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Overview of Atomic Theories and Models

Apr 23, 2025

Physics Notes for Class 12 - Chapter 12: Atoms

Dalton's Atomic Theory

  • Elements consist of small invisible particles called atoms.
  • Atoms of the same element are identical; atoms of different elements differ.

Thomson's Atomic Model

  • Atoms are uniformly positively charged spheres with embedded electrons.
  • The atom is neutral overall.

Limitations

  • Could not explain the spectral series of hydrogen and other atoms.
  • Failed to explain large angle scattering of particles.

Rutherford's Atomic Model

  • Positive charge and mass are concentrated in a nucleus (~10^-15 m).
  • Electrons revolve around the nucleus in orbits.
  • Atom is neutral due to equal positive and negative charges.
  • Centripetal force is provided by electrostatic attraction.

Key Concepts

  • Distance of Closest Approach: ( r_o = \frac{1}{4\pi\varepsilon_0} \frac{2Ze^2}{E_k} )
  • Impact Parameter: Perpendicular distance from the velocity vector of an alpha particle to the nucleus.
  • Rutherford's Scattering Formula: Explains scattering observed in experiments.

Limitations

  • Couldn't explain atomic stability; electrons should emit energy and spiral into the nucleus.
  • Failed to explain atomic line spectrum.

Bohr's Atomic Model

  • Electrons revolve in non-radiating orbits (stationary orbits).
  • Angular momentum ( mvr = \frac{nh}{2\pi} )
  • Energy emission occurs when electrons jump between orbits.
  • Radius of Orbit: ( r = \frac{n^2h^2}{4\pi^2mKZe^2} )
  • Velocity: ( v = \frac{2KZe^2}{nh} )
  • Kinetic Energy: ( E_k = 13.6 \frac{Z^2}{n^2} ) eV
  • Potential and Total Energy Equations
  • Hydrogen Spectrum Series: Lyman, Balmer, Paschen, Brackett, Pfund
    • Depend on electron transitions between orbits.

Wave Model

  • Based on wave mechanics.
  • Quantum Numbers:
    • Principal (n)
    • Orbital angular momentum (l)
    • Magnetic (m_e)
    • Magnetic spin angular momentum (m_s)

Hydrogen Spectrum

  • Lyman Series: Transitions to n=1, UV region.
  • Balmer Series: Transitions to n=2, visible region.
  • Paschen, Brackett, Pfund Series: Infrared region transitions.

These notes cover the essential concepts related to atomic models and spectra, providing a detailed study aid for understanding the development and limitations of atomic theory.