Atomic Structure, Electronic Configurations, and Ionisation Energy Trends

Fundamental Sub-Atomic Particles and Nuclear Structure

Atoms consist of three fundamental sub-atomic particles: protons, neutrons, and electrons. Protons reside in the central atomic nucleus, having a relative mass of $1$ and a relative charge of $+1$. Neutrons are likewise situated within the nucleus, possessing a relative mass of $1$ and a neutral relative charge of $0$. Electrons orbit the nucleus within defined regions designated as orbitals, exhibiting a negligible relative mass of $\frac{1}{1840}$ and a relative charge of $-1$.

The nuclear composition of an atom is defined by its atomic and mass numbers. The proton number, designated by the symbol $Z$ and commonly referred to as the atomic number, represents the total number of protons contained within the nucleus of an atom. The nucleon number, designated by the symbol $A$ and referred to as the mass number, constitutes the total combined number of protons and neutrons in the nucleus. Consequently, the total number of neutrons present in any given atom is calculated using the algebraic expression $A - Z$. For example, an atom of lithium is represented as $^7_3\text{Li}$, where the mass number $A$ equals $7$, the atomic number $Z$ equals $3$, and the neutron count is calculated as $7 - 3 = 4$.

Isotopes are defined as atoms of the same chemical element that possess the identical number of protons but different numbers of neutrons. Because chemical behavior is determined by the configuration of electrons surrounding the nucleus, isotopes exhibit identical or nearly identical chemical properties. However, because isotopes differ in their overall mass due to varying neutron counts, they display slightly different physical properties, such as density and rates of diffusion.

When collimated beams of fundamental sub-atomic particles pass through an electric field established between oppositely charged plates, their trajectories deviate according to their characteristic charges and masses. A beam of positively charged protons is deflected toward the negatively charged plate. Because protons possess a relatively large mass ($1$ relative mass unit), their deflection angle is comparatively small. In contrast, negatively charged electrons are attracted toward the positively charged plate and undergo a substantially larger deflection due to their extremely small mass ($\frac{1}{1840}$ relative mass unit). Neutrons carry no electrical charge ($0$) and are completely unaffected by the electric field, proceeding in a straight path without deviation.

Electronic Structure and Orbital Mechanics

Early descriptions of atomic architecture, such as the classical Bohr model, depicted electrons occupying concentric spherical orbits at increasing radii from the nucleus, holding a maximum of $2$ electrons in the first shell and $8$ electrons in the second shell. These foundational models established the principle that atomic and ionic configurations matching the complete valence arrangements of noble gases achieve notable energetic stability.

The advanced quantum mechanical framework organizes electron arrangements into principal energy levels, sub-energy levels, and individual orbitals. Principal energy levels are designated by integers ($n = 1, 2, 3, 4\dots$), where the principal level $1$ is positioned closest to the nucleus and corresponds to the lowest potential energy. Each principal level is split into sub-energy levels denoted by the letters $s$, $p$, $d$, and $f$. An $s$ sub-level holds a maximum capacity of $2$ electrons; a $p$ sub-level holds up to $6$ electrons; a $d$ sub-level accommodates up to $10$ electrons; and an $f$ sub-level holds up to $14$ electrons.

Each sub-energy level is further divided into orbitals, with each individual orbital possessing the capacity to hold up to $2$ electrons of opposite spin. Orbitals represent mathematical probability distributions that describe the likelihood of locating an electron at any specific point in three-dimensional space surrounding the nucleus. Every orbital possesses an approximate, characteristic geometry: $s$ orbitals are spherical, whereas $p$ orbitals have directional dumbbell shapes oriented along spatial axes. Due to the probabilistic nature of wavefunctions, orbital boundaries cannot be delineated with absolute geometric precision.

The distribution of sub-levels within successive principal shells follows a systematic hierarchy. Principal level $1$ contains only the $1s$ sub-level. Principal level $2$ comprises the $2s$ and $2p$ sub-levels. Principal level $3$ contains the $3s$, $3p$, and $3d$ sub-levels. Principal level $4$ contains the $4s$, $4p$, $4d$, and $4f$ sub-levels.

Electrons occupy sub-shells sequentially in order of increasing energy according to the Aufbau principle. The sequence of sub-shell occupation proceeds as follows:

$1s \rightarrow 2s \rightarrow 2p \rightarrow 3s \rightarrow 3p \rightarrow 4s \rightarrow 3d \rightarrow 4p \rightarrow 5s \rightarrow 4d \rightarrow 5p$

Because the $3d$ sub-level possesses a higher energy state than the $4s$ sub-level in neutral atoms, the $4s$ sub-shell fills completely before electrons enter the $3d$ sub-shell. In orbital box diagrams, each orbital is represented by a square box, and each electron is denoted by an arrow indicating its intrinsic magnetic spin direction ($\uparrow$ or $\downarrow$). When filling a set of degenerate orbitals within a given sub-level, such as the three orbitals of the $2p$ or $3p$ sub-shell, electrons occupy each orbital singly with parallel spins before any orbital receives a second, spin-paired electron. This singly occupied filling pattern minimizes electrostatic repulsion between electrons.

Electronic Configurations, Ion Formation, and Periodic Blocks

Standard electron configuration notation identifies the principal quantum level number, the sub-level letter, and a superscript denoting the total number of electrons within that sub-level. For example, calcium ($Z = 20$) has the ground-state electron configuration $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2$, while neutral oxygen ($Z = 8$) is represented as $1s^2\,2s^2\,2p^4$.

When atoms ionize, electrons are exchanged at the outer boundary of the electron cloud. When positive cations are generated, electrons are removed first from the outermost principal energy shell. For example, a neutral magnesium atom with configuration $1s^2\,2s^2\,2p^6\,3s^2$ loses its two valence $3s$ electrons to form the magnesium ion $\text{Mg}^{2+}$ with configuration $1s^2\,2s^2\,2p^6$. Conversely, when non-metallic elements form negative anions, additional electrons are gained into the lowest available valence orbital vacancies. For example, neutral oxygen ($1s^2\,2s^2\,2p^4$) gains two electrons into its partially filled $2p$ sub-shell to yield the oxide anion $\text{O}^{2-}$ with the stable noble gas arrangement $1s^2\,2s^2\,2p^6$.

The periodic table is structured into distinct structural blocks according to the sub-shell into which the highest-energy or outermost valence electron is placed. An $s$-block element possesses an outermost electron that occupies an $s$ sub-shell, such as sodium ($\text{Na}: 1s^2\,2s^2\,2p^6\,3s^1$). A $p$-block element is one whose valence electron enters a $p$ sub-shell, such as chlorine ($\text{Cl}: 1s^2\,2s^2\,2p^6\,3s^2\,3p^5$). A $d$-block element features an outermost electron occupying a $d$ sub-shell, such as vanadium ($\text{V}: 1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2\,3d^3$).

The electron configurations of the first transition series of the $d$-block exhibit two notable irregularities. The configurations for neutral atoms from scandium through zinc are:

$\text{Sc}: 1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2\,3d^1$

$\text{Ti}: 1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2\,3d^2$

$\text{V}: 1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2\,3d^3$

$\text{Cr}: 1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^1\,3d^5$

$\text{Mn}: 1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2\,3d^5$

$\text{Fe}: 1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2\,3d^6$

$\text{Co}: 1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2\,3d^7$

$\text{Ni}: 1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2\,3d^8$

$\text{Cu}: 1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^1\,3d^{10}$

$\text{Zn}: 1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2\,3d^{10}$

Chromium ($\text{Cr}$) and copper ($\text{Cu}$) adopt anomalous ground-state configurations characterized by a singly occupied, half-filled $4s^1$ sub-shell. Chromium acquires a half-filled set of $d$ orbitals ($4s^1\,3d^5$), while copper establishes a completely filled $d$ sub-shell ($4s^1\,3d^{10}$). Although conventional models write the filling order as $4s$ before $3d$, ongoing scientific analysis evaluates the exact energetic balance governing these sub-levels.

A fundamental rule governing $d$-block transition metals is that upon ionization, electrons are lost from the $4s$ sub-shell prior to the removal of any $3d$ electrons. Consequently, transition metal cations possess an empty $4s^0$ sub-shell, as illustrated in the following ion configurations:

$\text{Sc}^{3+}: [\text{Ar}]\,4s^0\,3d^0$

$\text{Ti}^{3+}: [\text{Ar}]\,4s^0\,3d^1$

$\text{V}^{3+}: [\text{Ar}]\,4s^0\,3d^2$

$\text{Cr}^{3+}: [\text{Ar}]\,4s^0\,3d^3$

$\text{Mn}^{2+}: [\text{Ar}]\,4s^0\,3d^5$

$\text{Fe}^{3+}: [\text{Ar}]\,4s^0\,3d^5$

$\text{Co}^{2+}: [\text{Ar}]\,4s^0\,3d^7$

$\text{Ni}^{2+}: [\text{Ar}]\,4s^0\,3d^8$

$\text{Cu}^{2+}: [\text{Ar}]\,4s^0\,3d^9$

$\text{Zn}^{2+}: [\text{Ar}]\,4s^0\,3d^{10}$

Fundamentals of Ionisation Energies

The first ionisation energy is defined as the energy required when one mole of gaseous atoms forms one mole of gaseous ions with a single positive charge. This process is represented by the general thermodynamic equation:

$\text{H}_{(g)} \rightarrow \text{H}^+_{(g)} + e^-$

Equations for first ionisation energy must always specify gaseous phase symbols ($(g)$), irrespective of whether the pure element exists as a gas under standard laboratory conditions or typically forms a $+1$ oxidation state in chemical compounds. Standard examples include:

$\text{Be}_{(g)} \rightarrow \text{Be}^+_{(g)} + e^-$

$\text{O}_{(g)} \rightarrow \text{O}^+_{(g)} + e^-$

The second ionisation energy is defined as the energy required when one mole of gaseous ions with a single positive charge forms one mole of gaseous ions with a double positive charge. This process is expressed as:

$\text{Ti}^+_{(g)} \rightarrow \text{Ti}^{2+}_{(g)} + e^-$

All ionisation energy quantities are positive numerical values, signifying that ionisation is strictly endothermic. Heat energy must be supplied to the system to overcome the attractive electrostatic force binding the negatively charged electron to the positively charged atomic nucleus. An individual chemical element possesses as many successive ionisation energies as it has total atomic electrons.

Three primary physical factors dictate the magnitude of atomic ionisation energy:

First, nuclear attraction: as the number of protons residing within the nucleus increases, the effective nuclear charge rises, exerting a stronger electrostatic pull on orbiting electrons.

Second, distance of electrons from the nucleus: as atomic radius expands, outer valence electrons reside further from the positive nuclear charge, causing the electrostatic force of attraction to weaken.

Third, electron shielding: electrons located in complete, inner principal shells repel outer electrons, shielding them from the full electrostatic attraction of the nucleus.

Successive Ionisation Energies and Shell Structure Evidence

Within any given chemical element, successive ionisation energies are always progressively larger ($\text{IE}_1 < \text{IE}_2 < \text{IE}_3 < \dots$). When an electron is removed, a positive cation is generated, leaving fewer remaining electrons bound to the unchanged positive nuclear charge. This increased ratio of protons to electrons contracts the electron cloud and enhances the net electrostatic pull on the surviving electrons, requiring greater energy input to extract each subsequent electron.

Superimposed on this gradual increase are pronounced discontinuous jumps in successive ionisation energies. These large jumps provide empirical verification of the existence of discrete, quantized principal electron shells. A significant jump occurs whenever an electron is removed from an inner principal shell situated closer to the nucleus. An electron in an inner shell experiences a much stronger nuclear attraction and is devoid of shielding from inner complete electron shells. For example, in an atom of carbon ($Z = 6$), successive removal shows a steady rise for the first four electrons, followed by a dramatic jump between the $4\text{th}$ and $5\text{th}$ ionisation energies, demonstrating that the fifth electron resides in the inner $n = 1$ shell.

Successive ionisation energy data allows the determination of an element's group number in the periodic table. For an unknown element possessing the first five successive ionisation energies of $590\,\text{kJ\,mol}^{-1}$, $1150\,\text{kJ\,mol}^{-1}$, $4940\,\text{kJ\,mol}^{-1}$, $6480\,\text{kJ\,mol}^{-1}$, and $8120\,\text{kJ\,mol}^{-1}$, a large numerical jump occurs between the second and third values ($1150\,\text{kJ\,mol}^{-1}$ to $4940\,\text{kJ\,mol}^{-1}$). This indicates that the third electron must be extracted from an inner principal energy shell that is closer to the nucleus with less shielding. Consequently, the neutral atom possesses exactly two outer valence electrons, confirming that the element belongs to Group $2$.

Periodic Trends in First Ionisation Energy

Plotting the first ionisation energy across sequential atomic numbers reveals clear recurring periodicity across periods and groups. Noble gas elements (Group $0$/Group $8$) reside at the maximum peaks of each period, whereas Group $1$ alkali metals occupy the absolute troughs.

Helium has the highest first ionisation energy of all elements in the periodic table ($2372\,\text{kJ\,mol}^{-1}$). Helium's valence electron resides in the first principal shell closest to the nucleus, experiencing zero inner-shell shielding effects. Helium has a higher first ionisation energy than hydrogen ($1312\,\text{kJ\,mol}^{-1}$) because helium possesses two protons in its nucleus, conferring a higher nuclear charge on the $1s$ electron pair.

Across any given period, there is a general increase in first ionisation energy. As atomic number increases across a period, additional protons are added to the nucleus, increasing the nuclear charge. The accompanying electrons are simultaneously added to the same principal energy shell, experiencing approximately the same degree of inner-shell shielding. This increased effective nuclear charge pulls the electron cloud closer to the nucleus, making valence electrons more difficult to remove.

Down any group in the periodic table, first ionisation energy decreases consistently. As successive periods are entered down a group, the outer electrons occupy principal energy shells situated further from the nucleus. These valence electrons experience greater shielding from complete intervening inner shells. The increased distance and shielding dominate over the increased nuclear charge, diminishing the net attraction of the nucleus and lowering the energy required for electron removal.

A sharp drop in first ionisation energy occurs between every Group $0$ noble gas and the subsequent Group $1$ alkali metal (such as between neon and sodium, or argon and potassium). The single valence electron of a Group $1$ metal occupies a brand new principal shell that is further from the nucleus and shielded by all underlying filled shells, resulting in a substantially reduced ionisation energy.

Sub-Shell Discontinuities in First Ionisation Energy

Superimposed on the general rise in first ionisation energy across Periods $2$ and $3$ are two systematic decreases that confirm the existence of sub-energy levels ($s$ and $p$).

The first anomaly is a small drop observed between Group $2$ and Group $3$ elements, specifically between beryllium and boron in Period $2$, and between magnesium and aluminium in Period $3$.

Magnesium possesses the ground-state configuration $1s^2\,2s^2\,2p^6\,3s^2$, with its outer electrons residing in the complete $3s$ sub-shell. Aluminium has the configuration $1s^2\,2s^2\,2p^6\,3s^2\,3p^1$, placing its valence electron into the newly occupied $3p$ sub-shell. The $3p$ sub-shell lies at a slightly higher energy level than the $3s$ sub-shell. Furthermore, the single $3p$ electron experiences additional shielding from the inner $3s^2$ electron pair. These two effects outweigh the increased nuclear charge of aluminium ($13$ protons versus $12$ in magnesium), making the $3p$ electron easier to remove.

The second anomaly is a small drop observed between Group $5$ and Group $6$ elements, specifically between nitrogen and oxygen in Period $2$, and between phosphorus and sulfur in Period $3$.

In phosphorus ($1s^2\,2s^2\,2p^6\,3s^2\,3p^3$), each of the three degenerate $3p$ orbitals is occupied by a single electron with parallel spin. In sulfur ($1s^2\,2s^2\,2p^6\,3s^2\,3p^4$), the fourth $3p$ electron must pair up with an existing electron of opposite spin in the first $3p$ orbital. The mutual electrostatic repulsion between two electrons sharing the same orbital volume destabilizes the electron pair, making this spin-paired electron easier to remove than an electron from the singly occupied $3p$ sub-shell of phosphorus.

Patterns in Second Ionisation Energies

When second ionisation energies are plotted against atomic number across a period, the resulting curve exhibits an identical structural pattern to the first ionisation energy profile, but shifted one element to the left.

Because the removal of the first electron leaves each ion isoelectronic with the element preceding it, Group $1$ alkali metals occupy the maximum peaks of the second ionisation energy graph. For sodium, removing a second electron requires extracting an electron from the complete, stable $2p^6$ inner shell of the $\text{Na}^+$ ion. This inner shell is much closer to the nucleus and experiences zero shielding from the absent $n = 3$ valence shell, producing a second ionisation energy of approximately $4562\,\text{kJ\,mol}^{-1}$.

Lithium exhibits the second largest second ionisation energy among all elements in the periodic table ($7298\,\text{kJ\,mol}^{-1}$). The second electron of lithium must be extracted from the $\text{Li}^+$ ion's inner $1s$ shell, which is closest to the nucleus and lacks inner-shell shielding. Lithium has a higher second ionisation energy than neutral helium because lithium has three nuclear protons attracting its remaining $1s$ electrons, compared to helium's two.

Electron Affinity Principles and Thermodynamics

The first electron affinity is defined as the enthalpy change that occurs when one mole of gaseous atoms gains one mole of electrons to form one mole of gaseous ions with a single negative charge ($-1$). This process is represented by the thermochemical equation:

$\text{O}_{(g)} + e^- \rightarrow \text{O}^-_{(g)} \quad [\Delta_{ea}H = -141.1\,\text{kJ\,mol}^{-1}]$

First electron affinity is exothermic (negative $\Delta_{ea}H$) for elements that typically form negative ions. Energy is released because the incoming electron experiences an attractive electrostatic pull toward the positive nucleus, yielding a stable anion.

The second electron affinity is defined as the enthalpy change that occurs when one mole of gaseous $1-$ ions gains one electron per ion to produce gaseous $2-$ ions. For oxygen, this second step is represented by:

$\text{O}^-_{(g)} + e^- \rightarrow \text{O}^{2-}_{(g)} \quad [\Delta_{ea}H = +798\,\text{kJ\,mol}^{-1}]$

Second electron affinities are invariably endothermic (positive $\Delta_{ea}H$). Significant energy must be absorbed to overcome the electrostatic repulsion operating between the existing negative charge of the $\text{O}^-$ anion and the incoming electron.