Chem 454

Spectra and Optics,

1. Continued
2. 2/7 and 2/9 notes overlap
3. 2-9-01

Superposition of Waves

If two waves are combined

• the sum is described as the sum of the two waves
• A₁ sin 2p(n₁t +f) + A₂ sin 2p(n₂t+f')
• if phase and frequency are the same
• = (A1+A2) sin 2p(n₁t +f)
• if phase differs by 180 degrees
• = (A1-A2) sin 2p(n₁t +f) ---> 0
• Intensity is proportional to square of the field
• (A₁+A₂)² x 1 (at peak) vs A₁2 + A₂2 separately
• constructive interference

Incandescent Objects

• Black body radiation
• spectrum fixed by the temperature
• little or no difference based on the material
  • hotter=more intense
  • hotter= more blue

Atomic Sources

• Transitions between electron orbitals
  • fixed energy levels
  • fixed transitions
  • fixed wavelengths
  • only a few characteristic wavelengths
  • unique to the species
• vary with energy available
  • none if cold
  • lowest orbitals if hot or gentle excitation
  • more levels if high energy
    • e.g. electrical discharge, electron bombard
  • kick hard-- get inner electrons too
    • X-rays

• questions: natual width of the spectra line
• subtle features: electron spin/ Zeeman effect

Molecular Sources

• similar to atomic
  • fixed energy levels
  • fixed energy transitions
• but now many levels
  • electronic+vib+rot energy
  • probably unresolved
  • see a band, not a line
• still unique to the species but probably similar and overlaps with related species
• in the IR
  • no electronic, see vib+rot

Quantitative Aspects

• Unless other factors enter
• effect increases as you increase concentration
  • intensity proportional to conc
  • absorbance (log %T) proportional to conc
• other factors often enter the discussion

Lifetimes and Relaxation

• Molecule in ground state stays there (forever)
  • unless it gets extra energy
• Molecule in excited state
  • loses energy as light (radiation)
  • loses energy to neighbors (nonradiative)
  • when?
    • lifetime ...
      • could be fast (<psec)
      • could be modest (nsec- microsec)
      • can be sec, hr, days

Uncertainty Principle

• Dt DE > h
• or Dt D n >1
• short lived species (Dt=10^-12 sec)
• have wide uncertainty in E and freq
  • Dn = 10¹² Hz
  • n = 10¹⁵-10¹⁶ Hz
  • 1/1000 uncertainty