|Planck used the hypothesis that|
E = h to explain the spectrum of light emitted by hot bodies.
The collapsing atom paradox
- what's the electron doing in an atom?
- electrons within the atom can't be stationary:
- positively charged nucleus will attract the negatively charged electron
- electron will accelerate towards the nucleus
- if electrons within the atom move,
- moving charges emit electromagnetic radiation
- emission will cause electrons to lose energy and spiral into the nucleus
- the atom will collapse!
- why don't atoms collapse?
- classical physics has no answer!
- key: electrons have wave/particle duality
Electrons as Waves
- the de Broglie hypothesis (Nobel Prize, 1929)
- connect wave and particle nature of matter using a relationship that applies to photons:
where p is the momentum of the particle (p = mass times velocity).
Compute the de Broglie wavelength of a tennis ball (m = 0.1 kg) and an electron (m = 9.1 x 10-31 kg), if both are moving at 1000 m/s.
- experimental evidence of electron wave/particle duality
- electron diffraction
- C. J. Davisson and G. P. Thomson observed interference fringes when electron beams hit crystal surfaces and thin metal films (Nobel Prize, 1937)
||Electron diffraction pattern collected from
Semiconductor Surface Physics Group
- electrons passing one at a time through a double slit. Each spot shows an electron impact on the detector.
- LEED surface analysis
- electron microscopy
Bound electrons have quantized energies
- model I: bead on a wire
- kinetic energy of bead can have any value, because velocity can have any value
- bead can be stationary
- bead is equally likely to be found anywhere on the wire
- exact position and velocity of the bead can be known simultaneously
- model II: wave on a wire
- there must be a whole number of peaks and troughs on the wire:
n ( /2) = L, where:
- n is an integer (1, 2, 3, ... )
- is the wavelength
- L is the length of the wire
- standing waves have quantized wavelengths
- model III: electron on a wire
- unite wave and bead models using the de Broglie relation:
|particle kinetic energy:
|de Broglie wave/particle relation:
|standing wave allowed wavelengths:
- The fact that E depends on an integer n means that only certain energy states are allowed
- the integer n labels each state; n is a quantum number
- Notice that n can't be zero, so the lowest energy state is not zero: the electron is never at rest!
- peaks and troughs correspond to buildup of negative charge- electron is not equally likely to be found anywhere on the wire.
- electrons behave like waves
- bound waves have restricted wavelengths
- therefore, electrons bound in atoms and molecules have restricted energies
The uncertainty principle
- Quantum theory puts a limit on the precision of measurements
- Werner Heisenberg's uncertainty principle (Nobel Prize, 1932)
- The uncertainty principle says that the act of measurement changes what you're trying to measure
- You can bounce a photon off a brick wall, and the wall doesn't change much...
- ...but bouncing a photon off an electron to measure its position will change its momentum
- Why atoms don't collapse
- The uncertainty in position is also the smallest space a particle can possibly be restricted to
- The position of an electron can't possible be known to better than ± 4 × 10-13 m by the uncertainty principle
so an electron can't be confined within the nucleus
General Chemistry Online! The quantum theory
Copyright © 1997-2005 by Fred Senese
Comments & questions to firstname.lastname@example.org
Last Revised 09/20/05.URL: http://antoine.frostburg.edu/chem/senese/101/quantum/print-index.shtml