lecture 36 chapter 31 light quanta matter waves ...physics.sfsu.edu/~lockhart/courses/phys101/p101...

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24-Nov-10

Chapter 31Light QuantaMatter Waves

Uncertainty Principle

Lecture 36


Birth of Quantum Theory• There has been a long historical debate about the

nature of light:– Some believed it to be particle-like.– Others believed it to be wave-like.

• Young’s double-slit interference experiment in 1801 proved that light had wave aspects.

• Emission of photons of light from atomic transitions suggested particle-like aspects

• Max Planck in 1900 hypothesized that radiant energy was emitted in discrete bundles, each of which he called a quantum. (Now called photon)


Quantization and Planck’s Constant• Quantum physics states that in the microworld of

the atom, the amount of energy in any system is quantized—not all values of energy are possible.– Example: The energy in a beam of laser light,

which is a whole-number multiple of a single lowest value of energy—one quantum

• The quanta of light, and of electromagnetic radiation in general, are photons.

• Energy of a photon of frequency f:E = hf where h is Planck’s constanth = 6.6 x 10-34 J/Hz or 6.6 x 10-34 J·sNote: Value of h on text p. 549 is wrong!


QuantizationQuantization• The idea that physical variables (energy, speed,

momentum) are granular rather than smoothly continuous. Values must change in minimum-sized steps.

Quantum• The “step size”, or smallest amount of change in

the value of a physical variable. – Example: The quantum of energy for a set of

red photons (frequency f) is the energy of one photon, E = h·f, where h is Planck’s constant.


The Photon Model

• A model for how matter radiates EM waves– Hypothesized by Max Planck, a German

theoretical physicist in early 1900s– Warm bodies emit radiant energy (light) in

individualized bundles (quanta) -- photons.– Energy in each photon is proportional to the

frequency of radiation.• E ~ f, or with Planck’s constant h, E = hf


Example

• What is the energy of a photon of frequency 3 x 1014 Hz?

(h = 6.6 x 10-34 J/Hz)


Example

• What is the energy of a photon of frequency 3 x 1014 Hz?

(h = 6.6 x 10-34 J/Hz)

E = hf = (6.6 x 10-34 J/Hz)(3 x 1014 Hz)= 2.0 x 10-19 J


The Photoelectric Effect• Light shining on a metal surface can liberate electrons.• The liberated electrons are attracted to the positive “plate”

and produce a measurable current. • If we instead put a large enough negative voltage on the

plate, the current can be stopped.• We can then calculate the energies of the ejected

electrons from the easily measured potential difference between the plates.


The Photoelectric Effect

The photoelectric effect (continued)



The photoelectric effect (continued)



• Einstein’s view on light interactions– Light (and all EM waves) are emitted and received as

a stream of particles; bundles of energy (photons).– Photons interact with matter one at a time.– High-energy photons dislodge electrons from certain

metals.


In the photoelectric effect, the brighter the illuminating lighton a photosensitive surface, the greater the

A. velocity of ejected electrons.B. number of ejected electrons per secondC. Both A and B.D. None of the above.

The Photoelectric EffectCHECK YOURSELF


In the photoelectric effect, the brighter the illuminating lighton a photosensitive surface, the greater the

A. velocity of ejected electrons.B. number of ejected electrons per second.C. Both A and B.D. None of the above.

The Photoelectric EffectCHECK YOUR ANSWER


In the photoelectric effect, the higher the frequency of the illuminating light on a photosensitive surface, the greater the


The Photoelectric EffectCHECK YOURSELF


In the photoelectric effect, the higher the frequency of the illuminating light on a photosensitive surface, the greater the


The Photoelectric EffectCHECK YOUR ANSWER


Wave–Particle Duality

Wave–particle duality• A photon behaves as a particle when emitted by

an atom or absorbed by photographic film or other detectors.

• But it behaves as a wave in traveling from a source to the place where it is detected.

• In this sense, light can be both a wave and a particle!


Wave–Particle DualityWave–particle duality (continued)

• This image is built up photon by photon.


Double-Slit ExperimentDouble-slit experiment

• Monochromatic light passing through two slits forms an interference pattern.


Double-Slit Experiment with Photons• Suppose we dim our light source so that only one

photon at a time reaches the barrier with thin slits. • If film behind the barrier is exposed to the light for

a very short time, the film gets exposed as shown below.– Each spot represents the place where the film has been

hit by a photon. – If the light is allowed to expose the film for a longer time,

a pattern of fringes begins to emerge


Double-Slit Experiment & Photons• If we cover one slit so that photons striking the

photographic film can pass only through a single slit, the tiny spots on the film accumulate to form a single-slit diffraction pattern.

• We find that photons hit the film at places they would not hit if both slits were open.


Double-Slit ExperimentHow do photons traveling through one slit “know”that the other slit is open and avoid certain regions, proceeding only to areas that will ultimately fill to form an interference pattern?• Each single photon has wave properties as well as particle

properties. • The photon displays different aspects at different times. • A photon behaves as a particle when it is being emitted by

an atom or absorbed by photographic film or other detectors, and behaves as a wave in traveling from a source to the place where it is detected.

• So, the photon strikes the film as a particle but travels to its position as a wave that can interfere with other waves.


Particles as waves: electron diffraction• Every particle of matter is associated with a

corresponding wave. According to de Broglie, a particle’s wavelength is related to its momentum.

where h is Planck’s constant. (h = 6.6 x 10-34 J·s)

Particles as Waves: Electron Diffraction

momentumWavelength = h

λ = h/p


When we speak of de Broglie waves, we’re speaking of the wave nature of

A. light.B. sound.C. massive particles.D. quantum uncertainties.

Particles as Waves: Electron DiffractionCHECK YOURSELF


When we speak of de Broglie waves, we’re speaking of the wave nature of

A. light.B. sound.C. massive particles.D. quantum uncertainties.

Particles as Waves: Electron DiffractionCHECK YOUR ANSWER


Example

• What is the de Broglie wavelength of a particle of mass 1 x 10-20 kg moving at a speed of 6.6 x 105 m/s?

• (h = 6.6 x 10-34 J·s)


Example• What is the de Broglie wavelength of a

particle of mass 1 x 10-20 kg moving at a speed of 6.6 x 105 m/s? (h = 6.6 x 10-34 J·s)

• λ = h/p = h/(mv)• = (6.6 x 10-34 J·s)/[(1 x 10-20 kg)(6.6 x 105 m/s)]• = 1 x 10-19 m



• Interference patterns of beams of light (left) and electrons (right) compared



Electron microscope uses the wave nature of electrons to create images similar to the image of the mosquito shown here.



Uncertainty principle• The act of observing something as tiny as an

electron disturbs the electron and, in so doing, produces a considerable uncertainty in either its position or its motion.


Uncertainty PrincipleUncertainty principle (continued)• German physicist Werner Heisenberg called

this the uncertainty principle.• When the uncertainties ∆p and ∆x in

measurements of momentum p and position xfor a particle are multiplied together, the product must be equal to or greater than Planck’s constant, h, divided by 2π, which is represented as (“ h-bar “).

∆p∆x ≥

h

h



Uncertainty principle (continued)

• The ∆ is “uncertainty in measurement of”: ∆p is uncertainty in measurement of p and ∆x the uncertainty in position. The product of uncertainties must be equal to or greater than (≥) the size of . h



Uncertainty principle (continued)

• Applies also to uncertainties of measurements of energy and time. The uncertainty in knowledge of energy, ∆E, and the duration taken to measure the energy, ∆t, are related by the expression: ∆E∆t ≥ . h


To which of these does Heisenberg’s uncertainty principle apply?

A. Measuring room temperature with a thermometerB. Momentum and distances of a high-speed bulletC. A public opinion surveyD. None of the above.

Uncertainty PrincipleCHECK YOURSELF


To which of these does Heisenberg’s uncertainty principle apply?

A. Measuring room temperature with a thermometerB. Momentum and distances of a high-speed bulletC. A public opinion surveyD. None of the above.

Explanation: Heisenberg’s uncertainty principle involves the unavoidable interaction between nature at the atomic level and the means by which we probe it.

Uncertainty PrincipleCHECK YOUR ANSWER


Complementarity

Complementarity• Wholeness often means accepting

alternate explanations for natural phenomena.

• Opposite ideas can complement one another (light can be both a wave and a particle).

• Bohr chose the yin-yang diagram to illustrate complementarity.


Key Points of Lecture 36Key Points of Lecture 36

Before Wednesday Dec. 1, read Hewitt Chap. 30.

Homework #24 due by 11:00 PM Monday Nov. 29

Homework #25 due by 11:00 PM Friday Dec. 3

• Birth of Quantum Theory• Quantization and Planck’s Constant• Photon Energy• Photoelectric Effect• Wave–Particle Duality• Double-Slit Experiment - Quantum View• Particles as Waves: de Broglie wavelength• Uncertainty Principle• Complementarity

lecture 36 chapter 31 light quanta matter waves ...physics.sfsu.edu/~lockhart/courses/phys101/p101...

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