From Last Time(s)

1
From Last Time(s)
Light shows both particle and wave-like properties
Atoms emit and absorb photons
Photon Ehf
2
Exam 3 is Thursday Dec. 3 (after Thanksgiving)

• Students w / scheduled academic conflict please
  stay after class Tues. Nov. 24 to arrange
  alternate time.

530-7 pm, Birge 145
Covers all material since exam 2.
Bring Calculator One (double-sided) 8 1/2 x 11
note sheet
Schedule Week14HW assigned Thur. Nov. 19, due
Fri. Dec. 4 (two weeks) Exam 3 practice problems
available at Mastering Physics Last material
for exam Lecture of Tues. Nov. 24 Exam review
Tuesday, Dec. 1, in class
3
Photon properties of light

• Photon of frequency f has energy hf
• Red light made of ONLY red photons
• The intensity of the beam can be increased by
  increasing the number of photons/second.
• (Photons/second)(Energy/photon) energy/second
  power

4
Emitting and absorbing light
Zero energy
n4
n4
n3
n3
n2
n2
Photon emittedhfE2-E1
Photon absorbed hfE2-E1
n1
n1
Absorbing a photon of correct energy makes
electron jump to higher quantum state.

• Photon is emitted when electron drops from one
  quantum state to another

5
Matter waves

• If light waves have particle-like properties,
  maybe matter has wave properties?
• de Broglie postulated that the wavelength of
  matter is related to momentum as
• This is called the de Broglie wavelength.

Nobel prize, 1929
6
Why h / p ? Works for photons

• Wave interpretation of light
• wavelength (Speed of Light) / Frequency
• ? c / f
• Particle interpretation of light (photons)
• Energy (Plancks constant) x Frequency
• E hf, so f E / h

But photon momentum p E / c
7

• We argue that applies to everything
• Photons and footballs both follow the same
  relation.
• Everything has both wave-like and particle-like
  properties

8
Wavelengths of massive objects

• deBroglie wavelength

• pmv

9
Matter Waves

• deBroglie postulated that matter has wavelike
  properties.
• deBroglie wavelength

Example Wavelength of electron with 10 eV of
energy Kinetic energy
10
Wavelength of a football

• Make the Right Call The NFL's Own
  interpretations and guidelines plus 100s of
  official rulings on game situations. National
  FootBall League, Chicago. 1999 "... short
  circumference, 21 to 21 1/4 inches weight, 14
  to 15 ounces. (0.43 - 0.40 kg)
• Sometimes I dont know how they catch that ball,
  because Brett wings that thing 60, 70
  mph, Flanagan said. (27 - 32 m/s)

Need m, v to find ?
Aaron
Wells
11
This is very small

• 1 nm 10-9 m
• Wavelength of red light 700 nm
• Spacing between atoms in solid 0.25 nm
• Wavelength of football 10-26 nm

• What makes football wavelength so small?

Large mass, large momentumshort wavelength
12
Suppose an electron is a wave

• Here is a wave
• where is the electron?
• Wave extends infinitely far in x and -x
  direction

l
13
Analogy with sound

• Sound wave also has the same characteristics
• But we can often locate sound waves
• E.g. echoes bounce from walls. Can make a sound
  pulse
• Example
• Hand clap duration 0.01 seconds
• Speed of sound 340 m/s
• Spatial extent of sound pulse 3.4 meters.
• 3.4 meter long hand clap travels past you at 340
  m/s

14
Beat frequency spatial localization

• What does a sound particle look like?
• Examplebeat frequency between two notes
• Two waves of almost same wavelength added.

15
Making a particle out of waves
440 Hz 439 Hz
440 Hz 439 Hz 438 Hz
440 Hz 439 Hz 438 Hz 437 Hz 436 Hz
16
Adding many sound waves

• Six sound waves with different wavelength added
  together?1? ?2 ?/1.05 ?3 ?/1.10 ?4 ?/1.15
  ?5 ?/1.20 ?6 ?/1.25

• Wave now resembles a particle, but what is the
  wavelength?
• Sound pulse is comprised of several wavelength
• The exact wavelength is indeterminate

17
Spatial extent of wave packet
?x

• ?x spatial spread of wave packet
• Spatial extent decreases as the spread in
  included wavelengths increases.

18
Same occurs for a matter wave

• Localized particlesum of waves with slightly
  different wavelengths.
• ? h /p, each wave has different momentum.
• There is some uncertainty in the momentum
• Still dont know exact location of the particle!
• Wave still is spread over ?x (uncertainty in
  position)
• Can reduce ?x, but at the cost of increasing the
  spread in wavelength (giving a spread in
  momentum).

19
Heisenberg Uncertainty Principle

• Using
• ?x position uncertainty
• ?p momentum uncertainty
• Heisenberg showed that the product
• ( ?x ) ? ( ?p ) is always greater than ( h /
  4? )
• Often write this as
• where is pronounced h-bar

Plancksconstant
20
Uncertainty principle question

• Suppose an electron is inside a box 1 nm in
  width. There is some uncertainty in the momentum
  of the electron. We then squeeze the box to make
  it 0.5 nm. What happens to the momentum
  uncertainty?
• A. Momentum becomes more uncertain
• B. Momentum becomes less uncertain
• C. Momentum uncertainty unchanged

21
The wavefunction

• Quantify this by giving a physical meaning to the
  wave that describing the particle.
• This wave is called the wavefunction.
• Cannot be experimentally measured!
• But the square of the wavefunction is a physical
  quantity.
• Its value at some point in space is the
  probability of finding the particle there!

22
Electron waves in an atom

• Electron is a wave.
• Its propagation direction is around
  circumference of orbit.
• Wavelength h / p
• Waves on a circle?

23
Waves on a circle

• My ToneNut.
• Produces particular pitch.
• Sound wave inside has wavelength ?v/f (red
  line).
• Integer number of wavelengths required around
  circumference
• Otherwise destructive interference
• wave travels around ring and interferes with
  itself

Blow in here
24
Electron Standing Waves

• Electron in circular orbit works same way
• Integer number of deBroglie wavelengths must fit
  on circumference of the orbit.
• Circumference (2?)x(orbit radius) 2?r
• So condition is
• This says

This is quantization angular momentum (Lmvr)
25
Electron standing-waves on an atom

• Electron wave extends around circumference of
  orbit.
• Only integer number of wavelengths around orbit
  allowed.

26
Hydrogen atom energies

• Wavelength gets longer in higher n states,
  (electron moving slower) so kinetic energy goes
  down.
• But energy of Coulomb interaction between
  electron (-) and nucleus () goes up faster with
  bigger n.
• End result is

27
Hydrogen atom question

• Here is Peter Flanarys sculpture Wave outside
  Chamberlin Hall. What quantum state of the
  hydrogen atom could this represent?
• A. n2
• B. n3
• C. n4

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Hydrogen atom music

• Here the electron is in the n3 orbit.
• Three wavelengths fit along the circumference of
  the orbit.
• The hydrogen atom is playing its third highest
  note.
• Highest note (shortest wavelength) is n1.

29
Hydrogen atom music

• Here the electron is in the n4 orbit.
• Four wavelengths fit along the circumference of
  the orbit.
• The hydrogen atom is playing its fourth highest
  note (lower pitch than n3 note).

30
Hydrogen atom music

• Here the electron is in the n5 orbit.
• Five wavelengths fit along the circumference of
  the orbit.
• The hydrogen atom is playing its next lowest
  note.
• The sequence goes on and on, with longer and
  longer wavelengths, lower and lower notes.

But Remember that these are higher and higher
energies!(Coulomb (electrostatic) potential
energy dominates).