1. Quantum Theory & the History of Light

2. The Beginning of Light In the beginning it was dark and cold.
No sun
No light
No earth
No solar system.
~ 4.5 billion years ago, a huge cloud of gas and dust was formed.
This cloud contracted and grew into a central molten mass of plasma that became our SUN.
Through the process of thermonuclear hydrogen fusion, the sun began to shine.

3. Is Light a Ray, Wave or Particle?
The question has been debated many times over the years dating back as far as Pythagoras.

4. History of Light
582 – 500 BC: Pythagoras theorized that light travels in particles where he assumed that every visible object emits a steady stream of particles, that bombard the eye.
427 – 347 BC: Plato suggested that vision was produced by rays of light that originate in the eye and then strike the object being viewed.
384 – 322 BC: Aristotle suggested that light travels in waves.
320 – 275 BC: Euclid said that light travels in rays which came from the eyes in straight lines.
~300 BC: First lenses made by Greeks and Romans consisting of glass spheres filled with water.

5. History of Light (cont.)
~1000 AD: al Hathan said that light enters the eye from an outside source rather than originating from within.
~1000 AD – early 1600’s: Many inventions occurred in the area of optics (glasses and telescopes) and an overall general understanding of the nature of light (Law of Reflection and Law of Refraction).

6. Wave Theory of Light
Christian Huygens (1629 – 1695): Light travels in wavelets
Huygen's Wavelets

7. Corpuscle Theory of Light: Sir Issac Newton (1642 –1727)
Newton believed that bodies emitted energy in particles or corpuscles that traveled in straight lines.
1666: Performed an experiment with a prism that showed that the sun’s light is white light consisting of all of the colors of the spectrum.

8. Wave Theory of Light: Thomas Young (1773 – 1829)-revisited
1801: Through use of the Double-Slit Experiment, the wave properties of light were first experimentally shown to exist.
Experiment demonstrated that light undergoes interference and diffraction in much the same way that water and sound waves do.
Used source of monochromatic light to eliminate the problems with phase differences associated with incoherent light.

9. Young Double-Slit Experiment
Huygen’s Wavelets

10. Wave Theory of Light: James Clerk Maxwell (1831 – 1879)
1860: James Maxwell hypothesized that electric fields changing in time would create magnetic fields and vice-versa.
These fields travel together in space as waves.
Electromagnetic Wave

11. Max Planck & Blackbody Radiation
All matter, whether cool or hot emits electromagnetic waves.
The light radiated from an incandescent body changes with temperature.
The higher the temperature, the greater the intensity and frequency of the light emitted.
Why does incandescent light come in all wavelengths then?
Incandescent light is produced by vibrating atoms, which are systems far more complex than a single electron. Thus they are able to emit many different energies because f can vary linearly, producing a largely continuous energy spectrum.

12. Blackbody Radiation
Planck’s theory and experimental evidence show that as wavelength decreases, the amount of energy being radiated approaches zero!
(per unit wavelength)
Intensity
Classical theory suggests that as the wavelength approaches zero, the amount of energy being radiated should be infinite!
Blackbody Radiation

13. Quantization of Energy
Energy exists in discrete quantities
Atoms oscillate at discrete frequencies that reflect discrete energy levels.
Energy is absorbed and emitted in the form of photons of radiation.
E = nhf
Where:
h = Planck’s Constant (6.626 x 10-34J•s)
f = vibrational frequency
n = 0, 1, 2, 3, …
Note: Energy is not permitted for values other than those which satisfy the equation (You cannot have ½ of a photon).
Each value of n can be thought of as a photon; where 1 photon would be 1hf and two photons would be 2hf; and so on….

14. The Photoelectric Effect
Einstein proposed that light (electromagnetic radiation) consists of energy packets (Photons or Quanta) where E = hf.
If a photon had a sufficiently high enough frequency (or high enough energy) it could cause an electron to be ejected by the atom it is incident upon.
Photon of light

15. The Photoelectric Effect (cont.)
The threshold frequency (fo) is the minimum frequency of a photon of light required to free an electron from an atom.
At the threshold frequency, the electron will have no kinetic energy.
Light intensity does not affect photoelectron emission if the threshold frequency has not been achieved.
In other words, if the frequency is below the threshold frequency, it does not matter how bright the light is; electrons will not be ejected.
The Photoelectric Effect

16. The Photoelectric Effect(cont.)
The maximum kinetic energy of an emitted electron is determined by the relationship of conservation of energy where:
KEe = hf – hfo
Note: this relationship implies that the photon has particle properties.
Also, only one photon can act on one electron at any given moment.
The work function is the minimum amount of energy required to remove an electron from an atom such that it does not have any kinetic energy.
Work Function

17. The Photoelectric Effect(cont.)
What is the relationship between light intensity and PE emission?
Intensity
# of Ph. Elect.
Intensity
Kinetic Energy
(a)
(b)
(a) If the threshold frequency is achieved, then increasing the intensity will emit more photons.
(b) Increasing the intensity has no affect on the kinetic energy of the emitted photons.

18. The Photoelectric Effect(cont.)
What is the relationship between the frequency of the photon and PE emission?
Frequency
# of Ph. Elect.
Frequency
Kinetic Energy
Slope = h
Threshold Frequency
(a)
(b)
(a) If the threshold frequency is achieved, then increasing it will NOT emit more photoelectrons.
(b) Increasing the frequency will impart more kinetic energy to the electron once fo is achieved.

19. The Photoelectric Effect(cont.)
Cathode E
Anode
Photoelectron
E = hf - hfo -
E = hf = hc/
Photon _ +
Note: for an electron to reach the anode, it must have a sufficient amount of kinetic energy.

20. The Photoelectric Effect(cont.)
Stopping Potential: The minimum electric potential required to prevent an electron from reaching the anode.
From electrostatics:
V = Ed
Where:
E = electric field intensity (V/m)
d = distance between two plates
W = KE
-qVo = ½mev2
Vo = stopping potential
q = charge of an electron
me = mass of an electron
v = speed of electron

21. Applications of the Photoelectric Effect
Photocells – Used to operate switches and relays, alarms, door openers and boilers.
CCD (Charged Coupled Devices) – Low light imagery.
Solar Cells
Research in quantum physics.

22. Quantum Energy Units The units for energy is Joules.
Joules is very large for atomic systems.
Use smaller unit instead – Electron Volt.
One electron volt is equal to the energy of an electron accelerated across a potential difference of one volt.
qe = 1.6 x C
1 eV = (1.60 x C)(1 V) = 1.60 x CV
1 eV = 1.60 x J
This is
Important!!

23. Wave-Particle Duality of Light
Einstein’s theory suggests that although a photon of light has no mass, it does possess kinetic energy.
Einstein further predicted that a photon of light should also have momentum as follows.
p* = hf/c = h/λ
The fact that a photon can have momentum again implies that it has particle properties.
*Momentum, p = mass x velocity

24. Wave-Particle Duality of Light
The Compton Effect (1922):
E = hf ’
p = hf ’/c
E = ½ mve2
p = mve -
Collision
Incident Photon = X-ray -
Momentum
p = hf/c
E = hf
This experiment validated Einstein’s Photoelectric effect.
Conservation of Energy & Momentum: The energy and momentum gained by the electron equals the energy and momentum lost by the photon.
hf/c – hf ‘/c = mve

25. Particles vs. Waves (Light)
Wave Theory:
Explained through polarization.
Explained through reflection.
Explained through diffraction & interference.
Explained through refraction.
Particle Theory:
Explained through photoelectric emission.
Explained through the Compton effect.

26. Wavelike Behavior of Particles
The photoelectric effect and Compton scattering showed that electromagnetic radiation has particle properties.
Could a particle behave like a wave?
The answer is yes!
p = mv = h/λ
λ = h/mv
Where:
λ = de Broglie wavelength

27. Wavelike Behavior of Particles
Proof of the wavelike behavior of particles was made by diffracting electrons off a thin crystal lattice.
The particles showed similar interference patterns to light when passed through a diffraction grating.

28. Particles vs. Waves Particles Waves
Mass
Frequency
Size
Wavelength
Kinetic Energy
Amplitude
Momentum
Physicists have demonstrated that light has both wavelike and particle characteristics that need to be considered when explaining its behavior.
Similarly, particles – such as electrons – exhibit wavelike behavior.

29. Key Ideas
Objects that are hot enough will emit light because of the charge particles inside their atoms.
The spectrum of light produced by an incandescent body is dependent on its temperature.
Planck suggested that the spectrum of an incandescent body can only be comprised of certain energy levels (E = nhf).
The photoelectric effect is the emissions of electrons from metals when exposed to EM radiation of a minimum frequency (fo).

30. Key Ideas
The minimum energy required to free an electron from the atom is the work function (E = hfo).
Light comes in discrete packets of energy called photons.
Photons of light have momentum (p = h/) - even though they are massless.
Energy and momentum are conserved in photon-electron collisions.
Particles have wavelike attributes similar to light.