Topic 2
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Topic 2 — Key Facts for DU Admission (Bangladesh) Core concept: Atomic Structure and the Periodic Table — arrangement of electrons determines chemical behavior High-yield point: Electronic configuration following Aufbau principle, quantum numbers, periodic trends in atomic properties ⚡ Exam tip: Aufbau diagram sequence, Hund’s rule, and periodic trend explanations are frequently tested in multiple-choice and short-answer questions
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Topic 2 — DU Admission (Bangladesh) Study Guide Overview: Understanding atomic structure illuminates why elements behave as they do and how the periodic table organizes chemical knowledge Core principles: Subatomic particle properties, evolution of atomic models, quantum mechanical description of electrons, periodic law Key points: Electronic configuration using Aufbau principle, four quantum numbers, orbital shapes and energies, periodic property trends across groups and periods Study strategy: Memorize the Aufbau diagram sequence, practice writing electron configurations, learn group trends with causal explanations
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Atomic Structure and Periodic Table — Complete Study Notes
The Subatomic Particle Zoo
All ordinary matter consists of just three fundamental particles, though nuclear physics reveals many more exotic species. These three determine the chemical identity and most physical properties of atoms.
| Particle | Symbol | Relative Charge | Rest Mass | Discovery |
|---|---|---|---|---|
| Electron | e⁻ | −1 | 9.109 × 10⁻³¹ kg (0.00055 amu) | J.J. Thomson (1897) |
| Proton | p⁺ | +1 | 1.673 × 10⁻²⁷ kg (1.007 amu) | Ernest Rutherford (1919) |
| Neutron | n⁰ | 0 | 1.675 × 10⁻²⁷ kg (1.008 amu) | James Chadwick (1932) |
The atomic number (Z) equals the number of protons and uniquely identifies an element — no two elements share the same Z. The mass number (A) is the total count of protons plus neutrons. Isotopes of a given element possess identical Z but different A values because they differ in neutron count. Isobars are nuclei with identical A but different Z, while isotones share the same neutron number despite different proton counts.
Evolution of Atomic Models
Dalton’s Atomic Theory (1808)
John Dalton proposed that all matter consists of indivisible atoms of each element, identical in mass and properties for a given element, and that atoms combine in simple whole-number ratios to form compounds. Though foundational, Dalton’s model failed to account for the electrical nature of matter and the existence of subatomic particles.
Thomson’s Plum Pudding Model (1898)
J.J. Thomson discovered the electron and proposed a model wherein the atom consisted of a diffuse sphere of positive charge containing electrons embedded within it — rather like plums distributed throughout a pudding. This explained overall atomic neutrality but was conclusively disproven by Rutherford’s gold foil experiment.
Rutherford’s Nuclear Model (1911)
Rutherford’s gold foil experiment fired alpha particles at a thin gold foil. The startling observation that most particles passed through undeflected while a few bounced backward at large angles led to the revolutionary conclusion that atoms consist mostly of empty space, with all positive charge and most mass concentrated in an extremely small, dense nucleus. The problem: classical electromagnetism predicted that orbiting electrons should continuously radiate electromagnetic energy and spiral into the nucleus within fractions of a second. Atoms should be unstable — they manifestly are not.
Bohr’s Quantized Model (1913)
Niels Bohr resolved the stability paradox by introducing three radical postulates:
- Electrons occupy only specific stationary states (orbits) without radiating energy
- These stationary states have quantized (discrete) energy levels
- An electron transitions between stationary states by absorbing or emitting a photon of energy exactly matching the energy difference: E_photon = E_final − E_initial
For hydrogen, electron energy in level n is: E_n = −13.6/n² electronvolts (eV)
Angular momentum quantization: mvr = nh/2π where h is Planck’s constant.
The Bohr model successfully explained the hydrogen emission spectrum, generating the famous series: Lyman (UV, transitions to n=1), Balmer (visible, transitions to n=2), Paschen (infrared, transitions to n=3). Despite these successes, Bohr’s model failed for multi-electron atoms, could not explain fine spectral structure, and was fundamentally incompatible with Heisenberg’s uncertainty principle.
Modern Quantum Mechanical Model (1926 onward)
Werner Heisenberg’s uncertainty principle establishes a fundamental limit on knowledge:
Δx · Δp ≥ ℏ/2 (or equivalently Δx · Δv ≥ ℏ/4πm)
where ℏ = h/2π. This principle implies that confining an electron to a small region (small Δx) necessarily increases its momentum uncertainty (large Δp), making its momentum and therefore its energy poorly defined. The classical concept of a definite electron orbit becomes meaningless. Instead, electrons occupy orbitals — three-dimensional probability distributions described by the Schrödinger wave equation (ψ). The probability density ψ² gives the probability of finding the electron in a given region of space.
The Four Quantum Numbers
Each electron in any atom is completely specified by four quantum numbers. No two electrons in the same atom can share all four quantum numbers (Pauli exclusion principle).
Principal Quantum Number (n)
- Designates the electron shell: K-shell (n=1), L-shell (n=2), M-shell (n=3), N-shell (n=4), and so forth
- Determines the electron’s energy level and approximate average distance from the nucleus
- Determines the maximum number of electrons a shell can hold: 2n²
| Shell (n) | Maximum electrons (2n²) |
|---|---|
| 1 (K) | 2 |
| 2 (L) | 8 |
| 3 (M) | 18 |
| 4 (N) | 32 |
Azimuthal Quantum Number (l)
- Also called orbital quantum number or subsidiary quantum number
- Specifies the sub-shell within a given shell: s (l=0), p (l=1), d (l=2), f (l=3)
- Values range from 0 to (n−1)
- Determines the shape of the orbital and contributes to electron energy
Magnetic Quantum Number (m_l)
- Specifies the orientation of the orbital in space
- Values range from −l through 0 to +l
- For p orbitals (l=1): m_l = −1, 0, +1 (three orientations: p_x, p_y, p_z)
- For d orbitals (l=2): m_l = −2, −1, 0, +1, +2 (five orientations)
Spin Quantum Number (m_s)
- Describes the direction of electron spin angular momentum
- Can only take two values: +½ (spin-up, ↑) or −½ (spin-down, ↓)
- Independent of the orbital quantum numbers
Electronic Configuration and the Aufbau Principle
Electrons occupy orbitals following systematic rules:
Aufbau Principle
Electrons fill orbitals in order of increasing energy level, determined by the (n + l) rule: when comparing two orbitals, the one with the lower (n + l) sum fills first; if sums are equal, the lower n value fills first.
The energy ordering sequence: 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f → 6d → 7p
Mnemonic aid: “Some Poor Fancy Students Rather Marry Pretty Science Teachers**”** (1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p)
Hund’s Rule of Maximum Multiplicity
When degenerate orbitals (orbitals of equal energy, such as the three p orbitals or five d orbitals) are available, electrons occupy them singly with parallel spins before any orbital receives a second electron. This maximizes total spin and produces the most stable electron configuration.
Example — Nitrogen (7 electrons):
- Configuration: 1s² 2s² 2p³
- p orbital occupation: ↑ ↑ ↑ (three unpaired electrons with parallel spins)
- NOT ↑↓ ↑ ↑ (which would place two electrons in one orbital)
Pauli Exclusion Principle
No two electrons in a single atom can possess identical values for all four quantum numbers. Since electrons in the same orbital share the same n, l, and m_l values, they must differ in spin (m_s = +½ vs −½). This limits each orbital to exactly two electrons with opposite spins.
Maximum electron capacity by sub-shell:
- s orbital (l=0): 2 electrons
- p subshell (l=1): 6 electrons (three orbitals × 2)
- d subshell (l=2): 10 electrons (five orbitals × 2)
- f subshell (l=3): 14 electrons (seven orbitals × 2)
The Periodic Table: Organization of Elements
The modern periodic table arranges 118 elements in 18 vertical groups and 7 horizontal periods. This arrangement is not arbitrary — it reflects recurring patterns in chemical behavior arising from electron configuration.
Electronic Configuration by Block
s-Block elements (Groups 1 and 2 plus helium): ns¹ and ns² configurations. These are generally reactive metals — alkali metals (Group 1) with +1 oxidation state and alkaline earth metals (Group 2) with +2 oxidation state.
p-Block elements (Groups 13 through 18): ns² np¹ through ns² np⁶ configurations. This block contains metals, metalloids, non-metals, halogens (Group 17, most reactive non-metals), and noble gases (Group 18, chemically inert).
d-Block elements (Groups 3 through 12, transition metals): Characterized by (n−1)d¹⁻¹⁰ ns⁰⁻² configurations. They exhibit variable oxidation states, form colored compounds, and display paramagnetic properties.
f-Block elements (Lanthanides and Actinides): 4f and 5f series respectively. All f-block elements are metals, and most actinides are radioactive.
Periodic Trends in Atomic Properties
Atomic Radius
Atomic radius decreases across a period (left to right) because increasing nuclear charge (more protons) pulls all electrons closer while no new shells are added. Atomic radius increases down a group because each successive period adds an entirely new electron shell, expanding the radius despite increased nuclear charge.
Ionization Energy (IE)
The energy required to remove the outermost electron from a neutral gaseous atom measures how tightly the electron is bound. Ionization energy increases across a period (more protons = stronger pull = harder to remove electron) and decreases down a group (outer electrons reside in higher shells farther from the nucleus and shielded by inner electrons). Notable exceptions occur at group boundaries where electron sub-shell stability creates irregular trends (e.g., IE of B is lower than Be because removing a p-electron is easier than removing an s-electron).
Electron Affinity (EA)
Electron affinity measures the energy released when a neutral atom gains an electron to form a negative ion. EA generally becomes more negative across a period (atoms increasingly attract additional electrons) and becomes less negative down a group. Chlorine possesses the most negative electron affinity among all elements.
Electronegativity
The tendency of an atom to attract shared electrons in a chemical bond — a conceptual blend of ionization energy and electron affinity. Electronegativity increases across a period and decreases down a group. Fluorine is the most electronegative element (EN = 4.0 on the Pauling scale); francium is least electronegative (EN ≈ 0.7).
Metallic Character
The tendency of an element to lose electrons and form positive ions. This trend decreases across a period (non-metals gain electrons) and increases down a group (outer electrons are farther from the nucleus and easier to remove). The most metallic elements occupy the bottom-left corner of the periodic table; the most non-metallic elements occupy the top-right corner.
Key Constants for the Examination
| Constant | Value |
|---|---|
| Electron charge | 1.602 × 10⁻¹⁹ C |
| Electron mass | 9.109 × 10⁻³¹ kg |
| Proton/neutron mass | 1.673 × 10⁻²⁷ kg |
| Rydberg constant | 1.097 × 10⁷ m⁻¹ |
| Bohr radius | 0.529 Å (5.29 × 10⁻¹¹ m) |
| Planck’s constant | 6.626 × 10⁻³⁴ J·s |
| h (reduced) | ℏ = h/2π |
Common Examination Question Types
- Writing electron configurations — follow Aufbau principle with exceptions (Cr, Cu, Mo, Ag, etc.)
- Quantum number problems — determine valid quantum numbers for a specified electron
- Periodic trends — predict relative atomic radius, ionization energy, or electronegativity and explain the reasoning
- Distinguishing isotopes, isobars, isotones — count protons, neutrons, or both
- Bohr model calculations — energy of photon emitted or absorbed during transition
- Photoelectric effect — K.E._max = hν − φ where ν is frequency and φ is work function
Examination Strategy
The most reliable approach to electron configuration questions is drawing the Aufbau diagram and filling orbitals sequentially. For quantum number problems, remember that n must be a positive integer, l ranges from 0 to (n−1), m_l ranges from −l to +l, and m_s is strictly +½ or −½. For periodic trend questions, always provide a causal explanation linking the property to nuclear charge, electron shells, or shielding — not merely stating the trend direction.
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