Structure of Atom

• 1. Subatomic Particles

  • Electron ($e^-$)
    • Discovered by J.J. Thomson via Cathode Ray Tube experiment
    • Charge: $-1.6 \times 10^{-19}\text{ C}$
    • Mass: $9.1 \times 10^{-31}\text{ kg}$
  • Proton ($p^+$)
    • Discovered by E. Goldstein via Anode/Canal Rays
    • Charge: $+1.6 \times 10^{-19}\text{ C}$
    • Mass: $1.672 \times 10^{-27}\text{ kg}$
  • Neutron ($n^0$)
    • Discovered by James Chadwick by bombarding Be with $\alpha$-particles
    • Charge: Neutral ($0$)
    • Mass: $1.675 \times 10^{-27}\text{ kg}$
  • Atomic Terms
    • Atomic Number ($Z$): Total number of protons
    • Mass Number ($A$): Protons + Neutrons (Nucleons)
    • Isotopes: Same $Z$, different $A$
    • Isobars: Same $A$, different $Z$
    • Isotones: Same number of neutrons

• 2. Early Atomic Models

  • Thomson's Model
    • Plum Pudding Model: Positive sphere with embedded electrons
    • Limitation: Failed to explain stability and spectrum
  • Rutherford's Model
    • Based on $\alpha$-particle Scattering Experiment
    • Key Findings: Dense positive core called Nucleus; electron orbits
    • Limitations: Couldn't explain atomic stability and line spectra

• 3. Developments Leading to Quantum Model

  • Electromagnetic Wave Theory
    • Electromagnetic radiation has wave nature ($c = \nu \lambda$)
  • Planck's Quantum Theory
    • Energy emitted/absorbed in discrete packets called quanta ($E = h\nu$)
  • Photoelectric Effect
    • Discovered by Hertz, explained by Einstein
    • Light has particle nature (Photons)
    • Equation: $E = W_0 + K.E._{max}$
  • Hydrogen Spectrum
    • Emission of discrete lines: Lyman (UV), Balmer (Visible), Paschen, Brackett, Pfund (IR)

• 4. Bohr's Atomic Model

  • Postulates
    • Electrons move in fixed stationary orbits
    • Quantized Angular Momentum: $mvr = \frac{nh}{2\pi}$
    • Energy absorbed/emitted during transitions: $\Delta E = h\nu$
  • Radii & Energy
    • Radius: $r_n = 0.529 \times \frac{n^2}{Z}\text{ \AA}$
    • Energy: $E_n = -13.6 \times \frac{Z^2}{n^2}\text{ eV/atom}$
  • Limitations
    • Fails for multi-electron atoms
    • Fails to explain Zeeman Effect (magnetic field) and Stark Effect (electric field)

• 5. Dual Behavior & Uncertainty Principle

  • de Broglie Relationship
    • Dual nature of matter (wave-particle duality)
    • Wavelength equation: $\lambda = \frac{h}{p} = \frac{h}{mv}$
  • Heisenberg's Uncertainty Principle
    • Impossible to simultaneously determine exact position and momentum
    • Equation: $\Delta x \cdot \Delta p \ge \frac{h}{4\pi}$

• 6. Quantum Mechanical Model

  • Schrödinger Wave Equation
    • Describes wave-like motion of electrons: $\hat{H}\Psi = E\Psi$
    • $\Psi^2$ represents Probability Density of finding an electron
  • Quantum Numbers
    • Principal ($n$): Defines shell size & energy ($n = 1, 2, 3...$)
    • Azimuthal ($l$): Defines subshell shape ($l = 0 \text{ to } n-1$)
    • Magnetic ($m_l$): Defines orbital orientation ($-l \text{ to } +l$)
    • Spin ($m_s$): Defines electron spin direction ($+\frac{1}{2}, -\frac{1}{2}$)
  • Shapes of Atomic Orbitals
    • s-orbital: Spherical ($l=0$)
    • p-orbital: Dumbbell ($l=1$)
    • d-orbital: Double dumbbell ($l=2$)

• 7. Electronic Configuration Rules

  • Aufbau Principle
    • Orbitals filled in increasing order of energy based on $(n+l)$ rule
  • Pauli Exclusion Principle
    • No two electrons can have the same set of 4 quantum numbers
    • Max 2 electrons per orbital with opposite spins
  • Hund's Rule of Maximum Multiplicity
    • Electron pairing in degenerate orbitals occurs only after each orbital is singly occupied
  • Exceptional Configurations
    • Chromium ($Z=24$): $[Ar] 3d^5 4s^1$ (extra stability of half-filled subshell)
    • Copper ($Z=29$): $[Ar] 3d^{10} 4s^1$ (extra stability of fully-filled subshell)