physics - particles and waves

8/18/2019 Physics - Particles and Waves

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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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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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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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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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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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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 −+=


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


( )-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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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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physics - particles and waves

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