Atomic Models

Summary

• Rutherford model (planetary model)
  • Gold foil experiment
    • Alpha particles from radioactive polonium where directed at a piece of gold leaf.
      • Alpha particles are helium nuclei, which are relatively heavy and double positively charged (⁴₂He²⁺).
    • Most of the alpha particles went nearly straight through with relatively little deflection.
    • A small fraction (1 in 100,000) were deflected nearly 180°.
  • Planetary model
    • The atom is mostly empty space.
    • The mass of the atom is concentrated in a small, central,fixed, positive nucleus.
    • The electrons are free to orbit the nucleus in a manner similar to the way planets orbit the Sun.
  • Problem
    • Electrons orbiting the nucleus would experience a centripetal acceleration.
    • Accelerating electrons would emit electromagnetic waves.
    • Since waves transfer energy, the electrons would lose energy and spiral into the nucleus.
    • A planetary atom would collapse.
• Bohr model
  • The orbits of the electrons in an atom…
    • exist as stationary states called orbitals
      • The electron is a standing wave that fits in the circumference of the orbit.
    • can only possess discrete values of angular momentum

      L = nℏ

      where…

      L =	orbital angular momentum of the electron
      n =	a positive integer greater than zero
      ℏ =	the reduced Planck constant (ℏ = h/2π)

    • are associated with an energy level
      • The n = 1 energy level is known as the ground state.
      • The n > 1 energy levels are known as excited states.
    • can only have specific radii
  • The discrete spectra of the elements are associated with energy level transitions.
    • A photon is emitted when an electron "falls" from a higher to lower energy level.
      • The energy of the emitted photon equals the absolute value of the difference in the energy levels.
    • A photon is absorbed when an electron "jumps" from a lower to higher energy level.
      • The electron can only jump up if the energy of the absorbed photon matches the energy of the transition.
    • The equation for both processes is…

      E_photon = |E_f −E_i|

  • Problems
    • The model does not work for atoms with more than one electron.
    • The model is two-dimensional (is flat), while atoms are three-dimensional (occupy volume)
• Schrödinger model
  • The orbital of an electron is a "cloud" that describe the probability of finding the electron in that location.
  • The electron is a standing wave in three dimensions that occupies the potential well of the nucleus.