Two Chapter 9

Taylor’s Experiment

• The Compton effect and the photoelectric effect reveal that light has a particle nature (behaves as a particle).
• For reflection, refraction, diffraction, interference etc., light acts like a wave, and its behaviour is best described by electromagnetic radiation theory.
• Quantum theory reconciles these two apparently contradictory behaviours.
• Geoffrey Taylor set up an experiment to find out whether interference results from the interactions between many photons, or if the behaviour of a single photon could be predicted by their wave properties.

• Light is passed through a series of dark filters to reduce the intensity of the light.
  • light then passes through a single slit and is diffracted by a needle.
  • The image on the screen is recorded on a photographic plate.
• In bright light, a diffraction pattern is noticed.
• As more and more filters are added, less light falls on the needle, and longer times are required to produce a picture (fewer photons are present)
• eventually enough filters were used so it took 3 months to take a picture.
• Calculations showed that for such dim light, no more than 1 photon was present in the apparatus at a time.
• Therefore, since the pattern still appeared, its presence could not be a result of the interaction between particles.
• This leaves us with the idea that the wave behaviour, predicts the particle behaviour.
  • Where more photons go through and land on the film, the probability of anyone photon landing there is higher (These will be brighter regions).
  • Where fewer photons land, the probability of any one photon landing there is lower (Darker regions).
  • Antinodal lines are brighter spots therefore more photons must go there (Vise Versa for nodal lines).
  • Therefore the interference pattern, gives us the probability of photons ending up at a certain place. Where there is constructive interference, light intensity is higher (Amplitude is higher for waves.), the numbers of photons is greater, and the probability for any one photon ending up there is greater.
• In General:
  • The amplitude of the wave gives us the probability of the particle ending up there. The higher the amplitude, the higher the probability.
  • Amplitude is determined by whether there is constructive or destructive interference.
• The above explanation works for any interference pattern.
• Wave Particle Duality - light is not just a wave and not just a particle. It is both. It has a dual nature.
• Principle of Complementarity - To understand a specific experiment, one must use either the wave or the photon theory but not both
  • To fully understand light, one must understand both wave and particle properties of light.
  • The two aspects complement each other.

AS A RULE

When light passes through space or a medium, its behaviour is best explained using wave properties. When light interacts with matter, its behaviour is more like a particle.

• Wave particle dualism is difficult to visualize.
• most laws in physics involve direct observation, but wave-particle duality is based on indirect observation.
• We cannot see directly how light energy is transmitted as a wave or particle.
• We can only observe the interactions of light and matter.
• From this we build abstract mathematical models which are difficult to understand.
• The older wave theory and particle theories of light have been replaced by wave-particle duality, because the wave-particle model does a better job of explaining observations.

The Wave Nature of Matter

• Since light energy transmitted like a wave can also behave like a particle, then maybe particles have this same nature.
• de Broglie In 1923 suggested that since light sometimes behaves like a particle with momentum P = h/l , then maybe any particle with momentum may have an associated wavelength.
• He suggested that since P = h/l and P = mv, then:

mv = h/l

or l = h/(mv)

• l equals the de Broglie wavelength.
• de Broglie waves have nothing to do with electromagnetic waves.
• MATTER WAVES - de Broglie waves (not electromagnetic waves)
• Matter waves have very small wavelengths. Because of these very small wavelengths, it is very difficult to detect the wave properties of particles.
• The wavelengths for electrons can be in the same range as for X-rays.
• In 1927, Davisson and Germer performed an experiment that proved de Broglie correct. Earlier W.H. and W.L. Bragg developed equations that described X-ray diffraction by crystals. Davisson and Germer used this same analysis to show that electrons could be diffracted in the same way as X-rays.
• They directed electrons at a crystal of nickel and observed a diffraction pattern that agreed with prediction.
• G.P. Thomson diffracted electrons through a metal which also showed de Broglie to be correct.
• Later experiments using protons, neutrons, helium nuclei. and other small particles, also showed diffraction patterns.
• For small particles, it is now evident that the principle of complementarity (wave - particle duality) also applies.
• This means, to understand matter requires us to be aware of both the particle and wave behavior of matter.
• Light shows wave characteristics like diffraction if opening sizes are less than or equal to the size of the wavelength. This is also true for matter waves.
• Ordinary objects have very small wavelengths, and therefore do not encounter openings of this size, therefore do not reveal their wave nature.
• Sub-atomic particles have matter waves whose wavelengths are of the same order of magnitude as the objects they interact with, and therefore show wave behavior.
• Matter waves predict the probability that a particle will follow a particular path through space.
• Matter wave interference patterns, therefore predict the interactions of particles just like light interference patterns predict the interaction between photons and matter.
• Wave - particle dualism for matter reinforces Einstein's contention that matter is a form of energy.
• Wave - particle dualism also answers the question left unanswered by Bohr about his model of the atom. What makes certain orbits in the Bohr model of the atom allowed, but not other orbits?
• Bohr felt that angular momentum in the atom must be quantized.
• The work of de Broglie showed that Bohr's hunch was correct. An allowed orbit would be an orbit where a whole number of electron waves fit into the circumference of the orbit.

• If a whole number did not fit, then the wave would interfere destructively with itself, and cancel itself (The electron would disappear.).
• The first allowed orbit is when:

2pr₁ = l = h/(mv₁)

• The second allowed orbit is when:

2pr₂ = (2h)/(mv₂)

• In general, the nth allowed orbit is when:

2pr_n = nl = (nh)/(mv_n)

• Rearranging gives:

mv_nr_n = (nh)/(2p)

• The left side of this equation is equal to angular momentum. The right side tells us that this angular momentum can take on only whole number values of a certain minimum value.
• n is the quantum number for the allowed orbit, and is the number of wavelengths in the circumference of the orbit.

Electron Microscopes

• The resolving ability of microscopes is dependent upon the wavelengths of the light used (magnification 1500X or we can see down to 2.0 X 10^-7m).
• An electron beam with a de Broglie wave of 1.0 nm can resolve to 0.5 nm. This means the magnification would be about 300 000X.
• Technological development involving focusing beams of electrons, led to the building of the electron microscope in the 1930's.
• Albert Prebus and James Hillier (Canadian), built the first North America electron microscope with 20 000 magnification.
• Transmission electron microscopes are similar to light microscopes, only the glass lenses are replaced by magnetic lenses. MAGNETIC LENSES are circular electromagnetic coils which create magnetic fields that exert forces on the electrons.

• Electrons are emitted by a hot filament, and then accelerated by an anode with an electric potential of 50 000 to 100 000 V. A condenser coil focuses electrons into parallel beams. After the electrons pass through a very thin specimen, the objective coil focuses the electrons to create an image. A projector coil projects this image onto a photographic plate.
• With electron microscopes, exposure times are short in order to prevent specimen destruction. The electrons must move in a vacuum to prevent scattering of the beam.
• SCANNING ELECTRON MICROSCOPE - A microscope similar to the electron microscope, which can produce a three dimensional image.
• In a scanning electron microscope, a beam of electrons is moved across the specimen. Secondary electrons are emitted from the surface and are collected. The secondary electrons are used to control a picture element on a television like display. The number of secondary electrons emitted determines the intensity or brightness of the picture.
• With the scanning electron microscope, the specimen is coated with a thin layer of gold so that it will not accumulate a negative charge from the electron beam. A negative charge would repel the beam and distort the image.
• Electron microscopes have produced fuzzy images of large atoms such as uranium atoms.

January 22, 2014