1.1 Early Atomic Models

1.1.1 Dalton’s Billiard-Ball Model (Early 19th Century)
John Dalton proposed that each chemical element consisted of tiny, indivisible particles called atoms. Atoms of the same element were identical in mass and properties, and chemical reactions were rearrangements of these atoms. Limitations: No explanation of subatomic structure; could not account for results of electrical or spectroscopic experiments.

1.1.2 Thomson’s "Plum-Pudding" Model (1897)
J. J. Thomson discovered the electron via cathode-ray experiments. He concluded that atoms contained negatively charged electrons. He proposed that electrons were embedded in a diffuse, positively charged sphere—like plums in a plum pudding—so the overall atom was electrically neutral. Limitations: Could not explain results of scattering experiments (e.g., Rutherford’s); no dense nucleus.

1.1.3 Rutherford’s Nuclear Model (1911)
Ernest Rutherford directed α-particles at thin gold foil and measured scattering angles. Most α-particles passed through with minimal deflection, but some scattered at large angles—impossible if positive charge were spread uniformly. Conclusion: Atom is mostly empty space; nearly all positive charge and most of the mass are concentrated in a very small, dense nucleus. Electrons orbit this nucleus at comparatively large distances. Key Features:
- Nucleus: Radius on the order of 10⁻¹⁵ to 10⁻¹⁴ m; contains protons and neutrons.
- Electron Cloud: Electrons occupy space around nucleus but classical orbits inconsistent with observed atomic spectra.

1.1.4 Bohr’s Planetary Model (1913)
Niels Bohr introduced quantization of electron orbits to explain hydrogen’s line spectrum. Postulates:
1. Electrons move in circular orbits around the nucleus without radiating energy, provided they remain in certain permitted orbits (stationary states) of quantized angular momentum: m_e·v·r = n·h, where n = 1, 2, 3, …
2. Electrons emit or absorb a photon only when transitioning between these permitted orbits; the photon’s energy equals the energy difference between initial and final states: ΔE = E_i - E_f = h·f.
Bohr’s model correctly predicted the hydrogen emission spectrum (Balmer series), giving energy levels: E_n = - (m_e·e^4) / (8·e_0^2·h^2·n^2) ≈ -13.6 eV/n². Limitations: Only strictly accurate for hydrogen-like (one-electron) atoms; failed for multi-electron systems and fine-structure details.

Quantum-Mechanical (Schrödinger) Model
Erwin Schrödinger (1926) treated electrons as wavefunctions Ψ(x,y,z) satisfying the time-independent Schrödinger equation:
−(ℏ² / (2·m_e)) ∇²Ψ + V(r)·Ψ = E·Ψ
For hydrogen, V(r) = -e² / (4πε₀r). Solutions yield quantized energy levels identical to Bohr’s but with additional quantum numbers (n, l, m). Electrons occupy orbitals—probability distributions—rather than fixed circular orbits.

1.2 Subatomic Particles

Electron (e^-): Charge: q_e = -1.602×10^-19 C. Rest mass: m_e = 9.109×10^-31 kg ≈ 0.511 MeV/c². Spin: 1/2 (fermion).
Proton (p^+): Charge: q_p = +1.602×10^-19 C. Rest mass: m_p = 1.673×10^-27 kg ≈ 938.3 MeV/c². Spin: 1/2 (fermion). Constituent quarks: two up-quarks (each +2/3 e) and one down-quark (-1/3 e).
Neutron (n^0): Charge: 0. Rest mass: m_n = 1.675×10^-27 kg ≈ 939.6 MeV/c². Spin: 1/2 (fermion). Constituent quarks: one up-quark (+2/3 e) and two down-quarks (each -1/3 e). Free neutron unstable (half-life ≈ 880 s, decaying via β⁻).

Binding Energy: The mass of a nucleus is slightly less than the sum of its constituent protons and neutrons. The 'missing' mass is the binding energy E_b, according to E = mc². Binding energy per nucleon generally increases from light nuclei up to iron-56.

1.3 Isotopes and Nuclear Notation
Isotopes are atoms of the same element with different numbers of neutrons. Notation: ^A_ZX, where A = Z + N is mass number, Z is atomic number. Example: Carbon-12 (^12_6C) has 6 protons, 6 neutrons; Carbon-14 (^14_6C) has 6 protons, 8 neutrons (radioactive).
Mass Number (A) vs. Atomic Number (Z): Z defines the element; A defines the isotope. Number of neutrons N = A - Z.