Structure of Atom

The atom, once thought indivisible, is now known to have an intricate internal architecture. Understanding atomic structure explains why elements differ in properties, how they bond, and how they interact with energy. This chapter traces the historical development of atomic models and introduces quantum mechanics at the introductory level.

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Key Concepts

• Discovery of Sub-atomic Particles
• Electron: Discovered by J.J. Thomson via cathode ray experiments. Charge = -1.6 x 10^-19 C; mass = 9.11 x 10^-31 kg.
• Proton: Discovered by Goldstein via canal (anode) rays. Charge = +1.6 x 10^-19 C; mass = 1.67 x 10^-27 kg.
• Neutron: Discovered by Chadwick by bombarding beryllium with alpha particles. Mass approximately equal to proton; no charge.

• Atomic Number, Mass Number, and Isotopes
• Atomic number (Z): Number of protons in the nucleus; defines the element.
• Mass number (A): Total number of protons + neutrons. Neutrons = A - Z.
• Isotopes: Atoms of the same element with different numbers of neutrons (same Z, different A). E.g., 1H-1, 1H-2 (deuterium), 1H-3 (tritium).
• Isobars: Atoms of different elements with the same mass number. E.g., 18Ar-40 and 20Ca-40.

• Atomic Models
• Thomson's model ("Plum pudding"): Atom is a sphere of uniform positive charge with electrons embedded in it.
• Rutherford's nuclear model: From the gold foil experiment — atom is mostly empty space with a tiny, dense, positively charged nucleus. Electrons orbit the nucleus. Problem: orbiting electrons should radiate energy and spiral into the nucleus (classical electrodynamics objection).
• Bohr's model (1913): Electrons move in fixed circular orbits (stationary states) at specific energies without radiating. Energy is absorbed or emitted only when an electron transitions between orbits.
• Energy of orbit: E_n = -2.18 x 10^-18 / n² J (for hydrogen)
• Radius: r_n = 0.529 x n² angstrom (Bohr radius, a₀)
• Wavenumber of spectral lines: v-bar = R_H (1/n₁² - 1/n₂²), where R_H = 1.097 x 10⁷ m^-1

• Quantum Mechanical Model
• Wave-particle duality: de Broglie proposed matter has wave nature: lambda = h / (mv), where h = Planck's constant (6.626 x 10^-34 J·s).
• Heisenberg's Uncertainty Principle: It is impossible to determine simultaneously the exact position and exact momentum of a particle: delta_x x delta_p ≥ h/(4 pi).
• Quantum numbers: Four numbers describe each electron:
• Principal quantum number (n): Shell; n = 1, 2, 3, … Energy and size.
• Azimuthal quantum number (l): Subshell; l = 0 to n-1. l=0 (s), l=1 (p), l=2 (d), l=3 (f).
• Magnetic quantum number (m_l): Orbital orientation; m_l = -l to +l.
• Spin quantum number (m_s): +1/2 or -1/2.
• Pauli's Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers.
• Aufbau Principle: Electrons fill orbitals in order of increasing energy.
• Hund's Rule: Electrons occupy separate orbitals of a subshell before pairing; all singly occupied orbitals have the same spin.

Electronic Configuration
Filling order (Aufbau): 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, ...
Notable exceptions: Cr (Z=24): [Ar] 3d⁵ 4s¹ and Cu (Z=29): [Ar] 3d¹⁰ 4s¹ (due to extra stability of half-filled/fully-filled d subshells).

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Worked Examples

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Students often confuse atomic number (protons only) with mass number (protons + neutrons). Also, remember that Aufbau filling uses the (n + l) rule — 4s (n+l = 4) fills before 3d (n+l = 5) — but 3d loses electrons before 4s in ionisation. The exceptions for Cr and Cu are frequently tested.

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From Thomson to the quantum mechanical model, our understanding evolved from a simple sphere to a complex probability-based picture. The key takeaways are the four quantum numbers, the three filling rules (Aufbau, Pauli, Hund), and Bohr's energy equation for hydrogen. Spectral lines arise from electron transitions between energy levels.