third principal quantum shell ($n = 3$):
  • Contains $s$, $p$, and $d$ orbital types.
  • Part b: Maximum electron capacities for each sub-shell in shell $n = 3$:
  • $3s$ sub-shell: Maximum $2$ electrons.
  • $3p$ sub-shell: Maximum $6$ electrons.
  • $3d$ sub-shell: Maximum $10$ electrons.
• Question 5 — Writing full $1s^2$ configurations:
  • Atomic number $16$ (Sulfur): $1s^2\,2s^2\,2p^6\,3s^2\,3p^4$
  • Atomic number $9$ (Fluorine): $1s^2\,2s^2\,2p^5$
  • Atomic number $20$ (Calcium): $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2$
• Question 6 — Transition and representative element configurations:
  • Vanadium ($V$, $Z = 23$): $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^3\,4s^2$
  • Copper ($Cu$, $Z = 29$): $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^{10}\,4s^1$
  • Selenium ($Se$, $Z = 34$): $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^{10}\,4s^2\,4p^4$
• Question 7 — Element identification from configurations:
  • Given configuration: $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^{10}\,4s^2\,4p^6\,4d^{10}\,5s^2\,5p^3$
  • Periodic Table block: p-block (highest-energy valence electrons reside in the $5p$ sub-shell).
  • Periodic Table group: Group 15 (possesses five valence electrons in shell $n = 5$: $5s^2\,5p^3$).
  • Identity of element: Antimony ($Sb$, $Z = 51$).
  • Given configuration: $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^5\,4s^1$
  • Periodic Table block: d-block (involves electron filling in the partially occupied $3d$ sub-shell; element is Chromium).
• Question 8 — Valence shell structure of Phosphorus ($P$, $Z = 15$):
  • Evaluated statement: Statement B is true — in the outermost principal quantum shell ($n = 3$) of phosphorus, there are three p-type electrons and two s-type electrons ($3s^2\,3p^3$).
• Question 9 — Electronic configurations of specific ions:
  • $\text{Al}^{3+}$ ($Z = 13$): Neutral atom is $1s^2\,2s^2\,2p^6\,3s^2\,3p^1$; losing three electrons leaves $1s^2\,2s^2\,2p^6$.
  • $\text{O}^{2-}$ ($Z = 8$): Neutral atom is $1s^2\,2s^2\,2p^4$; acquiring two electrons produces $1s^2\,2s^2\,2p^6$.
  • $\text{Fe}^{2+}$ ($Z = 26$): Neutral atom is $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^6\,4s^2$; losing the two $4s$ electrons yields $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^6$.
  • $\text{Cu}^{2+}$ ($Z = 29$): Neutral atom is $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^{10}\,4s^1$; losing the single $4s$ electron and one $3d$ electron yields $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^9$.
  • $\text{Cu}^+$ ($Z = 29$): Neutral atom is $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^{10}\,4s^1$; losing the single $4s$ electron yields $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^{10}$.