1. Early Quantum Theory
AP Physics
Chapter 27

2. 27.1 Discovery and Properties of the Electron
Early Quantum Theory
27.1 Discovery and Properties of the Electron

3. 27.1 Discovery and Properties of the Electron
Glass tube filled with
a small amount of
gas
When a large voltage
was applied
A dark shape
seemed to
extend from
the cathode
27.1

4. 27.1 Discovery and Properties of the Electron
Name Cathode Rays
Deflected by electric or magnetic fields
Negative charge
JJ Thompson – discovered the electron
Believed that the electron was
a part of the atom
Robert Millikan – determined
the charge on an electron
Experiment Video
27.1

5. 27.2 Planck’s Quantum Hypothesis
Early Quantum Theory
27.2 Planck’s Quantum Hypothesis

6. 27.2 Planck’s Quantum Hypothesis
Blackbody Radiation – all objects emit radiation proportional to T4 (in Kelvin)
Normal Temp – low intensity
Above 300K – we can sense
the IR as heat
At about 1000K objects glow
Above 2000K glow yellow
-white
27.2

7. 27.2 Planck’s Quantum Hypothesis
As temperature increases
EMR emitted increases
increases toward higher frequencies
27.2

8. 27.2 Planck’s Quantum Hypothesis
Blackbody – absorbs all the radiation that falls on it
Blackbody radiation – the EMR that a blackbody emits when hot and lumnous
Max Plank (1900) – purposed
his Quantum Hypothesis
Energy of any molecular vibration
could only be a whole number
multiple of a minimum value
27.2

9. 27.2 Planck’s Quantum Hypothesis
h is called Planck’s constant
Since energy has to be a whole number multiple
n – is a quantum number
It is quantized – occurs in only discrete quantities
27.2

10. 27.3 Photon Theory of Light and the Photoelectric Effect
Early Quantum Theory
27.3 Photon Theory of Light and the Photoelectric Effect

11. Einstein (1905) – when an object emits light its energy must be
27.3 Photon Theory of Light
Einstein (1905) – when an object
emits light its energy must be
decreased by hf, so light is
emitted in quanta where
Where f is the frequency of
the quanta emitted
Light is transmitted as tiny
particles called photons
27.3

12. When light shines on metals – electrons are emitted from the surface
27.3 Photon Theory of Light
When light shines on metals – electrons are emitted from the surface
Called the photoelectric effect
Both photon theory and wave
theory are consistent with
this basic result
27.3

13. Wave theory predicts (for monochromatic light)
27.3 Photon Theory of Light
Wave theory predicts (for monochromatic light)
Increased light intensity should
a. Increase the number of electrons ejected
b. The maximum kinetic energy of the should be higher
2. Frequency of light should not affect kinetic energy, only the intensity
27.3

14. Photon theory predicts (for monochromatic light)
27.3 Photon Theory of Light
Photon theory predicts (for monochromatic light)
All photons of the same frequency would have the same energy
All the energy of a photon would be transferred to an electron
Since electrons are held in the metal by some force, a minimum energy must be reached before an electron can be emitted
27.3

15. Photon theory predicts (for monochromatic light)
27.3 Photon Theory of Light
Photon theory predicts (for monochromatic light)
This minimum energy is called the work function (W0)
Electrons that absorb less than W0 will not be ejected
Those that are ejected the energy will be
For the least tightly held electrons
27.3

16. Photon theory predicts (for monochromatic light)
27.3 Photon Theory of Light
Photon theory predicts (for monochromatic light)
Increase in intensity will result in
a. More electrons being ejected
b. The same maximum kinetic energy for all the electrons
2. If frequency is increased, the maximum kinetic energy increase linearly
27.3

17. Photon theory predicts (for monochromatic light)
27.3 Photon Theory of Light
Photon theory predicts (for monochromatic light)
Below a cutoff frequency no electrons will be ejected
Experiments have proven that emitted electrons follow the photon theory
27.3

18. 27.4 Energy, Mass, and Momentum of a Photon
Early Quantum Theory
27.4 Energy, Mass, and Momentum of a Photon

19. 27.4 Mass, Energy, and Momentum of a Photon
The momentum of a particle at rest is given by
(from relativity chapter)
Since a photon travels a c, either it has infinite momentum, or its rest mass is 0 (makes sense, the photon is never at rest)
The energy of a photon is
27.4

20. 27.4 Mass, Energy, and Momentum of a Photon
The momentum of a photon is developed from the relativistic formula
Since m0=0
Usually written
27.4

21. 27.6 Photon Interactions; Pair Production
Early Quantum Theory
27.6 Photon Interactions; Pair Production

22. 27.6 Photon Interaction, Pair Production
Four interactions that photons undergo atoms
Photoelectric effect
Move an electron to
an excited state
Photon can be scattered
resulting in lower frequency
(energy) photon – called
the Compton Effect
27.6

23. 27.6 Photon Interaction, Pair Production
Four interactions that photons undergo atoms
Pair production – a photon creates matter
The photon disappears and produces a electron-positron pair
Example of mass being
produced in accord with
The positron will quickly
collide with an electron
27.6

24. 27.6 Photon Interaction, Pair Production
Pair production must occur near a nucleus so that momentum can be conserved
Used in PET scanners (positron emission tomography)
27.6

25. 27.7 Wave-Particle Duality
Early Quantum Theory
27.7 Wave-Particle Duality

26. 27.7 Wave-Particle Duality
Light properties can sometimes only be explained using particle theory (photons)
Sometimes the properties can only be explained using wave theory.
This realization that light has both properties is called wave-particle duality
The principle of complementarity – to fully understand light, we must be aware of both its particle and its wave natures
27.7

27. Early Quantum Theory
27.8 Wave Nature of Light

28. Louis de Broglie (1923) – proposed all particles have wave properties
27.8 Wave Nature of Matter
Louis de Broglie (1923) – proposed
all particles have wave
properties
The wavelength of a particle
is related to is momentum
This is called the de Broglie wavelength
27.8

29. The wavelength of a 0.20kg ball traveling at 15 m/s would be
27.8 Wave Nature of Matter
The wavelength of a 0.20kg ball traveling at 15 m/s would be
This is ridiculously small
Interference and diffraction only occur if a slit is not much larger than the wavelength
So the wave properties of ordinary objects is not detectable
27.8

30. 27.8 Wave Nature of Matter
But atomic particles have small enough masses that their de Broglie wavelength is measureable
This is the
diffraction
pattern of an
electron
27.8

31. 27.10 Early Models of the Atom
Early Quantum Theory
27.10 Early Models of the Atom

32. 27.10 Early Models of the Atom
Plum Pudding Model (1890)
JJ Thomson – homogeneous sphere of positive charge embedded with negative electrons
27.10

33. 27.10 Early Models of the Atom
Planetary Model (1911) Ernest Rutherford
Tiny positively charged nucleus contains most of the mass
Electrons orbit around the nucleus like planets around the sun
27.10

34. 27.11 Atomic Spectra: key to the Structure of the Atom
Early Quantum Theory
27.11 Atomic Spectra: key to the Structure of the Atom

35. When looked at through a
27.11 Atomic Spectra
If a pure gas in a tube is
excited
It produces a discrete
spectrum
When looked at through a
spectrometer we can observe a emission spectrum unique to that element
If a continuous spectrum passes through a gas, dark lines, or an absorption spectrum, is visible
27.11

36. 27.11 Atomic Spectra
It is assumed that in low density gases, the spectrum is from individual atoms
Hydrogen is the simplest atom, and shows a regular pattern to its spectral lines
JJ Balmer – showed that four lines in the visible spectrum of hydrogen have wavelength that fit the formula
27.11

37. R is called the Rydberg Constant
27.11 Atomic Spectra
R is called the Rydberg Constant
n = the integer values starting with 3
Later, the Lyman series was found to fit
Paschen series
27.11

38. Early Quantum Theory
27.12 The Bohr Model

39. Niels Bohr – electrons cannot lose energy continuously, but in
27.12 Bohr Model
Niels Bohr – electrons cannot lose
energy continuously, but in
quantum jumps
Light is emitted when an electron
jumps from a higher state to
a lower state
He compared a quantized angular momentum to the Balmer series
27.12

40. Although the results worked
27.12 Bohr Model
Although the results worked
n is an integer called the principle quantum number
It was simply chosen because it
worked
The lowest E1 – ground state
Higher levels – excited state
27.12

41. Often shown in an Energy Level Diagram
27.12 Bohr Model
The minimum energy level required to remove an electron from the ground state is called the ionization energy
For hydrogen is it 13.6eV and precisely corresponds to the energy to go from E1 to E=0
Often shown in an Energy Level Diagram
Vertical arrows show transitions
Energy released or absorvedcan be calculated by the difference between energy at each level
27.12

42. 27.13 de Broglie’s Hypothesis Applied to Atoms
Early Quantum Theory
27.13 de Broglie’s Hypothesis Applied to Atoms

43. 27.13 de Broglie’s Hypothesis Applied to Atoms
Bohr could give no reason why electrons were quantized
Reason was purposed by de Broglie
A particle of mass moving with a nonrelativistic speed would have
a wavelength such that
If each electron orbit is treated as a standing wave we get
This is the quantum condition
purposed by Bohr
27.13