Fundamental Particles and Their Discovery

Fundamental Particles

• Three fundamental particles are electrons, protons, and neutrons.
• Each particle possesses mass and charge.
• Relative masses: electron = 0, proton = 1, neutron = 1.
• Relative charges: electron = -1, proton = +1, neutron = 0.
• Atoms are electrically neutral due to equal numbers of protons and electrons.

Discovery of Subatomic Particles

• Electrons: Discovered by J.J. Thomson.
• Protons: Discovered by Goldstein.
• Neutrons: Discovered by Chadwick via bombarding Beryllium atoms with alpha particles.

Cathode Rays

• Cathode rays are high-speed electrons traveling from cathode to anode.
• Negatively charged, travel in straight lines, and exhibit mass, energy, and penetration power.
• Produce X-rays upon striking heavy nuclei (e.g., Tungsten, Molybdenum).
• Charge-to-mass ratio (specific charge) is constant, independent of discharge tube gas.

Anode Rays

• Anode rays, also called canal rays, are high-speed positive ions traveling from anode to cathode.
• Composed of positively charged ions, travel in straight lines, and exhibit mass and energy.
• Charge-to-mass ratio varies depending on the discharge tube gas.

Energy Units

• Electron Volt (eV) and Joule are important energy units.
• 1 eV = 1.6 x 10^-19 J.

Unit of Distance

• 1 nanometer (nm) = 10^-9 meters.
• 1 angstrom (Å) = 10^-10 meters.

Iso Series

• Groups of atoms exhibiting similar characteristics.
• Isotopes: Same atomic number (Z), different mass number (A). Same protons, different neutrons.
• Isobars: Same mass number (A), different atomic number (Z). Same nucleons, different protons and neutrons.
• Isoelectronic: Same number of electrons.
• Isotones: Same number of neutrons (A-Z).
• Isosters: Same atoms and electrons.
• Isodiapheres: Same isotopic number or neutron excess (A-2Z).

Atomic Models

• J.J. Thomson's Model (Plum Pudding):
  • Positively charged sphere with embedded electrons.
  • Positive charge and mass uniformly distributed.
  • Rejected by Rutherford's alpha-particle scattering experiment.
• Rutherford's Model (Nuclear):
  • Tiny, dense, positively charged nucleus at the center (protons and neutrons).
  • Electrons orbit the nucleus in circular paths.
  • Atom is mostly empty space.
  • Explained alpha-particle scattering.
  • Nucleus radius ~ 10^-15m using r = r₀ A^1/3
    • r₀ = 1.4 x 10^-15m
    • A = mass number
  • Limitations: Couldn't explain atomic stability (electrons losing energy and spiraling into nucleus). Couldn't explain electron distribution.

Dual Nature of Light

• Light exhibits both wave and particle properties.
• Wave nature explained by reflection, refraction, diffraction.
• Particle nature explained by Planck's quantum theory and the photoelectric effect.

Electromagnetic Waves (EM Waves)

• EM waves are oscillating electric and magnetic fields perpendicular to each other and the direction of propagation.
• The electromagnetic spectrum encompasses various frequencies and wavelengths of EM radiation (cosmic rays, gamma rays, X-rays, UV, visible light, IR, microwaves, radio waves).
• Spectrum ordered from highest to lowest energy.
• Left to right:
  • Wavelength increases
  • Frequency decreases
  • Energy decreases
• Energy, frequency, and wavelength related by c = νλ
  • c = speed of light ~ 3 x 10⁸ m/s
  • ν = frequency
  • λ = wavelength

Planck's Quantum Theory

• Explains particle nature of light.
• Energy is quantized, existing in discrete units (quanta/photons).
• Photon is a small packet of energy.
• Energy of a photon: E = hν = hc/λ
  • h = Planck's constant, 6.626 x 10^-34 Js
  • ν = frequency
  • λ = wavelength

Photoelectric Effect

• Emission of electrons from a metal surface when light of sufficient frequency falls upon it.
• Work Function (Φ): Minimum energy to remove an electron from a metal surface.
• Threshold Frequency (ν₀): Minimum frequency for photoelectric emission.
• Threshold Wavelength (λ₀): Maximum wavelength for photoelectric emission (inversely proportional to ν₀).
• Supports light's particle nature.
• KE = hν - Φ (Kinetic energy = energy of incident photon - work function).

Energy of Photon

• Energy of a photon is hf, where h is Planck's constant and f is the frequency

Photoelectric Effect

• Emitted electron KE depends on light frequency, not intensity.
• Photocurrent (number of emitted electrons) depends on light intensity, not frequency.

Bohr Model of the Atom

• Quantized angular momentum: mv_r = n h / 2π, for electron orbiting.
• Discreet energy levels (shells) for electrons.
• Ground state = lowest energy level, first shell.
• Excited state = higher than ground state.
• Sixth excited state corresponds to the 7th shell.
• Energy increases as electron distance increases from nucleus.
• First shell has lowest energy, infinite shell's energy is zero.
• Electron transitions between levels by absorbing or releasing energy.
• Model applicable to single-electron species.
• Energy difference between energy levels decreases with increasing distance from nucleus.
• Atom comprised of a nucleus and extranuclear part (electrons).
• Nucleus contains protons and neutrons; extranuclear part contains electrons

Bohr Model Formulas

• Radius: r = 0.529n² / Z Å
• Velocity: v = 2.18 x 10⁶ Z/n m/s
• Energy: E = -13.6 Z²/n² eV or E = -2.18 x 10^-18 Z²/n² J

Bohr Model Energy Ratios

• Total energy / kinetic energy = -2/1.
• Potential energy / kinetic energy = 1/-1.
• Example: If total energy = -13.6 eV, kinetic energy = +13.6 eV, potential energy = -27.2 eV

Hydrogen Spectrum

• Wavelength of spectral lines: 1/λ = RZ² (1/n₁² - 1/n₂²)
• R = Rydberg constant (1.1 × 10⁷ m⁻¹)
• Z = atomic number
• n₁ = lower energy level
• n₂ = higher energy level
• Hydrogen spectrum has series (Lyman, Balmer, Paschen, Brackett, Pfund, Humphrey).
• Lyman (UV, n₁ =1)
• Balmer (visible, n₁ =2)
• Paschen, Brackett, Pfund, Humphrey (IR, n₁ = 3, 4, 5, 6).

de Broglie Wavelength

• λ = h/p, where λ is wavelength, h is Planck's constant, and p is momentum.
• p = mv (momentum = mass × velocity)
• λ = h/√2mKE (alternate formula)

Heisenberg Uncertainty Principle

• Impossible to simultaneously know precise position and momentum of an electron.
• ΔxΔp ≥ h/4π, where Δx = position uncertainty, Δp = momentum uncertainty. -Also Δp = mΔv, where Δv = velocity uncertainty.
• Zero position uncertainty implies infinite momentum uncertainty and vice versa.

Bohr Model Drawbacks

• Only applicable to single-electron species.
• Ignores Heisenberg uncertainty principle.
• Ignores de Broglie wavelength (wave-like nature of electrons).
• Doesn't explain spectral line splitting in electric/magnetic fields.

Wave-Mechanical Model (Quantum Model)

• Developed by Erwin Schrödinger.
• Four quantum numbers describing electron state:
  • n Principal (energy level/shell; n=1, 2, 3...).
  • l Azimuthal (subshell/orbital shape; l = 0 to n-1). s, p, d, f.
  • ml Magnetic (orbital orientation; ml= -l to +l)
  • ms Spin (intrinsic angular momentum; ±½)
• Maximum electrons per shell: 2n²
• Orbital angular momentum: √l(l+1)h/2π
• n² determines number of orbitals per shell
• 2l + 1 determines number of orbitals per subshell.
• 0 possible value of magnetic quantum number (ml) for s orbitals, pz orbitals, and dz² orbitals.
• Multi-electron energy depends on n and l; lower (n+l) is lower energy; if same (n+l), lower n is lower energy.

Electronic Configuration Rules

• Aufbau Principle: Fill orbitals with increasing energy.
• Pauli Exclusion Principle: No two electrons share all four quantum numbers.
• Hund's Rule: Fill each orbital individually before pairing electrons.
• Exceptions: Cr (4s¹ 3d⁵) and Cu (4s¹ 3d¹0) due to half-filled or full d-orbitals.

Orbital Shapes

• s: Spherical
• p: Dumbbell
• d: More complex
• f: Even more complex
• Number of nodal planes = azimuthal quantum number (l)

Understanding Atomic Orbitals

• Nodes: Regions with zero electron probability.
• Nodal planes in orbitals: -p: one nodal plane -d: two nodal planes -Specific d-orbital nodal plane descriptions (d_xy, d_yz, d_xz, d_x²−y², d_z²) -d-orbital shapes (double dumbbell/cloverleaf; four lobes) and types: -Non-azimuthal: d_xy, d_yz, d_xz -Azimuthal: d_x²−y², d_z² -Magnetic Dipole Moment: Formula: n(n+2)
• Radial vs. Angular Nodes: -Radial: Spherical shell with zero probability. -Angular: Plane with zero probability. -Total nodes in orbital = n - 1 -Calculating nodel planes: number of nodel planes = azimuthal quantum number (l)

Explore the three fundamental particles: electrons, protons, and neutrons. Discover the history behind their discovery and the nature of cathode rays, including their properties and uses. Test your knowledge on the essential concepts of atomic structure and subatomic particles.