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Quiz 7:9am

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Physics 7C Fa 2008Quantum Mechanics

Light as a particle

Energy of light

Energy levels in atoms

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Outline

Quiz Introduction to quantum mechanics Extremely brief overview of major models in

the course (will be posted online if we don’t reach it)

Final Exam Logistics Course reviews

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Quiz 7:7:30am

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Quantum Mechanics Model

It can be non-intuitive We can make sense of it using two models:

Particle Wave

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Quantum Mechanics Model

Light and matter both behave like waves sometimes and like particles other times

Confining waves to an area leads to standing wave patterns For bound matter, this results in only certain

available energy levels Bound matter can gain or lose energy only

between the available levels To conserve energy, usually a photon is absorbed

or emitted with the correct energy (frequency)

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Experimental Evidence: Photons

Electrons in metal: Free to move Bound to metal

Think of as binding energy Goal: free from metal

Shine light to add energy. How can we get high energy

light?!

Laser

Metal

v

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Experimental Evidence: Photons

Binding Energy

KEelec

Light Energy

Laser

Metal

v

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Energy: Wave Model

What makes a high energy wave?a) Big wavelength

b) Big amplitude

c) High wave speed In light, what would this look like?

What do we observe if we increase the energy as the wave model suggests?

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Energy: Wave Model

High energy wave Large amplitude Large amplitude means more intensity More intensity means brighter

Result of increasing brightness: If electrons were not freed at low brightness, they

are also not freed at high brightness If electrons were freed at low brightness:

Maximum energy at high brightness is unchanged More electrons are freed

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Energy: Photon Model

Changing color of light: If red light does not free electrons, sometimes

other colors will If purple light does not free electrons, no visible

light will. Color (frequency) of light is related to the energy!

E = hf = energy of one photon h: Plank’s Constant = 6.62610-34Js

Increasing intensity corresponds to increasing number of photons.

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Which type of EM radiation is highest energy?

a) Radio b) Visible c) X-ray

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Quantum Mechanics:

Light As a wave As a particle: E=hf

Matter As a wave: =h/p As a particle: as you have always studied!

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Quantum Mechanics

Consequences of wave nature of matter 2-slit interference occurs for particles Confining a particle leads to standing waves

Different standing waves have different wavelengths Different wavelengths correspond to different

momenta Different momenta correspond to different energies

All these things are quantized: only certain values are allowed

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Atoms: electrons bound to nucleus

Molecules: can model bonds as springs, with atoms bound together

Examples of bound particles

N N

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Example of energy levels: Emission Spectra

Add energy to an element and wait. Each element emits light of certain colors. Why?

Hydrogen

Helium

Iron

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Emission Spectra

Each of the three marked transitions correspond to visible light. Which one is responsible for the red photon?

E1

E2

E3

E4

E5

a b c

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The three previous transitions corresponded to visible light. What part of the spectrum might the bold arrow correspond to?

a) Green light

b) Infrared (IR)

c) Ultraviolet

d) Microwave

e) Gamma ray

Emission Spectra

E1

E2

E3

E4E5

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The three previous transitions corresponded to visible light. What part of the spectrum might the bold arrow correspond to?

a) Green light

b) Infrared (IR)

c) Ultraviolet

d) Microwave

e) Gamma ray (way too high E)

Answers to previous 2 Qs

E1

E2

E3

E4E5

Lowest E makes red photon

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Vibrational States: An example of discrete energy The images show energy levels for two different

molecules. Which molecule can emit the longest wavelength photon, and why?

1) A: biggest ground state

2) A: highest spacing

3) C: goes up to E6

4) C: lowest ground state

5) C: smallest spacing

6) Equal: constant spacing

7) Either: both can emit photons

with arbitrarily long wavelengths.

E1 E1

E2

E2

E3

E3

E4

E4

E5

E6

A C

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Vibrational States: An example of discrete energy The images show energy levels for two different

molecules. Which molecule can emit the shortest wavelength photon, and why?

1) A: biggest ground state

2) A: highest spacing

3) C: goes up to E6

4) C: lowest ground state

5) C: smallest spacing

6) Equal: constant spacing

7) Either: both can emit photons

with arbitrarily short wavelengths.

E1 E1

E2

E2

E3

E3

E4

E4

E5

E6

A C

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Answers to previous 2 Qs Which molecule can emit the shortest

wavelength photon, and why? (7) The longest ? (4)

E1 E1

E2

E2

E3

E3

E4

E4

E5

E6

A C

4) C: smallest spacing (longest corresponds to lowest energy. We are looking for the closest together levels.)

7) Either: both can emit photons with arbitrarily short wavelengths. (shortest corresponds to highest energy. These levels continue to arbitrarily high values, so dropping from an incredibly high level to the ground level will produce a very short wavelength photon.

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Fluorescence

Observe. You will discuss more in DL

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Main Models

Wave Model Ray Model Field Model (Electricity & Magnetism) Quantum Mechanics

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Wave Model

Waves in 1, 2, and 3 dimensions Interference

1D: pathlength & phase 2D: double slit Frequency dependent: Beats Standing Waves

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Ray Model

Rays perpendicular to wavefronts Rays do not interact (i.e. no interference) Optics

Reflection Refraction Lenses (converging, diverging) Ray Tracing & Thin Lens Equations

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Field Model

Something (source) creates a field Field has magnitude at all points Field has direction at all points The net field is the vector sum of all source fields

Something else (test) interacts with the field resulting in a force Force has magnitude we can determine Force has a direction we can determine

Gravitation, Electricity, Magnetism

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Final Exam

Review sessions: probably Friday, Monday, Tuesday. Maybe some on the weekend. Check webpage for details!

Exam: When: Wednesday 3:30-5:30 Where: Giedt 1001 & Giedt 1003

Check webpage for details!

Questions?