1. Modern Physics

2. Modern Physics
Light as a Particle

3. Quantum Physics Physics on a very small scale is “quantized”.
Quantized phenomena are discontinuous and discrete.
Atoms can absorb and emit energy, but the energy intervals are very tiny, and not all energy levels are “allowed” for a given atom.

4. Quantum physics centers on light
Visible spectrum
Electromagnetic spectrum

5. Light is a ray
We know from geometric optics that light behaves as a ray. This just means it travels in a straight line.
When we study ray optics, we ignore the nature of light, and focus on how it behaves when it hits a boundary and reflects or refracts at that boundary.

6. But light is also a wave!
We will study the wave nature of light in more depth later in the year.
In quantum optics, we use one equation from wave optics.
c = lf
c: 3 x 108m/s (the speed of light in a vacuum)
l: wavelength (m) (distance from crest to crest)
f: frequency (Hz or s-1)

7. And light behaves as a particle!
Light has a “dual nature”.
In addition to behaving as a wave, it also behaves like a particle.
It has energy and momentum, just like particles do. This particle behavior shows up under certain circumstances.
A particle of light is called a “photon”.

8. Calculating photon energy
The energy of a photon is calculated from it the frequency of the light.
E = hf
E: energy (J or eV)
h: Planck’s constant
6.62510-34 J s
4.14 10-15 eV s
f: frequency of light (s-1, Hz)

9. Conceptual checkpoint
Which has more energy in its photons, a very bright, powerful red laser or a small key-ring red laser?
Neither! They both have the same energy per photon. The big one has more power.
Which has more energy in its photons, a red laser or a green laser?
The green one has shorter wavelength and higher frequency. It has more energy per photon.

10. The “electron-volt” (eV)
The electron-volt is the most useful unit on the atomic level.
If a moving electron is stopped by 1 V of electric potential, we say it has 1 electron-volt (or 1 eV) of kinetic energy.
1 eV = 1.60210-19 J

11. Sample Problem
What is the frequency and wavelength of a photon whose energy is 4.0 x 10-19J?

12. The bonding energy of H2 is 104. 2 kcal/mol
The bonding energy of H2 is kcal/mol. Determine the frequency and wavelength of a photon that could split one atom of H2 into two separate atoms. (1 kcal = 4186 J).
Sample Problem

13. Sample Problem
How many photons are emitted per second by a He-Ne laser that emits 3.0 mW of power at a wavelength of nm?

14. Atomic Energy Levels

15. Quantized atomic energy levels
This graph shows allowed quantized energy levels in a hypothetical atom.
More stable states are those in which the atom has lower energy.
The more negative the state, the more stable the atom.
0.0 eV
-1.0 eV
-3.0 eV
-5.5 eV
-11.5 eV
Ionization level
Ground state (lowest energy level)
First excited state
Second excited state
Third excited state
more stable
less stable

16. Quantized atomic energy levels
The highest allowed energy is 0.0 eV. Above this level, the atom loses its electron. This level is called the ionization or dissociation level.
The lowest allowed energy is called the ground state. This is where the atom is most stable.
States between the highest and lowest state are called excited states.
0.0 eV
-1.0 eV
-3.0 eV
-5.5 eV
-11.5 eV
Ionization level
Ground state (lowest energy level)
First excited state
Second excited state
Third excited state

17. Quantized atomic energy levels
Transitions of the electron within the atom must occur from one allowed energy level to another.
The atom CANNOT EXIST between energy levels.
0.0 eV
-1.0 eV
-3.0 eV
-5.5 eV
-11.5 eV
Ionization level
Ground state (lowest energy level)
First excited state
Second excited state
Third excited state

18. Absorption of photon by atom
When a photon of light is absorbed by an atom, it causes an increase in the energy of the atom.
The photon disappears.
The energy of the atom increases by exactly the amount of energy contained in the photon.
The photon can be absorbed ONLY if it can produce an “allowed” energy increase in the atom.

19. Absorption of photon by atom
When a photon is absorbed, it excites the atom to higher quantum energy state.
The increase in energy of the atom is given by DE = hf.
0 eV
-10 eV DE l
Ground state

20. Absorption Spectrum
When an atom absorbs photons, it removes the photons from the white light striking the atom, resulting in dark bands in the spectrum.
Therefore, a spectrum with dark bands in it is called an absorption spectrum.

21. Absorption Spectrum 0 eV
ionized
0 eV
-10 eV
Absorption spectra always involve atoms going up in energy level.

22. Emission of photon by atom
When a photon of light is emitted by an atom, it causes a decrease in the energy of the atom.
A photon of light is created.
The energy of the atom decreases by exactly the amount of energy contained in the photon that is emitted.
The photon can be emitted ONLY if it can produce an “allowed” energy decrease in an excited atom.

23. Emission of photon by atom
When a photon is emitted from an atom, the atom drops to lower quantum energy state.
The drop in energy can be computed by DE = hf.
0 eV
-10 eV
Excited state DE l

24. Emission Spectrum
When an atom emits photons, it glows! The photons cause bright lines of light in a spectrum.
Therefore, a spectrum with bright bands in it is called an emission spectrum.

25. Emission of photon by atom
ionized
0 eV
-10 eV
Emission spectra always involve atoms going down in energy level.

26. What is the frequency and wavelength of the light that will cause the atom shown to transition from the ground state to the first excited state?
Draw the transition.
Sample Problem
0.0 eV
-1.0 eV
-3.0 eV
-5.5 eV
-11.5 eV
Ionization level
Ground state (lowest energy level)
First excited state
Second excited state
Third excited state

27. What is the longest wavelength of light that when absorbed will cause the atom shown to ionize from the ground state?
Draw the transition.
Sample Problem
0.0 eV
-1.0 eV
-3.0 eV
-5.5 eV
-11.5 eV
Ionization level
Ground state (lowest energy level)
First excited state
Second excited state
Third excited state

28. The atom shown is in the second excited state
The atom shown is in the second excited state. What frequencies of light are seen in its emission spectrum?
Draw the transitions.
Sample Problem
0.0 eV
-1.0 eV
-3.0 eV
-5.5 eV
-11.5 eV
Ionization level
Ground state (lowest energy level)
First excited state
Second excited state
Third excited state

29. Photoelectric effect

30. Remember atoms can absorb photons
We’ve seen that if you shine light on atoms, they can absorb photons and increase in energy.
The transition shown is the absorption of an 8.0 eV photon by this atom.
You can use Planck’s equation to calculate the frequency and wavelength of this photon.
Ionization level
0.0 eV
-4.0 eV
Ground state (lowest energy level)
-12.0 eV

31. Photoelectric Effect e- Kinetic energy Photon energy Work function
Some “photoactive” metals can absorb photons that not only ionize the metal, but give the electron enough kinetic energy to escape from the atom and travel away from it.
The electrons that escape are often called “photoelectrons”. e-
Photon energy
Kinetic energy
Ionization level
0.0 eV
Work function
-8.0 eV
The binding energy or “work function” is the energy necessary to promote the electron to the ionization level.
The kinetic energy of the electron is the extra energy provided by the photon.
Ground state (lowest energy level)
-12.0 eV

32. Photoelectric Effect Photon Energy = Work Function + Kinetic Energy
hf = f + Kmax
Kmax = hf – f
Kmax: Kinetic energy of “photoelectrons”
hf: energy of the photon
f: binding energy or “work function” of the metal. e-
Photon energy
Kinetic energy
Ionization level
0.0 eV
Work Function
-8.0 eV
Ground state (lowest energy level)
-12.0 eV

33. Suppose the maximum wavelength a photon can have and still eject an electron from a metal is 340 nm. What is the work function of the metal surface?
Sample problem

34. Sample problem
Zinc and cadmium have photoelectric work functions given by WZn = 4.33 eV and WCd = 4.22 eV.
A) If illuminated with light of the same frequency, which one gives photoelectrons with the most kinetic energy?
B) Calculate the maximum kinetic energy of photoelectrons from each surface for 275 nm light.

35. Question
The photoelectric equation is Kmax = hf – f. Suppose you graph f on horizontal axis and Kmax on vertical. What information do you get from the slope and intercept?
Slope: Planck’s Constant
Intercept: -

36. The Photoelectric Effect experiment
The Photoelectric Effect experiment is one of the most famous experiments in modern physics.
The experiment is based on measuring the frequencies of light shining on a metal, and measuring the energy of the photoelectrons produced by seeing how much voltage is needed to stop them.
Albert Einstein won the Nobel Prize by explaining the results.

37. Photoelectric Effect experiment
At voltages less negative than Vs, the photoelectrons have enough kinetic energy to reach the collector.
If the potential is Vs, or more negative than Vs, the electrons don’t have enough energy to reach the collector, and the current stops.
light
light
Collector (-)
metal
(+) e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- e- V e- e- A e- e- e- e- e-

38. Experimental determination of the Kinetic Energy of a photoelectron
The kinetic energy of photoelectrons can be determined from the voltage (stopping potential) necessary to stop the electron.
If it takes 6.5 Volts to stop the electron, it has 6.5 eV of kinetic energy.

39. Strange results in the Photoelectric Effect experiment
Voltage necessary to stop electrons is independent of intensity (brightness) of light. It depends only on the light’s frequency (or color).
Photoelectrons are not released below a certain frequency, regardless of intensity of light.
The release of photoelectrons is instantaneous, even in very feeble light, provided the frequency is above the cutoff.

40. Graph of Photoelectric Equation
Kmax
slope = h
(Planck’s
Constant)
Kmax = h f - f
y = m x + b
Cut-off frequency f
f (binding energy)

41. Nuclear Decay

42. C A typical nucleus 12 6 Element name Atomic mass:
protons plus neutrons C 12 6
Element name
Atomic number:
protons

43. Isotopes
Isotopes have the same atomic number and different atomic mass.
Isotopes have similar or identical chemistry.
Isotopes have different nuclear behavior.
Examples:

44. Uranium isotopes U
238 92 U
235 92
Fission!
Low Radioactivity

45. Nucleons
Nucleons are particles that exist in the nucleus of an atom.
Proton
Charge: +e
Mass: 1 amu
Neutron
Charge: 0 p 1 n

46. Nuclear reactions
Nuclear Decay: a spontaneous process in which an unstable nucleus ejects a particle and changes to another nucleus.
Alpha decay
Beta decay
Beta Minus
Positron
Fission: a nucleus splits into two fragments of roughly equal size.
Fusion: Two nuclei combine to form another nucleus.

47. Decay Reactions Alpha decay Beta decay Positron decay Simulations
A nucleus ejects an alpha particle, which is just a helium nucleus.
Beta decay
A nucleus ejects a negative electron.
Positron decay
A nucleus ejects a positive electron.
Simulations

48. Alpha Decay
Alpha particle (helium nucleus) is released. Alpha decay only occurs with very heavy elements.

49. Beta (b-) Decay
A beta particle (negative electron) is released. Beta decay occurs when a nucleus has too many neutrons for the protons present. A neutron converts to a proton. An antineutrino is also released.

50. Positron (b+) Decay
Positron (positive electron) is released. Positron decay occurs when a nucleus has too many protons for the neutrons present. A proton converts to a neutron. A neutrino is also released.

51. Neutrino and Anti-Neutrino
Proposed to make beta and positron decay obey conservation of energy.
These particles possess energy and spin, but do not possess mass or charge.
They do not react easily with matter, and are extremely hard to detect.

52. Gamma Radiation, g Gamma radiation is electromagnetic in nature.
Gamma photons are released by atoms which have just undergone a nuclear reaction when the excited new nucleus drops to its ground state.
The high energy in a gamma photon is calculated by E = hf.

53. Calculation of energy released in nuclear reactionss
Add up the mass (in atomic mass units, u) of the reactants. You can find the mass in Appendix E of your textbook.
Add up the mass (in atomic mass units, u) of the products.
Find the difference between reactant and product mass. The missing mass has been converted to energy.
Convert mass to kg ( 1 u = 1.66 x kg)
Use E = mc2 to calculate energy released.

54. Complete the reaction, identify the type of decay, and calculate the energy.
Sample Problem

55. Complete the reaction, identify the type of decay, and calculate the energy.
Sample Problem

56. Nuclear Fusion and Fission

57. Fission
Fission occurs when an unstable heavy nucleus splits apart into two lighter nuclei, forming two new elements.
Fission can be induced by free neutrons.
Mass is destroyed and energy produced according to E = mc2.

58. Neutron-induced fission
Neutron-induced fission produces a “chain reaction.” What does that mean?
Nuclear power plants operate by harnessing the energy released in fission in by controlling the chain reaction.
Nuclear weapons depend upon the initiation of an uncontrolled fission reaction.

59. Critical Mass
The neutrons released from an atom that has undergone fission cannot immediately be absorbed by other nearby fissionable nuclei until they slow down to “thermal” levels.
How can this concept be used to explain why a chain reaction in nuclear fission will not occur unless a “critical mass” of the fissionable element is present at the same location?

60. Nuclear Reactors
Nuclear reactors produce electrical energy through fission.
Advantages are that a large amount of energy is produced without burning fossil fuels or creating greenhouse gases.
A disadvantage is the production of highly radioactive waste.
Another simulation appears at
University of Wisconsin Nuclear Reactor Tour

61. Nuclear Weapons
Nuclear weapons have been used only twice, although they have been tested thousands of times.
Weapons based on nuclear fission involve slamming together enough material to produce an uncontrolled fission chain reaction.
Nagasaki, Japan
Little Boy was dropped on Hiroshima and contained U-235 produced in Oak Ridge, TN.

62. Fission
Fission occurs only with very heavy elements, since fissionable nuclei are too large to be stable.
A charge/mass calculation is performed to balance the nuclear equation.
Mass is destroyed and energy produced according to E = mc2.

63. Complete the following reaction and determine the energy released.
Sample problem

64. Fusion
Fusion occurs when two light nuclei come together to form a new nucleus of a new element.
Fusion is the most energetic of all nuclear reactions.
Energy is produced by fusion in the sun.
Fusion of light elements can result in non-radioactive waste. He 2 H 1

65. Fusion
Fusion is the reaction that powers the sun, but it has not been reliably sustained on earth in a controlled reaction.
Advantages to developing controlled fusion would be the tremendous energy output and the lack of radioactive waste products.
Disadvantages are – we don’t know if we’ll be technical able to do it on earth!

66. You fuse a free proton with a free neutron to form a deuterium nucleus
You fuse a free proton with a free neutron to form a deuterium nucleus. How much energy is released?
Sample Problem

67. Mass defect
This strange term is used to indicate how much mass is destroyed when a nucleus is created from its component parts.
The mass defect is generally much, much less than the mass of a proton or neutron, but is significant nonetheless.
The loss of mass results in creation of energy, according to E = mc2.

68. Sample problem
What is the mass defect of 12C in atomic mass units? How does this relate to mass in kg and energy in eV and J?

69. Wave-Particle Duality
Wednesday, January 24, 2007
Wave-Particle Duality

70. Announcements Due in folder today -- Modern #4
You will do Modern #5 in lunch bunch today.
Next Wednesday
Free Response Problems in packet will be due at beginning of Lunch Bunch; we’ll correct them during Lunch Bunch.
Homework Quiz will be given.
We’ll review for the exam.
Clicker Quiz

71. Wave-Particle Duality
Waves act like particles sometimes and particles act like waves sometimes.
This is most easily observed for very energetic photons (gamma or x-Ray) or very tiny particles (elections or nucleons).

72. Particles and Photons both have Energy
We know from mechanics that a moving particle has kinetic energy
E = K = ½ mv2
However, a particle really has most of its energy locked up in its mass.
E = mc2
A photon’s energy is calculated using its frequency
E = hf

73. Particles and Photons both have Momentum
We know from mechanics that a particle that is moving has momentum
p = mv
For a photon
p = h/
Check out the units! They are those of momentum.

74. Particles and Photons both have a Wavelength
A photon of light has a wavelength, since light is also a wave
 = c/f
Hard as it may be to believe, particles also have wavelengths
 = h/p where p = mv
This is referred to as the deBroglie wavelength and is pronounced for very tiny particles.

75. We have experimental proof of Wave-Particle Duality
Compton scattering
Proof that photons have momentum.
High-energy photons collided with electrons exhibit conservation of momentum.
Davisson-Germer Experiement
Verified that electrons have wave properties by proving that they diffract.
Electrons were “shone” on a metal surface and acted like light by diffraction and interference.

76. Sample problem
What is the momentum of photons that have a wavelength of 620 nm?

77. Sample problem
What is the wavelength of a 2,200 kg elephant running at 1.2 m/s?

78. Wednesday, January 31, 2007
Review for Exam