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Chapters 29-30: Quantum Physics

Brent Royuk Phys-112

Concordia University

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Introduction The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote.... Our future discoveries must be looked for in the sixth place of decimals. - Albert. A. Michelson, speech at the dedication of Ryerson Physics Lab, U. of Chicago 1894

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Introduction “There is nothing new to be discovered in physics now. All that remains is more and more precise measurement” -Lord Kelvin, 1900

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Modern Physics

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Relativistic Review from 111 •  Time Dilation

•  Length Contraction

€

t = γto

€

L =Lo

γ

€

γ =1

1 − β 2

€

β =vc

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Relativistic Review from 111 •  The Equivalence Principle

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Relativistic Review from 111 •  Relation: E = K + mc2 •  Total Energy

E = m γ c2

•  Rest Energy Eo = m c2

•  Relativistic Kinetic Energy •  K = E - Eo = m c2(γ - 1)

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Introduction •  The central quantum idea. •  What does “quantum” mean? •  Uncertainty and randomness •  Waves vs. Particles

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The Correspondence Principle

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Blackbody Radiation •  What is a blackbody?

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The Ultraviolet Catastrophe •  Planck’s Hypothesis

–  Light is emitted by radiators that radiate at discrete frequencies

–  En = (n + ½) hf •  Planck’s Constant

–  h = 6.63 x 10-34 Js

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The Photoelectric Effect •  Einstein used Planck’s Hypothesis

to explain the photoelectric effect.

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Experimental Results 1.  Brighter light makes more current. 2.  The energy of the liberated electrons depends on the

frequency of the light but not its brightness. 1.  KEe = hf - BE

3.  There’s a cutoff frequency. If the light isn’t blue enough, no current flows. fc = BE/h

4.  Current flows immediately, without a delay. •  Result #1 agrees with classical theory. The others are a

problem.

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Photoelectric Effect •  Einstein: Light comes in little bits

(pieces, quanta) called photons. •  Energy of a photon:

–  E = hf •  Example: What is the energy of a

photon of microwave radiation, with a wavelength of 12.2 cm?

•  How many photons are given off in a second by a 0.5 mW He-Ne laser with a wavelength of 670 nm?

•  Photons also have momentum, p = h/λ

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Duality •  So is light a wave or a particle?

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Spectroscopy •  A nineteenth century mystery:

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Spectroscopy •  The Rydberg Formula:

•  nf = 2; ni = 3,4,5,6; R = 1. 0973732 x 107 m-1

€

1λ

= R 1nf

2−

1ni

2

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

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Rutherford’s Experiment •  Electrons discovered, 1887 •  J.J. Thomson: The Plum Pudding Model •  Rutherford, 1909

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Rutherford’s Results •  “It was almost as incredible as if

you fired a fifteen-inch shell at a piece of tissue paper and it came back and hit you.”

•  So this implies a planetary model? •  Problems

–  What causes bright-line spectra? –  The atomic death spiral.

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Bohr’s Model Assumptions of the model: 1.  The electron moves in a circular orbit

around the nucleus, held in place by charge attraction.

2.  Only certain orbits are naturally “stable,” preventing the death spiral.

3.  Electron “jumps” create radiation according to Ef - Ei = hf.

4.  The size of the orbits is determined by quantization of angular momentum, and L = mvr = nh/2π

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Bohr’s Derivation

€

E = K + U =12

mv2 − k e2

r

F =mv2

r= k e2

r 2⇒ K =

12

mv2 =ke2

2r

E =ke2

2r− k e2

r= −

ke2

2r

Introduce Bohr's Assumption: v =n!mr

F =mv2

r= k e2

r 2⇒

m n!mr

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

2

r= k e2

r 2

Solve for r to get : rn =n2!2

mke2

•  For n = 1, you get the Bohr Radius, the smallest possible radius in the model:

r1 =0.529 Å

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Bohr’s Energy Levels

€

E = −ke2

2r

But rn =n2!2

mke2

E = −ke2

2mke2

n2!2= −

mk2e4

2!2

1n2

For a level change, a photon is emitted with

f =Ef − Ei

h=

Ef − Ei

2π! and

1λ

=fc

=Ef − Ei

2π!c=

mk2e4

4π!3c1nf

2−

1ni

2

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

So what is mk2e4

4π!3c? Bohr, 1913: 1%!

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Energy-Level Transitions

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Energy-Level Transitions

•  So what is a quantum leap? •  Why is energy quantized?

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Energy Transitions •  Typically, excited atoms only stay

excited for 0.5-20 ns. –  So fluorescent lights are strobe

lights.

•  Metastable states can stay excited for a long time. –  Phosphorescent materials

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Matter Waves •  So light is a particle. Guess what… •  Louis deBroglie, 1924 doctoral thesis.

€

λ =hp

There is a wave “associated with” particles, such that

How big is the wave for a baseball? An electron?

What is the nature of this wave?

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Matter Waves •  Can matter waves be observed?

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Electron Interference •  What if you cover one slit? •  What if you detect which slit? •  Can you predict where electrons will hit?

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Heisenberg’s Uncertainty Principle •  How do you know where a wave is?

–  Wave packets

•  The Principle:

€

ΔpΔx ≥!2

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Heisenberg’s Uncertainty Principle Heisenberg Uncertainty principle shows that higher dimensions exist and

manifest through virtual particles India Daily Technology Team Aug. 19, 2007 The biggest problem in contemporary physics is the concept of unidirectional time

dimension. That is creating a shield that does not allow us to see beyond our three dimensions.

However, Heisenberg Uncertainty principle throws some light. Indirectly it shows that higher dimensions exist and manifest through virtual particles.

In many decays and annihilations, a particle decays into a very high-energy force-carrier particle, which almost immediately decays into low-energy particle. These high-energy, short-lived particles are virtual particles.

The conservation of energy seems to be violated by the apparent existence of these very energetic particles for a very short time. However, according to the above principle, if the time of a process is exceedingly short, then the uncertainty in energy can be very large. Thus, due to the Heisenberg Uncertainty principle, these high-energy force-carrier particles may exist if they are short lived. In a sense, they escape reality's notice.

The bottom line is that energy is conserved. The energy of the initial decaying particle and the final decay products is equal. The virtual particles exist for such a short time that they can never be observed.

The fact that these particles conceptually exist when we agree to an infinitesimal time, confirms the theory that higher dimensions exist.

The virtual particles show up and disappear into the higher dimensions. Otherwise the conservation of energy principles are violated.

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The Wave Function •  The Schrodinger Equation

€

−! 2

2m∇2Ψ x, t( ) + U x( )Ψ x, t( ) = i!

∂Ψ x, t( )∂t

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Quantum Collapses •  What travels through the slits in the electron

interference experiment? –  What hits the screen?

•  The Copenhagen Interpretation of Quantum Mechanics –  Where is the electron just before it hits?

•  The Repeated Measures Argument

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The Wave Function •  What is an orbital?

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Schrodinger’s Cat

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Tunneling

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Nonlocality