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ISP209s8 Lecture 14: Electromagnetic Waves and Quantum Mechanics, Assignments of Physical Education and Motor Learning

Michigan State University (MSU)Physical Education and Motor Learning

A set of lecture notes from isp209s8, covering topics such as the electromagnetic spectrum, wave-particle duality of light, quantum mechanics, and heisenberg's uncertainty principle.

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Uploaded on 07/23/2009

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ISP209s8 Lecture 14 -1-
Today
• Announcements:
– HW#7 is due after Spring Break on Wednesday March 12th
– Exam #2 is on Thursday after Spring Break
– The fourth extra credit project will be a “super bonus”
points project. This extra credit can let your homework
score go over 100%
• Light
• Wave-particle duality of nature
• Quantum Mechanics
ISP209s8 Lecture 14 -2-
The Electromagnetic Spectrum
• Maxwell’s 4 equations describe the unity of
electric and magnetic forces.
• They predict an electromagnetic wave that
travels at the speed of c (3.00E+8 m/s)
ISP209s8 Lecture 14 -3-
Wavelength and Frequency
λ = 1.0 m
Wavelength Frequency = 1/period
Distance over which the wave
repeats Number of cycles (repeats) per
second.
period = 2.0 s
ISP209s8 Lecture 14 -4-
The Electromagnetic Spectrum
Prentice-Hall 2005
Speed = λf
λ– wavelength
f – Frequency, Hz
(1/period)(1/s)
For light
Speed c = 3.0E+8m/s
pf3
pf4
pf5

Partial preview of the text

Download ISP209s8 Lecture 14: Electromagnetic Waves and Quantum Mechanics and more Assignments Physical Education and Motor Learning in PDF only on Docsity!

ISP209s8 Lecture 14

-1-

Today

Announcements:

  • HW#7 is due after Spring Break on Wednesday March 12

th

  • Exam #2 is on Thursday after Spring Break– The fourth extra credit project will be a “super bonus”

points project. This extra credit can let your homeworkscore go over 100%

Light

Wave-particle duality of nature

Quantum Mechanics

ISP209s8 Lecture 14

The Electromagnetic Spectrum

  • Maxwell’s 4 equations describe the unity of

electric and magnetic forces.

  • They predict an electromagnetic wave that

travels at the speed of c (3.00E+8 m/s)

ISP209s8 Lecture 14

-3-

Wavelength and Frequency

λ = 1.

m

Wavelength

Frequency = 1/period

Distance over which the waverepeats

Number of cycles (repeats) persecond.

period = 2.0 s

ISP209s8 Lecture 14

The Electromagnetic Spectrum

Prentice-Hall 2005

Speed =

λ

f

λ

  • wavelength

f – Frequency, Hz(1/period)(1/s)For lightSpeed c = 3.0E+8m/s

ISP209s8 Lecture 14

-5-

What is Light?

  • Wave Picture – oscillating

electric and magnetic fields

  • Waves can interfere• Examples
    • 2-slit interference– diffraction

2-slit interference

diffraction

ISP209s8 Lecture 14

Light as a particle

  • Light also behaves like a particle• Light comes in small bundles of energy we

call photons

  • Energy (of a photon) = h fh = 6.625E-34 Js

= 4.136E-15 eVs

ISP209s8 Lecture 14

-7-

Around Visible Electromagnetic Spectrum

ISP209s8 Lecture 14

Explanation of Electric Forces and GravityCoulomb’s Law (Electric Force)Coulomb force is carried by photonsNewton’s Universal Law of Gravity:

2

2

2

2

1

kg

Nm

E

G

r

m

Gm

F

2

2

2

2

1

C

Nm

E

k

r

q

kq

F

Gravity is carried by the graviton.

ISP209s8 Lecture 14

-13-

An even bigger surprise!

  • Particles like electrons also behave like waves!• Example Demo: electron diffraction• de Broglie wavelength of a particle (h is Plank’s constant)

s

J

h

h p

×

−

34

λ

What is the wave length an electron with an energy of 30 keV?

eV

J

keV

eV

keV

kg

Js

E

h m

h p

e

19

31

34

−

−

−

×
×
×

λ

m

12

−

×

ISP209s8 Lecture 14

What is waving?

Probability – all particles are characterized by a “wavefunction”. The square of the wave functions give theprobability density of finding a particle per unitvolume. The wave function extends over all space.

The square of the wave function times a volume givethe probability of finding the particle in that volume.

This is the picture of Erwin Schrödinger: Matter isdefined by the evolution in time of a wave function.

function

wave

→

Ψ

Ψ

=

Ψ

E

H

ISP209s8 Lecture 14

-15-

Bosons and Fermions

  • Particles come in two types• Bosons have the property that they can

overlap. Examples are photons and certainatoms (helium)

  • Fermions can not exist in the same state.

Examples – electrons, protons.

  • The fermion nature of elections explains

atomic structure

ISP209s8 Lecture 14

Electron Wave functions in atoms

The nucleus sits at the center and these picture show possibleregions were the electrons might be.

Old picture

Examples ofwave functions

New Picture:

ISP209s8 Lecture 14

-17-

Heisenberg’s Uncertainty Principle

If a particle has a wavelength, its position andspeed are not perfectly defined.

Uncertainty Principle: It is not possible to knowexactly the position and momentum of a particle atthe same time.

There is no absolute knowledge. The Newtonianview of the world (if everything were known,everything could be predicted) in not attainable.

π

h

p

x

ISP209s8 Lecture 14

Uncertainty depends on mass

electron

momentum

position

proton

baseball, highlyexaggerated (by 10

25

ISP209s8 Lecture 14

-19-

Sample Problem

π

h

p

x

h

t

E

There are two versions If the position of a proton, mass 1.67E-27 kg, is known to 1E-9 m themomentum and velocity could have a range of

s

m

kg

m Js

x

h

p

−

− −

26

9 34

s

m

kg

s

m

kg

s

m

kg

m

p

v

v

27

26

26

−

−

−

ISP209s8 Lecture 14

Summary

  • Nature is governed by the rules of

probability. No one can predict the exactoutcome of a measurement.

All knowledge is imperfect.

There is no

absolute knowledge of the position andvelocity of objects.