Electron Structure

The Nature of Light

Studies on the nature of light, and understanding of vision, have existed for >3000 years
The Greeks and Alexandrians: 800 BC-200 AD
600-1000: expansion of the ancient knowledge of optics through mathematics.
1543: Nicholaus Copernicus’s De Revolutionibus Orbium Coelestium (On the Revolutions of the Heavenly Spheres) marks the beginning of the scientific revolution.
The Classical Background (17th to 20th century)
- Newton demonstrated that white light consists of the individual colors of the rainbow and explained his findings using a “corpuscular” theory
- Huygens explained “reflection” and “refraction” of light in terms of light waves traveling through the “ether”
- Young’s “double-slit-experiment” explained interference patterns in terms of waves
- Maxwell develops the theory of electromagnetic radiation and showed that light was visible part of a spectrum of electromagnetic waves, discrediting the particle view of light

The wave model of light does not explain certain phenomena including:
1. Blackbody Radiation: light is emitted from a hot object
2. The Photoelectric Effect: electrons ejected from metals when hit with light of sufficient energy
3. Emission Spectra: emission of light from electronically-excited gas atoms

Blackbody Radiation: light is emitted from a hot object
Wavelength of the emitted radiation depends on T°
Planck (1900) assumed energy can only be absorbed or released in discrete amounts called Quanta
E = hv
- E = the energy of one quantum
- h = 6.626 x 10-34 J-s (Planck’s constant)
Matter can absorb or emit energy only as whole- number multiples of hv… 2hv, 3hv, 4hv
- E = nhv
- n = 1,2,3,…

Photoelectric effect: electrons are ejected from metals when hit with light of sufficient energy
Threshold energy: the energy at which a metal ejects its electrons
- Each metal has a different energy at which it ejects electrons.
At lower energy, electrons are not emitted
Photons with low frequencies do not have enough energy to cause electrons to be ejected via the photoelectric effect.
For any frequency of light above the threshold frequency, the kinetic energy of ejected electron will increase linearly with the energy of the incoming photon.
Einstein used Planck’s theory to explain this (1905)
Assumed light is behaving like a stream of tiny energy packets or “photons”
Energy of one photon = E = hv
Radiant energy is quantized
Increasing the intensity of the light source does not increase the energy of the light; only changing the frequency does this.
The intensity (brightness) of light is related to the number of photons striking the surface per unit time, but not to the energy of each photon

Spectrum: results when light from a source is separated into its different wavelength components
Balmer Series (1885) : Line spectrum of hydrogen in the visible region
- violet (410nm), blue (434nm), blue-green (486nm), red (656nm)
- Derived a simple formula to relate wavelength to simple integers
Rydberg developed a more general formula to fit all the lines of hydrogen including the UV region (Lyman Series) and IR region (Paschen Series)

Bohr’s postulates
- Only orbits of certain radii are allowed for the electron in a hydrogen atom.
- An electron in an “allowed” orbit has an “allowed” energy and will not radiate energy.
- Energy is emitted or absorbed by the electron as it changes from one allowed state to another. Energy is emitted or absorbed as a photon where E = hv
Limitations of the Bohr model
- Only works for the hydrogen atom
- Radiation appears to have wavelike as well as particle-like character; model does not account for this
- Model avoids the issue of why the negatively-charged particle does not spiral into the positively-charged nucleus.
Bohr’s Ideas that are incorporated into current model of the atom:
- Electrons exist only in certain discrete energy levels, which are described by quantum numbers
- Energy is involved in the transition of an electron from one
  level to another.