Chapter 2: Structure of Atom (CBSE Class 11)

Main Takeaways

  • Atoms are divisible into electrons, protons, and neutrons.
  • Early atomic models (Thomson, Rutherford, Bohr) progressively incorporated experimental findings.
  • Modern quantum‐mechanical model describes electrons as wavefunctions (orbitals) defined by four quantum numbers.

1. Discovery of Subatomic Particles

1.1 Cathode‐Ray Experiments and the Electron
 - Cathode rays: straight, negatively charged particles emitted from cathode → electrons.
 - Charge‐to‐mass ratio (e/m) measured by J.J. Thomson: 1.7588 × 10¹¹ C kg⁻¹.
 - Millikan’s oil‐drop experiment (1906–14): charge on electron = –1.602176 × 10⁻¹⁹ C.
 - Electron mass mₑ = 9.1094 × 10⁻³¹ kg.

1.2 Canal Rays, Protons, and Neutrons
 - Canal rays: positively charged ions; lightest = H⁺ (proton).
 - Charge on proton = +1.602176 × 10⁻¹⁹ C; mass = 1.6726 × 10⁻²⁷ kg.
 - Chadwick (1932): bombarding Be with α‐particles produced neutrons (mass ≈ 1.675 × 10⁻²⁷ kg).

Fundamental Particle Properties

ParticleSymbolCharge (C)Mass (kg)Relative mass (u)
Electrone⁻–1.6022 × 10⁻¹⁹9.1094 × 10⁻³¹0.00054
Protonp⁺+1.6022 × 10⁻¹⁹1.6726 × 10⁻²⁷1.0073
Neutronn⁰01.6749 × 10⁻²⁷1.0087

2. Historical Atomic Models

2.1 Thomson’s “Plum‐Pudding” Model (1898)
 - Atom = uniform positive sphere (r ≈ 10⁻¹⁰ m) with embedded electrons → explained neutrality but not later scattering results.

2.2 Rutherford’s Nuclear Model (1911)
 - α‐particle scattering through thin gold foil: most passed through, some deflected, very few backscattered → led to:
  – Atom is mostly empty space.
  – Mass and positive charge concentrated in tiny nucleus (r ≈ 10⁻¹⁵ m).
  – Electrons orbit nucleus under electrostatic attraction.
 - Limitations: classical orbits predict rapid radiation‐loss collapse, and no explanation for discrete spectra.

2.3 Bohr’s Model for H Atom (1913)
 Postulates:
  1. Electrons orbit in discrete circular orbits with quantized angular momentum mevr=nℏmevr=nℏ.
  2. No radiation emitted/absorbed within an allowed orbit; transitions between orbits emit/absorb hν=ΔEhν=ΔE.
  3. Radius rn=n2a0rn=n2a0; energy En=−RHn2En=−n2RH.
  4. Explained H line spectra (Rydberg formula).

Drawbacks:
 - Only works for one‐electron species; fails for multi‐electron atoms.
 - Contradicts Heisenberg uncertainty principle and ignores wave nature of electrons.

3. Wave–Particle Duality & Quantum Mechanics

3.1 Dual Nature of Radiation
 - Wave: explains interference, diffraction; speed in vacuum c=3.00×108c=3.00×108 m s⁻¹; c=λνc=λν.
 - Particle (photon): energy E=hνE=hν, h=6.626×10−34h=6.626×10−34 J s; explains black‐body radiation, photoelectric effect
  – Photoelectric effect: threshold frequency ν0ν0; KE of ejected electron =hν−hν0=hν−hν0.

3.2 de Broglie Hypothesis (1924)
 - Matter waves: λ=hp=hmvλ=ph=mvh. Confirmed by electron diffraction.

3.3 Heisenberg Uncertainty Principle (1927)
 - Δx Δp≥h4πΔxΔp≥4πh.
 - For electrons, ∆x and ∆v uncertainties dominate—no precise orbit trajectories.

4. Quantum‐Mechanical Model of the Atom

4.1 Schrödinger Equation (1926)
 - Time‐independent form: H^ ψ=E ψH^ψ=Eψ.
 - Solutions for hydrogen atom yield quantized energy levels and wavefunctions (orbitals).

4.2 Quantum Numbers & Orbitals
 - Principal n=1,2,3,…n=1,2,3,… (shell, size, energy).
 - Azimuthal l=0,1,…,n−1l=0,1,…,n−1 (subshell, shape; s, p, d, f …).
 - Magnetic ml=−l,…,+lml=−l,…,+l (orientation; number of orbitals = 2l+1).
 - Spin ms=±12ms=±21 (two electrons per orbital, opposite spins).

4.3 Orbital Shapes & Nodes
 - Radial probability ∣ψ(r)∣2∣ψ(r)∣2 vs. r: s‐orbitals spherical with (n–1) radial nodes.
 - p‐orbitals: two lobes, one angular node; d‐orbitals: cloverleaf shapes with two angular nodes.
 - Boundary surfaces drawn to enclose ~90% probability volume.

4.4 Orbital Energy Ordering
 - Hydrogen‐like: E∝−1/n2E∝−1/n2 → all l within same n are degenerate.
 - Multi‐electron: energies depend on n + l rule (lower n + l → lower energy; if tie, lower n favours).
  Order: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p …

4.5 Electron Configuration Rules
 1. Aufbau Principle: fill lowest‐energy orbitals first (1s, 2s, 2p, 3s…).
 2. Pauli Exclusion Principle: max two electrons per orbital, opposite spins.
 3. Hund’s Rule: maximize unpaired electrons (parallel spins) in degenerate orbitals before pairing.

4.6 Exceptional Stability
 - Half‐filled (e.g., d⁵) and fully filled (d¹⁰) subshells gain extra exchange‐energy stability → Cu (3d¹⁰ 4s¹) and Cr (3d⁵ 4s¹) exceptions.

5. Electronic Configurations of Elements

  • Write using noble‐gas core: e.g., Fe = [Ar] 4s² 3d⁶.
  • Valence electrons = electrons in outermost n.
  • Blocks in periodic table correspond to filling s, p, d, f orbitals.

6. Summary of Key Concepts

  • Subatomic Particles: electrons (–), protons (+), neutrons (0).
  • Atomic Models: Thomson (plum pudding) → Rutherford (nuclear) → Bohr (quantized orbits) → Schrödinger (wave mechanics).
  • Quantum Numbers: n, l, mₗ, mₛ define each electron’s orbital.
  • Electron Configurations: determined by aufbau, Pauli, Hund’s rules; noble‐gas shorthand streamlines notation.
  • Chemical Behavior: explained by valence configurations and subshell stabilities.