Overview — Module 2: Atomic Structure

Chemistry is defined as the study of matter in terms of its structure, composition and properties. Matter is made up of atoms, and therefore an understanding of the internal structure of the atom is fundamental to chemistry. Ancient Indian and Greek philosophers (600–400 BC) proposed the earliest concept of the atom as the smallest indivisible part of matter — without experimental evidence, based on thought experiments about continuous subdivision. John Dalton revived the atomic concept in the nineteenth century through his atomic theory, which explained the laws of chemical combination. Later experiments showed that the atom is not indivisible but possesses an internal structure.

In this lesson you will learn about the internal structure of an atom, which helps you understand correlations between structure and properties studied in later lessons. Topics span fundamental particles, atomic and mass numbers, isotopes, historical atomic models (Thomson, Rutherford, Bohr), electromagnetic radiation, the hydrogen line spectrum, wave–particle duality, Heisenberg's uncertainty principle, the quantum mechanical model, quantum numbers, orbital shapes, and rules for electronic configuration including the stability of half-filled and completely filled subshells.

Section 1: Fundamental Particles and Atomic Notation (2.1–2.2)

2.1 Discovery of Fundamental Particles

In 1897, J.J. Thomson discovered the electron as a constituent of the atom. He determined that an electron carries a negative charge and has very little mass compared to the whole atom. Since atoms are electrically neutral, a source of positive charge must exist within the atom. This led to the experimental discovery of the proton — a positively charged subatomic particle approximately 1840 times heavier than an electron.

Further experiments revealed that atomic masses exceeded what protons and electrons alone could account for. For example, helium's mass was expected to be double hydrogen's but was found to be almost four times greater. This suggested neutral particles with mass comparable to protons. In 1932, Sir James Chadwick discovered the neutron. Atoms are therefore composed of three fundamental particles:

• Electron (e): mass 9.109 × 10⁻³¹ kg, charge −1.602 × 10⁻¹⁹ C (relative charge −1)
• Proton (p): mass 1.673 × 10⁻²⁷ kg, charge +1.602 × 10⁻¹⁹ C (relative charge +1)
• Neutron (n): mass 1.675 × 10⁻²⁷ kg, charge 0

Because atoms contain still smaller particles, they must have an internal structure — the subject of the rest of this chapter. Comparing masses: an electron is about 1/1840 the mass of a proton, yet both are dwarfed by the atom as a whole because most atomic mass resides in the nucleus (protons + neutrons). This mass discrepancy for helium (four times hydrogen, not twice) was the crucial clue that forced scientists beyond the proton–electron picture.

2.2 Atomic Number, Mass Number, Isotopes and Isobars

All atoms are identified by the number of protons and neutrons they contain. The atomic number (Z) is the number of protons in the nucleus of each atom of an element. In a neutral atom, protons equal electrons, so Z also gives the electron count. Chemical identity depends solely on Z — every atom with 7 protons is nitrogen.

The mass number (A) is the total number of protons and neutrons in the nucleus: A = Z + N, where N is the number of neutrons. Except for ordinary hydrogen (one proton, no neutrons), all nuclei contain both protons and neutrons. Neutrons = A − Z. For fluorine (A = 19, Z = 9), neutrons = 10.

Atoms of the same element can differ in mass. Most elements have isotopes — same Z, different A. Hydrogen has three isotopes: ¹H (protium, 0 neutrons), ²H (deuterium, 1 neutron), ³H (tritium, 2 neutrons). Uranium-235 and uranium-238 share Z = 92 but differ in properties — U-235 is used in reactors; U-238 lacks those properties. Isotopes are named by mass number (except hydrogen's special names). Chemical properties depend on protons and electrons; neutrons do not participate in ordinary chemical change, so isotopes of an element have similar chemistry.

Isobars are atoms of different elements with the same mass number A but different Z — for instance ⁴⁰Ar₁₈ and ⁴⁰Ca₂₀ both have A = 40 but are different elements. Do not confuse isotopes (same Z) with isobars (same A).

Isotope notation places mass number A as superscript and atomic number Z as subscript on the element symbol X. Hydrogen isotopes are written ¹H₁, ²H₁, ³H₁ (protium, deuterium, tritium). For uranium: ²³⁵U₉₂ versus ²³⁸U₉₂ — same chemistry (both uranium) but very different nuclear behaviour. Example 2.1: In ¹⁷O₈: 8 protons, 9 neutrons, 8 electrons. In ¹⁹⁹Hg₈₀: 80 protons, 119 neutrons, 80 electrons. ²⁰⁰Hg₈₀ is a chemically similar isotope with 120 neutrons. All three values Z, N and A must be positive integers.

Section 2: Earlier Models of the Atom (2.3)

2.3.1 Thomson's Plum Pudding Model

After establishing that atoms are divisible, scientists proposed models for internal structure. J.J. Thomson, from discharge tube experiments, suggested atoms as a large positively charged body with small negative electrons scattered throughout — the plum pudding model (electrons = plums in positive pudding) or watermelon model (pulp = positive charge, seeds = electrons).

2.3.2 Rutherford's Gold Foil Experiment

Ernest Rutherford tested Thomson's model with the α-ray scattering experiment (1908 Nobel Prize in Chemistry). A beam of fast-moving α-particles (He²⁺ ions) passed through very thin gold foil. Most particles passed straight through, but some were deflected — a few through large angles, and about 1 in 10,000 rebounded.

Rutherford's conclusions: (1) Atom contains a dense, positively charged nucleus at the centre. (2) Nearly all positive charge and mass reside in the nucleus. (3) Remaining volume is mostly empty space containing small negative electrons.

Rutherford's model explained scattering data elegantly: undeflected α-particles pass through empty space; near-miss deflections occur when α-particles approach the nucleus; direct collision causes rebound. Yet the model could not explain why electrons do not radiate while orbiting.

Failure of Rutherford's model: Maxwell's electromagnetic theory states that an accelerating charged particle radiates energy continuously. An orbiting electron is accelerating (centripetal force) and should continuously lose energy, spiralling inward (Fig. 2.5) until the atom collapses in about 10⁻⁸ s — but atoms are stable and emit line spectra, not continuous radiation. This contradiction motivated Niels Bohr, a student of Rutherford, to introduce quantisation of electron energy in 1913.

Section 3: Electromagnetic Radiation (2.4)

Before explaining atomic spectra, we need electromagnetic radiation (EMR). EMR is energy transmitted through space as oscillating electric and magnetic fields perpendicular to each other and to the direction of propagation — no medium required. Examples: visible light, heat, radio waves, X-rays, gamma rays. EMR travels at c = 3.0 × 10⁸ m s⁻¹ in vacuum.

2.4.1 Characteristic Parameters

• Amplitude: maximum height of crest or depth of trough
• Wavelength (λ): distance between consecutive crests; units m, cm, nm, Å (1 Å = 10⁻¹⁰ m)
• Frequency (ν): wave crests passing a point per second; unit Hz (s⁻¹)
• Wave number (ν̄): waves per unit length = 1/λ; SI unit m⁻¹, often cm⁻¹
• Velocity (c): distance travelled per second; c = νλ

EM radiation also exhibits particle nature. Energy is carried in bundles called quanta; a quantum of visible light is a photon. Photon energy is proportional to frequency:

Example 2.2: 12 GHz microwave: E = 6.626×10⁻³⁴ × 1.2×10¹⁰ = 7.95×10⁻²⁴ J. Example 2.3: Green light λ = 535 nm: E = hc/λ = 3.71×10⁻¹⁹ J.

The electromagnetic spectrum spans radio waves through gamma rays; visible light is a tiny portion (Fig. 2.7). Radiation with shorter wavelength (higher frequency) carries more energy per photon — gamma rays at one extreme, radio waves at the other. Wave number ν̄ is especially convenient in spectroscopy because it is directly proportional to energy: E = hcν̄.

Quantisation of energy was revolutionary: unlike classical waves that can have any energy, photons come in discrete packets proportional to ν. This particle picture complements the wave picture — together they foreshadow the wave–particle duality developed later in this chapter.

Section 4: Line Spectrum and Bohr's Model (2.5–2.6)

2.5 Line Spectrum

Sunlight through a prism gives a continuous spectrum (VIBGYOR) — wavelengths vary without break. Flame tests (Na = yellow, Cu = green, Sr = crimson) produce light that, when passed through a prism, splits into discrete lines — a line spectrum (Fig. 2.8).

2.5.1 Hydrogen Line Spectrum

Electric discharge through low-pressure H₂ emits light that forms discrete lines in UV, visible and IR. The general Rydberg formula:

Named series (Table 2.2): Lyman (UV, n₁=1, n₂=2,3,4…), Balmer (visible, n₁=2, n₂=3,4,5…), Paschen (IR, n₁=3), Brackett (IR, n₁=4), Pfund (IR, n₁=5). Johann Balmer first found a simple formula for visible lines. Example 2.4: For Balmer n₂=3: ν̄ = 109677(1/4 − 1/9) = 109677 × 5/36 cm⁻¹; λ = 1/ν̄ = 656 nm (red line). The discrete lines prove that electron energies in hydrogen are quantised, not continuous.

2.6 Bohr's Model (1913)

Niels Bohr proposed electrons moving in definite circular orbits around the nucleus. Postulates:

• Electrons in a given orbit have fixed energy — stationary or non-radiating orbits.
• Electron changes orbit by absorbing or emitting a photon: E = hν = E_f − E_i.
• Angular momentum is quantised: mvr = nh/2π where n = 1, 2, 3… (principal quantum number).

Bohr explained the hydrogen line spectrum: transitions between stationary states give hν = E_i − E_f, yielding the Rydberg formula when combined with E_n = −R_H/n². Energy levels are inversely proportional to n² — E₁ is most negative (most stable); as n increases, energy approaches zero (ionisation limit). Bohr correlated R_H to fundamental constants: R_H = m_ez²e⁴/(8ε₀²h³) for nuclear charge z (Z for hydrogen).

Bohr won the 1922 Nobel Prize in Physics. His model was a landmark but limited: it works well for one-electron species (H, He⁺, Li²⁺) but fails for multi-electron atoms (no account of electron–electron repulsion), cannot explain fine structure (multiple closely spaced lines), Zeeman effect (magnetic field splitting) or the varying intensities of spectral lines. These failures pointed toward a more complete quantum mechanical treatment.

Section 5: Wave–Particle Duality and Uncertainty (2.7–2.8)

2.7 de Broglie Hypothesis

Light shows both wave properties (diffraction, interference) and particle properties (photoelectric effect). In 1923, Louis de Broglie proposed that matter particles also have wave nature. A particle of mass m and velocity v has wavelength:

Example 2.5: A 380 g cricket ball at 140 km/h (38.89 m s⁻¹) has λ = h/(mv) ≈ 4.48×10⁻³⁵ m — far too small to measure. Electrons, with tiny mass, have measurable wavelengths. In 1927, G.P. Thomson and C.J. Davisson demonstrated electron diffraction by nickel crystals (Fig. 2.13) — the diffraction pattern proved electrons behave as waves under appropriate conditions. de Broglie received the 1929 Nobel Prize in Physics for his 1924 PhD thesis proposing this duality.

Wave–particle duality is not contradiction but complementarity: diffraction and interference demand wave models; photoelectric effect and α-scattering demand particle models. The same electron can display either behaviour depending on the experiment.

2.8 Heisenberg's Uncertainty Principle (1927)

Wave–particle duality implies we cannot simultaneously measure position and momentum of an electron with perfect precision:

If Δx = 0 (electron located exactly), Δp → ∞ (momentum completely unknown). Conversely, precise momentum means position is entirely uncertain. In practice both have finite uncertainty. Because h = 6.626×10⁻³⁴ J s is extraordinarily small, the principle is negligible for cars, cricket balls and aeroplanes — but dominant for electrons.

Heisenberg (Nobel Prize 1932) showed Bohr's simultaneous exact radius and velocity for each orbit is impossible. You cannot trace a definite path for an electron; only speak of probability of finding it in a region. This directly motivated Schrödinger's wave mechanical model replacing orbits with orbitals.

Section 6: Quantum Mechanical Model and Orbitals (2.9)

Erwin Schrödinger (1926) proposed the wave mechanical model. Electron motion is described by a wave function ψ obtained from the Schrödinger wave equation (SWE). |ψ|² gives the probability of finding the electron in 3D space around the nucleus. The region of maximum probability is an atomic orbital — not a fixed path (orbit) but a probability cloud.

2.9.1 Quantum Numbers

Each electron has a unique set of four quantum numbers:

• Principal quantum number (n): energy level / shell; n = 1, 2, 3… Shell capacity = 2n² electrons (n=1→2, n=2→8, n=3→18).
• Azimuthal quantum number (l): subshell shape; l = 0 to (n−1). l=0 → s (spherical); l=1 → p (dumb-bell, 3 orbitals); l=2 → d (cloverleaf, 5); l=3 → f (7 orbitals).
• Magnetic quantum number (m_l): orbital orientation; m_l = −l to +l. For l=1: m_l = −1, 0, +1 (p_x, p_y, p_z).
• Spin quantum number (m_s): +½ or −½ (clockwise / anticlockwise); introduced via Pauli's principle.

2.9.2 Shapes of Orbitals

1s orbital: radial probability peaks at 52.9 pm for H; boundary surface encloses 95% probability — drawn as a sphere. 2s orbital: larger sphere with one spherical node (region of zero probability). Number of spherical nodes = n − l − 1. A nodal plane is a flat region of zero probability (p orbitals have one nodal plane). 3s has 2 spherical nodes.

Orbit vs orbital: Bohr's circular path = orbit (definite trajectory). Quantum orbital = 3D probability region — no fixed path. The wave function ψ itself has no direct physical meaning; only |ψ|² (probability density) is observable.

For n = 3 shell, Table 2.3 lists all allowed combinations: l = 0 (one 3s), l = 1 (three 3p with m_l = −1,0,+1), l = 2 (five 3d). Each orbital holds max 2 electrons (Pauli), giving 2 + 6 + 10 = 18 total — matching 2n² = 2(9) = 18. Every electron in the atom has a unique set of four quantum numbers — no two electrons are identical in all four.

p_x, p_y, p_z differ in orientation (m_l) but have equal energy in the absence of external fields (degenerate). Five d orbitals (d_xy, d_yz, d_xz, d_x²−y², d_z²) are also degenerate. Nodal planes in p and d orbitals arise where wave function changes sign — zero probability of finding the electron in that plane.

Section 7: Electronic Configuration (2.10–2.11)

2.10.1 Aufbau Principle

Electrons fill orbitals in order of increasing energy so the atom has minimum energy. For multi-electron atoms, use the (n + l) rules:

• Rule 1: Lower (n + l) fills first — 4s (n+l=4) before 3d (n+l=5).
• Rule 2: Same (n+l) → lower n first — 3d before 4p.

Order: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s …

2.10.2 Pauli's Exclusion Principle

No two electrons in an atom can have all four quantum numbers identical. Since three quantum numbers define an orbital, only two electrons per orbital with opposite spins (+½ and −½).

2.10.3 Hund's Rule of Maximum Multiplicity

Electrons occupy degenerate orbitals singly with parallel spins before pairing. Carbon: 1s² 2s² 2p_x¹ 2p_y¹ 2p_z⁰ (not paired in one p orbital). Electrons repel — they spread across orbitals.

Notation methods: superscript (1s² 2s² 2p¹_x 2p¹_y 2p¹_z for N) and orbital box diagram with ↑↓ arrows. Shorthand: [He] 2s¹ for Li; core electrons in noble gas brackets, valence electrons outside.

2.11 Stability of Half-Filled and Completely Filled Subshells

Aufbau sometimes fails when subshell energies are close (4s/3d, 5s/4d). Chromium: predicted [Ar] 4s² 3d⁴, actual [Ar] 4s¹ 3d⁵. Copper: predicted 3d⁹ 4s², actual 3d¹⁰ 4s¹. Reasons:

• Symmetry: half-filled or fully-filled d subshell is more symmetrical and stable.
• Exchange energy: more electrons with parallel spin → more exchange possibilities → greater stability. 3d⁵ 4s¹ has 10 exchange ways vs 6 for 3d⁴ 4s².

These exceptions are exam favourites — memorise Cr and Cu configurations. Similar reasoning applies to other half-filled d⁵ and fully-filled d¹⁰ cases (e.g. Mo, Ag) though NIOS highlights Cr and Cu specifically.

Electronic configuration determines valence electrons and hence chemical behaviour. Core electrons ([noble gas] configuration) are buried in inner shells; valence electrons participate in bonding. Nitrogen 1s² 2s² 2p_x¹ 2p_y¹ 2p_z¹ has 5 valence electrons (2s + 2p); lithium [He] 2s¹ has 1. Understanding filling order explains periodic trends studied in later modules.

Intext checkpoints from the textbook reinforce key skills: comparing e⁻ and p⁺ masses (Intext 2.1), listing Rutherford conclusions (2.2), computing photon energies (2.3–2.4), distinguishing line vs continuous spectra (2.4), calculating de Broglie λ for electrons (2.5), defining wave function and quantum numbers (2.6), counting spherical nodes in 3s (answer: 2, from n−l−1 = 3−0−1) (2.7), and applying (n+l) rules to decide 4s before 3d (2.8).

Chapter Summary

Atoms contain electrons, protons and neutrons. Z defines the element; isotopes share Z but differ in N. Thomson's plum pudding gave way to Rutherford's nuclear model, which failed on stability. Bohr quantised orbits and explained the H spectrum via E = hν and E_n = −R_H/n². de Broglie and Heisenberg established wave–particle duality and uncertainty, leading to Schrödinger's quantum model with orbitals defined by quantum numbers n, l, m_l, m_s. Electron filling follows Aufbau, Pauli and Hund's rules, with Cr and Cu as notable exceptions due to half-filled/full d-subshell stability.