CHAPTER 31 LIGHT QUANTA

1
CHAPTER 31LIGHT QUANTA

• Quantum Mechanics and Classical Mechanics
• Quantization and Plancks Constant
• Photoelectric Effect
• Double-Slit Experiment
• Wave-Particle Duality
• Particles as Waves Electron Diffraction
• Uncertainty Principle
• Complementarity

2
Quantum Mechanics and Classical Mechanics

• Up to the beginning of the 20th century there was
  a controversy over whether light is a particle or
  a wave, but virtually everyone thought that
  matter was made of particles
• The breakthrough of Quantum Mechanics was to
  realize that BOTH light and particles need to be
  considered as particles and waves to explain
  their behavior
• In 1900, Max Planck proposed that EM radiation
  must be quantized in order to explain the
  emission of blackbody radiation, i.e. light is a
  particle
• In 1905, Albert Einstein proposed an explanation
  of the photoelectric effect in which light was
  treated as a particle
• In 1924, Louis de Broglie proposed that electrons
  must act as waves in order to explain diffraction
  and other effects
• Quantum Mechanics has become a tool that
  complements Classical Mechanics- they are both
  true, but apply in different regimes of size and
  energy, and not necessarily at the same time

3
Quantization and Plancks Constant

• The basic idea is that on a very small scale,
  energy is quantized- not all values are possible
  for an electron in an atom, or other small
  objects in other small spaces
• When treated as a wave with frequency f c / l
  , the energy of the particle is given by E h
  f h c / l , where h 6.6x10-34 Js
• Notice the tiny value of h, even though f is very
  large, it takes a vast number of particles to add
  up to very much energy
• Since the values in Joules are so small, we
  frequently convert them to electron volt units
  where E(eV) h c / (e l)
• In these units, visible photons have energies of
  1.8 to 3.1 eV, and electrons in atoms typically
  have energies between 0 and 60 eV

4
Photoelectric Effect

• The Photoelectric Effect occurs when energetic
  light photons are incident on some surfaces.
  Electrons are ejected from the surface into the
  vacuum, and can be accelerated and collected on a
  nearby plate to give a measurable current.
• If the wavelength of the photons is too long (the
  frequency and energy too small), NO electrons are
  ejected.
• If the photon energy is above a critical value,
  the electrons are ejected with extra energy
• Ee Ep - W, where W energy needed to release
  the electron Work Function
• Emin W h fmin -gt f min W / h
• If the light beam is more intense, we get more
  electrons (but with the same energy)

5
(No Transcript)
6
Double-Slit Experiment

• In 1801, Thomas Young demonstrated the
  interference of light with a Double-Slit
  experiment (see Fig. 29.16,17 p. 570)
• If we build up the images by detecting individual
  particles, we can see that each one actually goes
  through a particular slit (see Fig. 31.6, next
  chart), and the interference pattern becomes more
  noticeable as more of them add their exposure to
  that of the preceding.
• Some of the photons arrive at positions that they
  could not reach is only one slit were open!
• SO, each photon behaves as a particle when it is
  being emitted by an atom or absorbed by
  photographic film or other detectors and behaves
  as a wave in traveling from a source to a place
  where it is detected!

7
(No Transcript)
8
Wave-Particle Duality

• SO, photons, electrons, and other sub-atomic
  particles behave as if they are BOTH particles
  and waves. Whatever they truly are, we NEED to
  use both models in order to describe their
  physical behavior

9
QUESTIONS/COMMENTS

• What is the significance of having two models for
  the behavior of one thing?
• Is there anything wrong with it, or is it just
  our human minds trying to simply reality?

10
Particles as Waves Electron Diffraction

• Since electrons have both energy and wave
  properties, we can figure out what the effective
  wavelength would be
• E h f h c / l
• Wavelength h c / E h / (meV) 6.6x10-34
  Js/ (9.1x10-31 kg V) l 3.6x10-4 m/V(m/s)
• At 1 eV of energy, the electron velocity will be
• V sq rt2eV/me 5.9x105 m/s
• so the wavelength will be
• l 3.6x10-4 m/ sq rt(2eV/me ) 6.1x10-10 m/sq
  rt E(ev)
• l 0.61 nm/sq rt E(ev) 1/2000 of the
  wavelength of a 1 eV photon
• That is why we dont see electron diffraction
  effects very often

11
(No Transcript)
12
Uncertainty Principle

• Since particles are not really dots, but waves
  they must occupy some space
• The uncertainty of where the particle is located
  is related to the uncertainty in how much
  momentum it has Dp Dx gt h/2/p ,
• i.e. the more certain we are of where it is, the
  less certain we are of its momentum or speed
• The uncertainty of when the particle is located
  somewhere is also related to the uncertainty of
  its Energy DE Dt gt h/2/p ,
• Since h is such a small number, the quantum
  mechanical uncertainties are only significant for
  very small momentum, energies, positions and
  times. If any one of the parameters is large,
  then the limitation to the knowledge of the other
  is more likely to be due to some other factor
  rather than QM
• Example if DE 1 ev 1.6x10-19 J, then Dt gt
  h/2/p / DE 6.6x10-16 s i.e. not much time
  to worry about
• Example if Dp mV m5.9x105 m/s, Dx gt h/2/p /
  Dp 200 nm, about 1/2 p of the wavelength of
  the light wave corresponding to that energy, and
  a very small dimension

13
Complementarity

• The wave and particle properties of particles and
  EM waves are complementary to each other. We
  need both of them to understand the behavior of
  these small entities, but not exactly at the same
  time.

14
QUESTIONS/COMMENTS

• Do you feel at ease about quantum phenomena, or
  does this realm make you feel queasy?
• For many people, the quantum realm is so
  unfamiliar, that it takes some time to feel at
  ease with it (like learning a foreign language,
  or driving on the opposite side of the road)...