physics - particles and waves
TRANSCRIPT
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Physics
Particles and Waves
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AP Learning Objectives
ATOMIC AND NUCLEAR PHYSICS
Atomic physics and quantum !!cts
Photons" th photo#ct$ic !!ct" Comptonscatt$in%" &'$ays
Students should know the properties of photons,so they can:
elate the energy of a photon in joules orelectron!volts to its wavelength or fre"uency#
elate the linear $o$entu$ of a photon to itsenergy or wavelength, and apply linear$o$entu$ conservation to si$ple processes
involving the e$ission, absorption, orreflection of photons#
%alculate the nu$ber of photons per seconde$itted by a $onochro$atic source ofspecific wavelength and power#
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AP Learning Objectives
ATOMIC AND NUCLEAR PHYSICS
Atomic physics and quantum !!cts Photons" th photo#ct$ic !!ct" Compton scatt$in%" &'
$ays Students should understand the photoelectric effect, so they
can: &escribe a typical photoelectric!effect e'peri$ent, and
e'plain what e'peri$ental observations provide evidence forthe photon nature of light# &escribe "ualitatively how the nu$ber of photoelectrons and
their $a'i$u$ kinetic energy depend on the wavelengthand intensity of the light striking the surface, and accountfor this dependence in ter$s of a photon $odel of light#
&eter$ine the $a'i$u$ kinetic energy of photoelectrons
ejected by photons of one energy or wavelength, whengiven the $a'i$u$ kinetic energy of photoelectrons for adifferent photon energy or wavelength#
Sketch or identify a graph of stopping potential versusfre"uency for a photoelectric!effect e'peri$ent, deter$inefro$ such a graph the threshold fre"uency and workfunction, and calculate an appro'i$ate value of h (e#
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AP Learning Objectives
ATOMIC AND NUCLEAR PHYSICS
Atomic physics and quantum !!cts
(a)'pa$tic# dua#ity
Students should understand the concept of de*roglie wavelength, so they can:
%alculate the wavelength of a particle as afunction of its $o$entu$#
&escribe the &avisson!+er$er e'peri$ent,and e'plain how it provides evidence for
the wave nature of electrons#
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able of %ontents
-# he Wave!Particle &uality
.# *lackbody adiation and Planck)s %onstant
/# Photons and the Photoelectric 0ffect
1# he 2o$entu$ of a Photon and the %o$pton 0ffect
3# he &e *roglie Wavelength and the Wave 4ature of
2atter
5# he 6eisenberg 7ncertainty Principle
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%hapter .8:Particles and Waves
Section -:
he Wave!Particle &uality
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Wave!Particle &uality
When a bea$ ofelectrons is used in a9oung)s double slite'peri$ent, a fringepattern occurs, indicatinginterference effects#
Waves can exhibit particle-like
characteristics
Particles can exhibit
wave-likecharacteristics.
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29.1.1. A beam of electrons is directed at two narrow slits and the
resulting pattern is observed on a screen that produces a flash
whenever an electron strikes it. What is the most surprising
observation that is made in this experimental apparatus?
a) he electrons do not all strike the screen at the same location.
b) he electrons produce flashes on the screen.
c) he pattern on the screen is an interference pattern.
d) he shadow of the two slits is observed on the screen.
e) he electrons produce the same pattern on the screen with or
without the slits in place.
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29.1.2. Which one of the following experiments demonstrates the wave
nature of electrons?
a) !mall flashes of light can be observed when electrons strike a specialscreen.
b) "lectrons directed through a double slit can produce an interference pattern.
c) he #ichelson$#orle% experiment confirmed the existence ofelectrons and their nature.
d) &n the photoelectric effect' electrons are observed to interfere withelectrons in metals.
e) "lectrons are observed to interact with photons (light particles).
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%hapter .8:Particles and Waves
Section .:*lackbody adiation
Planck)s %onstant
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All bodies, no matter how hot or cold,
continuously radiate electromagnetic
waves.
Electromagnetic energy is
quantized.
')'2'1'* == n f n E
s+1*,2,.,
-⋅×=
−
Planck’s
constant
frequency
*lackbody adiation
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29.2.1. Which one of the following processes occurs when a chargedatomic particle emits radiation?
a) he particles charge is reduced.
b) he particle turns into a light particle (photon).
c) he particle shows no ph%sical changes.
d) he particle changes from a higher energ% state to a lower energ%state.
e) he particle turns into a wave.
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29.2.2. /pon which one of the following parameters does theenerg% of a photon depend?
a) the mass of the photon
b) the amplitude of the electric field
c) the direction of the electric field
d) the relative phase of the electromagnetic wave relative to thesource that produced it
e) the fre0uenc% of the photon
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29.2.. wo 0uantum oscillator energ% levels are .2 3 1*−
19 + and1.1, 3 1*−14 +. 5etermine the fre0uenc% of the photon that is
emitted from this atom when a transition is made between these
two levels and determine n for the lower energ% level.
a) 2.1 3 1*1- 67
b) 2.-4 3 1*1- 67
c) .41 3 1*1- 67
d) .-22 3 1*1- 67
e) -.,9 3 1*1-
67
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%hapter .8:Particles and Waves
Section /:
Photons
the Photoelectric 0ffect
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Electromagnetic waves are composed of particlelike
entities called photons.
f E = λ = p
Photons
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0'peri$ental evidence
that light consists of
photons co$es fro$ a
pheno$enon called the
photoelectric effect.
he ;2agic *rick Wall
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When light shines on a $etal, a photon can give upits energy to an electron in that $etal# he$ini$u$ energy re"uired to re$ove the leaststrongly held electrons is called the work function.
electrone8ecttoneededwork
#inimum
electrone8ectedof energ%kinetic
#aximum
max
energ%hoton
:" oW hf +=
Photoelectric 0ffect
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electrone8ecttoneededwork
#inimumenerg%hoton
electrone8ectedof energ%kinetic
#aximum
max:" oW hf −=
+raph of =inetic 0nergy
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Example 2 The Photoelectric Effect for a Silver Surface
!he work function for a silver surface is ".#$ e%. &ind the minimumfrequency that light must have to e'ect electrons from the surface.
oo W hf +=
=+*
max:"
( ) ( ) 671*1-.1s+1*,.,2, e;+1*,*.1e;.-1
)-
19
×=⋅×
×== −
−
hW f oo
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Photoelectric 0ffect in &igital %a$eras
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29..1. &n the photoelectric effect experiment' what t%pe of energ%
process is occurring?
a) :inetic energ% is transformed into thermal energ%.
b) hermal energ% is transformed into electromagnetic energ%.
c)
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29..2. Wh% can we not see individual photons' but rather light appears to us
to be continuous?
a) A light beam contains a multitude of photons' each with a ver% small
amount of energ%.
b) he wave part of a photon superposes with the wave part of other photons
in the beam' making the beam appear to be continuous.
c) he wave part of the photon extends over a spatial region that is larger
than our e%es can detect.
d) he particle properties of photons do not interact with our e%es.
e) "ach photon carries information from the whole electromagnetic
spectrum= and our e%es cannot interpret this information.
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29... >onsider the photoelectric effect experiment from the point of view
of classical (or ewtonian) ph%sics. Which one of the following is not
one of the effects %ou would predict from a classical point of view?
a) here should be a measurable time dela% between the time that light first
strikes the metal surface and the time when electrons are first emitted
from the surface of the metal.
b) he kinetic energ% of the emitted electrons should var% linearl% with the
fre0uenc% of light shining on the metal.
c) @ight of an% fre0uenc% shining on the metal surface should cause
electrons to be emitted.
d) he kinetic energ% of the emitted electrons should increase
proportionatel% to the intensit% of the light.
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29..-. A special camera has been designed that opens and closes its
shutter for a ver% short time. A picture of an illuminated ob8ect istaken with this camera. When the film is developed' onl% tin%' bright
dots appear randoml% distributed on the picture. What does this
experiment tell us about the nature of light?
a) he dots are an interference pattern' which proves the wave nature oflight.
b) he small number of dots indicates that light waves were cut off b%the shutter as it closed.
c) he camera lens could not focus the light waves at a point on the filmwith such a short time.
d) he random distribution of dots shows the particle nature of light.
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29... When the photoelectric effect experiments were performed'
one effect was inconsistent with classical ph%sics. What was it?
a) he kinetic energ% of the e8ected electrons did not var% with light
intensit%.
b) he fact that electrons could form a current within a vacuum.
c) he kinetic energ% of the e8ected electrons increased as the
fre0uenc% of light increased.
d) he fact that light could free electrons from the surface of a metal.
e) he kinetic energ% of the e8ected electrons increased as the
wavelength of light decreased.
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29..,. What was a surprising result of the photoelectric effectexperiments?
a) he electrons behaved like matter waves.
b) elow a certain fre0uenc%' no electrons could be e8ected from themetal surface.
c) &ndividual photons behaved like waves.
d) Above a certain light fre0uenc%' the current became 7ero amperes.
e) @ight was proven to exhibit onl% a wave nature.
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29... &f light onl% had wave$like properties' %ou would not expectthere to be a cutoff fre0uenc%. Wh% is this true?
a) Bnl% particles can e8ect electrons from a surface.
b) he energ% of a wave does not depend on its fre0uenc%.
c) @ight waves of lower fre0uenc% would still be able to e8ect
electrons.
d) An electromagnetic wave would be able to e8ect an electron from a
surface. &t would 8ust take longer.
e) one of the above answers are correct.
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29..4. &n an ideall% dark room' a double$slit experiment is carried
out using a source that releases one photon at a time at a slowrate. he observation screen in the experiment is replaced with
photographic film which provides a recording of the photons
striking it over time. After some time has passed' the film is
removed and developed into a photograph. What is observedon the photograph?
a) two bright bands that correspond to the two slits
b) an interference pattern
c) a single bright band
d) &ts impossible to guess.
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29..9. &f a double$slit experiment is carried out using a source that releases
one photon at a time at a slow rate' an interference pattern ma% beobserved if the screen is replaced with photographic film. What
produces the interference?
a) "ach photon interferes with the photons that have previousl% passed
through a slit.
b) "ach photon interferes with the photons that pass through the slit after it.
c) "ach photon interferes with all of the photons that ever go through theslit.
d) "ach photon interferes with itself.
e) "ach photon interferes with the slit.
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%hapter .8:Particles and Waves
Section 1:
he 2o$entu$ of a Photon
the %o$pton 0ffect
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Energy is
conserved in the collision.
&erivation of %o$pton Wavelength
electronrecoilof
"nerg%:inetic
photonscattered
of "nerg%
electronof "nerg%
&nitial
'
photonincident
of "nerg%
' e poeo p E E E E +=+
oo p f E =' f E p =2
' cm E eoe = ( ) ( )
222cmc p E eee +=
( ) ( )2222 cmc p f cm f eeeo ++=+
(olve for )pec*+
( ) -22222 cm f cm f c p eeoe −−+=
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omentum isconserved in the collision.
electronrecoilof
#omentum
photonscatteredof
#omentum
photonincidentof
#omentum
' e po p p p p +=
po pe p p p −= '
( )
2
'
2
po p p p p e−=
( ) ( ) po p po p p p p p p e −⋅−= ''2
θ cos2'
22
'
2
po p po p p p p p pe
−+=
θ cos2 2
'
2222
'
22 c p pc pc pc p po p po pe −+=
&erivation of %o$pton Wavelength
λ f c =
θ cos2 2222222 f f f f c p ooe −+=
λ
= p
λ
λ f pc
= f =
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( )θ λ λ cos1−=−cm
h
e
o
&erivation of %o$pton Wavelength
( )-22222
cm f cm f c p eeoe −−+=
( ) BC AC ABC B AC B A 2222222 −−+++=−+
( ) ( ) ( ) -22222222 222 cmc fm f f cm f f cm f eeoeoeo
−−−+++
θ cos2 22222
f f f f oo −+=
θ cos2 22222 f f f f oo −+=
θ cos2222 2222 f f f f c fmcm f ooeeo −=−−
&ivide both sides by .hf of$ec
θ cos2222 2222 f f f f c fmcm f ooeeo −=−
( )θ cos1−=−cm f
c
f
c
eo
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Conceptual Example 4 Solar Sails and the Propulsion of Spaceships
-ne propulsion method that is currently being studied for interstellar
travel uses a large sail. !he intent is that sunlight striking the sailcreates a force that pushes the ship away from the sun, much as wind
propels a sailboat. oes such a design have any hope of working and,
if so, should the surface facing the sun be shiny like a mirror or black,
in order to produce the greatest force/
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29.-.2. An x$ra% photon with an initial wavelength λ strikes an
electron that is initiall% at rest. Which one of the followingstatements best describes the wavelength of the photon after the
collision?
a) o photon remains after the collision.
b) he scattered photons wavelength will still be λ' but its fre0uenc%
will decrease.
c) he scattered photons wavelength will be longer than λ.
d) he scattered photons wavelength will be λD2.
e) he scattered photons wavelength will be between λD2 and λ.
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29.-.. E$ra%s with a wavelength of *.1* nm are scattered froman argon atom. he scattered x$ra%s are detected at an angle
of 4° relative to the incident beam. What is the >ompton
shift for the scattered x$ra%s?
a) *.**22 nm
b) *.*11 nm
c) *.*22 nm
d) *.*-1 nm
e) *.12 nm
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Wave 4ature of 2atter>
http:((www#youtube#co$(watch>v@&fPeprBo+c
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!he wavelength of a particle is givenby the same relation that applies to a
photon0
p=λ
he de *roglie Wavelength
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Example 5 The de Broglie Wavelength of an Electron and a Baseball
etermine the de 1roglie wavelength of )a* an electron moving at a speed
of 2.34532 m6s and )b* a baseball )mass 7 3.58 kg* moving at a speed
of 5$ m6s.
( )( )( ) m1*2.1sm1**.,kg1*1.9 s+1*,).,1*
,1
-
−−
−
×=
××
×== phλ
( )( )( ) m1*).)sm1)kg1.* s+1*,).,-
-
−
−
×=×
== phλ
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29..1. "stimate the de roglie wavelength of a hone% bee
fl%ing at its maximum speed.
a) A hone% bee cannot have a wavelength.
b) 2 × 1*−14 m
c) × 1*−2 m
d) -×
1*−,
m
e) 1 × 1*−-* m
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29..2. What is the de roglie wavelength of a particle' such as anelectron' at rest?
a) he wavelength would be 7ero meters.
b) he wavelength would be infinitel% small and not measureable.
c) his has no meaning. he de roglie wavelength onl% applies to
moving particles.
d) 5avisson and Fermer measured this wavelength in their apparatus
and found it to be around 1*−1* m.
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%hapter .8:Particles and Waves
Section 5:
he 6eisenberg 7ncertainty
Principle
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Momentum and position
( )( )π -
≥∆∆ y p y
9ncertainty in y component
of the particle’s momentum
9ncertainty in particle’s
position along the y direction
he 6eisenberg 7ncertainty Principle
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Energy and time
( )( )π -
≥∆∆ t E
9ncertainty in the energy
of a particle when the particle
is in a certain state
time interval during
which the particle is
in that state
he 6eisenberg 7ncertainty Principle
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Conceptual Example 7 What if Planck’s Constant Were Large?
A bullet leaving the barrel of a gun is analogous to an electron passing
through the single slit. :ith this analogy in mind, what would huntingbe like if Planck’s constant has a relatively large value/
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29.,.1. Which one of the following statements provides the best description
of the 6eisenberg /ncertaint% rinciple?
a) &f a particle is confined to a region ∆ x' then its momentum is within some
range ∆ p.
b) &f the error in measuring the position is ∆ x' then we can determine theerror in measuring the momentum ∆ p.
c) &f one measures the position of a particle' then the value of the
momentum will change.
d) &t is not possible to be certain of an% measurement.
e) 5epending on the degree of certaint% in measuring the position of a
particle' the degree of certaint% in measuring the momentum is affected.
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29.,.2. he position along the x axis of an electron is known to be
between −*.1 nm and G *.1 nm. 6ow would the uncertaint% in themomentum of the electron change if the electron were allowed to be
between −*.,2 nm and G*.,2 nm?
a) he uncertaint% in the momentum would be twice its previous value.
b) he uncertaint% in the momentum would be half of its previous value.
c) he uncertaint% in the momentum would not be affected b% thischange.
d) he uncertaint% in the momentum would be four times its previousvalue.
e) he uncertaint% in the momentum would be one fourth its previousvalue.
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