Modern Physics Light as a Particle Quantum Physics Physics

1
Modern Physics

• Light as a Particle

2
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.

3
Quantum physics centers on light
Visible spectrum
Electromagnetic spectrum
4
Light is a ray

• We know from geometric optics that light behaves
  as a ray.
• This 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.

5
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)

6
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.
• Particle behavior is pronounced on a very small
  level.
• A particle of light is called a photon.

7
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 Plancks constant
• 6.625?10-34 J s
• 4.14 ?10-15 eV s
• f frequency of light (s-1, Hz)

8
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.

9
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

10
Sample Problem (similar to 30.10)

• What is the frequency and wavelength of a photon
  whose energy is 4.0 x 10-19J?

11
Solution

• E hf
• 4.0 x 10-19 J (6.625 x 10-34 J s) f
• f 6.04 x 1014 /s (or s-1 or Hz)
• c lf
• 3.00 x 108 m/s l(6.04 x 1014/s)
• l 4.97 x 10-7m 497 nm

12
Sample Problem

• The bonding energy of H2 is 104.2 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).

13
Solution

• Convert energy from kcal/mole to joules/molecule
• E (104.2)(4186)/6.02x1023) J/molecule
• E 7.2455 x 10-19 J
• Now find frequency and wavelength as in previous
  problem
• E hf
• 7.2455 x 10-19 J (6.625 x 10-34 J s) f
• f 1.09 x 1015 /s (or s-1 or Hz)
• c lf
• 3.00 x 108 m/s l(1.09 x 1015 )
• l 2.74 x 10-7m 274 nm

14
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 632.8 nm?

15
Solution

• Find total energy in one second from power
• P W/t Etot/t
• Etot P t 3.0 x 10-3 J
• Now see how many photons, n, will produce this
  energy
• E hf (one photon)
• Etot n hf (for n photons)
• E n hc/l (since wavelength is given and not
  frequency)
• 3.0 x 10-3
• n (6.625 x 10-34 J s) (3.0 x 108 m/s) /
  632.8 x 10-9 m
• n 9.55 x 1015

16
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.

17
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.

18
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.

19
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.

20
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.

Ground state
21
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.

22
Absorption Spectrum

• Absorption spectra always involve atoms going up
  in energy level.

23
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.

24
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.

Excited state
25
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.

26
Emission of photon by atom

• Emission spectra always involve atoms going down
  in energy level.

27
Sample Problem

• 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.

28
Solution

• DE Ef - Ei
• -5.5 eV (-11.5 eV)
• 6.0 eV
• DE Ephoton hf
• f Ephoton /h
• 6.0 eV / 4.14x10-15 eV s
• 1.45 x 1015 Hz
• c fl
• l c/f
• 3.00 x 108 /1.45 x 1015
• 2.1 x 10-7 m 210 nm

29
Sample Problem

• What is the longest wavelength of light that when
  absorbed will cause the atom shown to ionize from
  the ground state?
• Draw the transition.

30
Solution

• DE Ef - Ei
• 0 eV (-11.5 eV)
• 11.5 eV
• DE Ephoton hf hc/l
• l hc/ Ephoton
• (4.14 x 10-15)(3.00 x 108) /11.5
• 1.08 x 10-7 m 108 nm

31
Sample Problem

• The atom shown is in the second excited state.
  What frequencies of light are seen in its
  emission spectrum?
• Draw the transitions.

32
Solution

• From second to ground
• Ephoton 8.5 eV
• f E/h
• 8.5 eV / 4.14x10-15 eV s
• 2.05 x 1015 Hz
• From second to first
• E 2.5 eV
• f E/h 6.04 x 1014 Hz
• From first to ground
• E 6.0 eV
• f E/h 1.45 x 1015 Hz

33
Remember atoms can absorb photons

• Weve 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 Plancks 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
34
Photoelectric Effect

• 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-
Ionization level
0.0 eV
-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
35
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-
Ionization level
0.0 eV
-8.0 eV
Ground state (lowest energy level)
-12.0 eV
36
Sample problem

• 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?

37
Solution

• The longest wavelength is the lowest energy, and
  will provide no extra kinetic energy for the
  electron.
• Kmax hf f
• f hf Kmax hc/l Kmax
• f 4.14E-153E8 / 340E-9 0
• f 3.7 eV

38
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.

39
Solution

• A) Since Cd has the smaller work function, its
  photoelectrons have more energy given Kmax hf
  f.
• B) Kmax hf f and f c/l
• Kmax hc/l - f
• for Cd
• Kmax 4.14E-153E8 / 275E-9 4.22 eV
• Kmax 0.30 eV for Zn
• Kmax 4.14E-153E8 / 275E-9 4.33 eV
• Kmax 0.19 eV

40
Review of Photoelectric Effect

• Kmax hf f
• Kmax Kinetic energy of photoelectrons
• hf energy of the photon
• f binding energy or work function of the
  metal.

Ionization level
0.0 eV
-8.0 eV
Ground state (lowest energy level)
-12.0 eV
41
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 Plancks Constant
• Intercept -?

42
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.

43
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 dont have enough energy to reach
the collector, and the current stops.
Collector (-)
metal ()
e-
e-
e-
e-
e-
e-
e-
e-
e-
e-
e-
e-
e-
e-
e-
e-
e-
e-
V
e-
e-
e-
A
e-
e-
e-
e-
e-
44
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.

45
Strange results in the Photoelectric Effect
experiment

• Voltage necessary to stop electrons is
  independent of intensity (brightness) of light.
  It depends only on the lights 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.

46
Voltage versus current for different intensities
of light.
Number of electrons (current) increases with
brightness, but energy of electrons doesnt!
I
V
Vs, the voltage needed to stop the electrons,
doesnt change with light intensity. That means
the kinetic energy of the electrons is
independent of how bright the light is.
Stopping Potential
47
Voltage versus current for different frequencies
of light.
Energy of electrons increases as the energy of
the light increases.
f3 gt f2 gt f1
I
V
Vs changes with light frequency. That means the
kinetic energy of the photoelectrons is dependent
on light color.
Stopping Potential
48
Graph of Photoelectric Equation
Kmax
Kmax h f - f y m x b
f
49
Photoelectric simulations

• Link for simulated photoelectric effect
  experiment
• http//lectureonline.cl.msu.edu/mmp/kap28/PhotoEf
  fect/photo.htm

50
Assignment (due Friday next week)

• Run the photoelectric experiment for all three
  metals. You must collect at least 5 data points
  for each metal.
• Graph the data such that Plancks constant can be
  determined from the slope and the work function
  of the metal can be determined from the
  y-intercept.
• Your report consists of three data tables and
  three graphs, one for each metal. Clearly
  indicate the results you got for each metal.
• Graphs and tables may be done by hand on graph
  paper, or you may use Excel or another
  spreadsheet program if you like.

51
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)

52
Particles and Photons both have Energy

• A moving particle has kinetic energy
• E K ½ mv2
• A particle has most of its energy locked up in
  its mass.
• E mc2
• A photons energy is calculated using its
  frequency
• E hf

53
Particles and Photons both have Momentum

• For a particle that is moving
• p mv
• For a photon
• p h/?
• Check out the units! They are those of momentum.s

54
Particles and Photons both have a Wavelength

• For a photon
• ? c/f
• For a particle
• ? h/p where p mv
• This is referred to as the deBroglie wavelength

55
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.

56
Sample problem

• What is the momentum of photons that have a
  wavelength of 620 nm?

57
Sample problem

• What is the wavelength of a 2,200 kg elephant
  running at 1.2 m/s?