Download April 3 PHYS 1030 Final Exam - University of Manitoba Physics

WileyPLUS Assignment 3
Chapters 22, 24 - 27
Due Friday, March 27 at noon
Q24.21: Intensity = Power/Area
Q25.10: Concave mirror - not covered in course, do not attempt
Assignment 4 to follow, due last day of term
Monday, March 23, 2009
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Week of March 23-27
Experiment 5: Spectroscopy
Week of March 30 - April 3
Tutorial and Test 4: ch. 27, 28
PHYS 1030 Final Exam
Wednesday, April 15
9:00 - 12:00
Frank Kennedy Gold Gym
30 multiple choice questions
Formula sheet provided
Monday, March 23, 2009
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Chapter 29: Particles and Waves
Wave-particle duality – waves behave as particles and particles as waves
Waves as Particles
• Blackbody radiation from a heated object, Planck’s constant
• Photons and the photoelectric effect (and Planck’s constant)
Particles as Waves
• The de Broglie wavelength of a moving mass (and Planck’s constant)
• Heisenberg Uncertainty Principle (and Planck’s constant)
• Omit 29.4 – Compton effect
Monday, March 23, 2009
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Waves and Particles
Toward the end of the 19th century, it was thought that just about
everything was known about physics and that only a few more decimal
places of precision needed to be added to physical constants.
But then, a number of puzzling phenomena were discovered...
• Electrons can be diffracted –!they behave as waves.
• Calculations indicated that a heated object should radiate an infinite
amount of electromagnetic radiation (blackbody radiation and the
ultraviolet catastrophe).
• Light is concentrated in packets of energy that behave as particles
(photoelectric effect).
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Particles as waves
If electrons behaved as particles, they
would form an image of the slits on the
screen.
Under the right conditions, electrons
form an interference pattern on the
screen, as if they were waves, passing
through both slits.
–!when do electrons behave as particles,
and when do they behave as waves?
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Wave-particle duality
In a Young’s type experiment with electrons
instead of light passing through the slits,
individual electrons can be seen to have hit the
screen – they appear on the screen as particles.
As numbers build up, an interference pattern
becomes clear – each electron must have
travelled as a wave through both slits!
And then: if particles behave as waves, can
waves also act as particles?
...de Broglie and his wavelength...
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Blackbody Radiation
violet
red
Heated objects emit electromagnetic
radiation – “blackbody radiation”. The
higher the temperature, the shorter
the average wavelength.
Calculations of the spectrum of
blackbody radiation were wildly
inaccurate – intensity became
infinite at zero wavelength –
the “ultraviolet catastrophe”.
Planck (1900): radiation is emitted or absorbed by atomic oscillators
in the surface of the heated body. Oscillators vibrating at frequency f
can only have energy, E = nhf, n = 1, 2, 3..., and h is Planck’s constant
(6.626"10-34 J.s, adjusted to fit the spectrum of blackbody radiation).
The radiation is emitted or absorbed as packets of energy, E = hf,
whenever an atomic oscillator changes energy state.
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Blackbody Radiation
Revolutionary ideas introduced by Planck to solve the problem of the
ultraviolet catastrophe (and that Planck didn’t believe at the time):
• Quantum Hypothesis: The energy of an
atomic oscillator cannot take on any value,
but only certain “quantized” values, nhf.
• Light is emitted and absorbed in packets.
The minimum energy of a packet is hf
corresponding to an atomic oscillator
changing energy by an amount hf.
E
em radiation
of energy hf
4hf
3hf
hf
2hf
hf
Permitted energies of an
oscillator of frequency f
Classical physics was incomplete. An object cannot have just any
energy, but only certain energies. Light is not emitted as a
continuous wave, but as packets of radiation of energy hf.
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Blackbody Radiation
The significance of blackbody
radiation was realized by Josiah
Wedgwood, of pottery fame,
grandfather of Charles Darwin:
– everything inside the oven in which
the pottery was heated glowed with the
same colour and intensity, so that
individual shapes could not be made out.
Realized there was a universal spectrum of light emitted by heated objects.
Invented the pyrometer for measuring temperature of heated objects from
the colour of light radiated. Found use in steel and other industries, just in
time for the industrial revolution... Left a fortune of £500,000.
Elected Fellow of the Royal Society, 1783, largely for invention of
pyrometer.
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The Photoelectric Effect – Photons
Shine light onto a metal surface. If
the wavelength of the light is short
enough, electrons (“photoelectrons”)
are liberated from the metal surface.
They are accelerated to the positively
charged collector. The current is
measured with an ammeter.
vacuum
+
–
This was not unexpected, but the
details were.
By reversing the battery, photoelectrons are slowed down rather than
accelerated. Increase the potential
until even the most energetic
photoelectrons are turned back...
Monday, March 23, 2009
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Maximum kinetic energy of the photoelectrons
The current is reduced to zero when
photoelectrons of the highest
energy, KEmax, are stopped and
turned back to the metal plate by
the applied electric field:
Collector
Metal plate
–V0
–
KEmax
+
KEmax = eV0
(they do not have enough energy to
get up the potential energy hill, eV0)
battery
reversed
It is found that KEmax is linearly related to the frequency of the light...
Monday, March 23, 2009
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Maximum kinetic energy of the photoelectrons
Slope = Planck’s constant
There is a threshold
frequency for the
photoelectric effect
The slope of the line has the
same numerical value as Planck’s
constant, h = 6.626"10-34 J.s.,
that was found by fitting the
spectrum of blackbody radiation.
Surprising, as there was no
apparent relation between the
photoelectric effect and
blackbody radiation.
The equation of the straight line
(Einstein’s photoelectric equation)
KEmax = h f −W0
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Surprising features (~1900) of photoelectric
effect when light is considered as a wave
• The maximum kinetic energy of the photoelectrons does not depend
on the intensity of the light.
– More intensity means more energy falling on the metal, so more
kinetic energy for the photoelectrons...? No!
• Why is the photoelectron current and not KEmax proportional to the
intensity of the light?
• Why does the energy of the photoelectrons rise with the frequency
of the light? And why is there a threshold frequency, fo?
• Why is there no time delay in generating photoelectrons when the
light intensity is very weak? If the energy of the light is spread over
the wavefront, there should not be enough energy hitting a single
atom for the photoelectric effect to occur promptly.
Monday, March 23, 2009
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Einstein’s Photoelectric Equation – Interpretation
KEmax = h f −W0
The energy of the light is concentrated in packets – “photons” – each of
which has energy: E = hf.
A minimum amount of energy is needed to knock an electron out of the
surface of the metal. That energy is the “work function”, Wo.
The maximum kinetic energy of the electron is the energy of the
photon, minus the energy to remove the electron from the metal
surface.
If the photon has too low a frequency, KEmax < 0 and no photoelectrons
are produced. The minimum frequency to release photoelectrons is:
f0 =
Monday, March 23, 2009
W0
h
and then, KEmax = 0
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Photoelectric Effect
Photon: E = hf
Electron: KEmax = hf – W0
e
e
Surface of metal,
work function Wo
Energy of a photon, E = hf = hc/λ
Work function, Wo = minimum energy to remove electron from surface
KEmax = h f −W0
Monday, March 23, 2009
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Photoelectric Effect
• The photoelectron current is proportional to the intensity of the
light because the intensity is proportional to the number of
photons per second.
• The maximum kinetic energy of the photoelectrons depends on the
energy of each photon, E = hf, and not on the intensity of the
light.
• Photoelectrons are generated immediately, because the energy of
the light is concentrated in photons and it takes just one photon
to liberate a photoelectron.
Monday, March 23, 2009
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Blackbody Radiation (Planck)
• Energy is “quantized” – can take on only certain values
• Light is emitted and absorbed as bundles of energy – photons
• Planck’s constant determines the energy of the photons, E = hf
Photoelectric Effect (Einstein)
Photon: E = hf
Electron: KEmax = hf – W0
e
e
Surface of metal
• The energy of the light beam is concentrated in photons of energy hf
• A single photon can eject an electron from the surface, but only if the
photon has sufficient energy, hf > work function, W0
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Prob. 29.C6: In the photoelectric effect, suppose that the intensity
of the light is increased, while the frequency is kept constant. The
frequency is greater than the threshold frequency f0.
State whether each of the following will increase, decrease, or
remain constant, and explain why.
a) The current of photoelectrons.
b) The number of electrons emitted
per second from the metal surface.
c) The maximum kinetic energy an
electron can have.
Monday, March 23, 2009
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Photons
• Photons are “particles” of light.
• Photons of frequency f have energy E = hf = hc/!.
• Photons travel at the speed of light, v = c, and so:
mc2 = E
!
1 − v2/c2 = 0
!
2
mc
From E = "
1 − v2/c2
#
That is, photons have zero rest energy and mass.
• As E2 = p2c2 + m2c4 and m = 0, then E = pc for photons.
photons should carry momentum,
! p = E/c = hf/c = h/!
verified by Compton effect (not covered)
Monday, March 23, 2009
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Momentum
A solar sail would use the
momentum of photons of
sunlight to accelerate a space
craft away from the sun.
How would you get back???
Newton’s 2nd law: force =
rate of change of momentum.
If the light is reflected
back, each photon changes
momentum by:
!p
Δp = 2p = 2E/c
−!p
The force per unit area of sail is, F = "p/"t = 2P/c, where P is the light
power falling on the sail per square metre.
(F # 7 $N/m2 at earth).
Monday, March 23, 2009
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Prob. 29.4: The maximum wavelength that an electromagnetic wave
can have and still eject electrons from a particular metal surface is
485 nm.
What is the work function W0 of this metal?
Monday, March 23, 2009
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Prob. 29.7/42: Radiation of a certain wavelength causes electrons
with a maximum kinetic energy of 0.68 eV to be ejected from a
metal whose work function is 2.75 eV.
What will be the maximum kinetic energy when the same radiation is
used to eject electrons from a metal whose work function is 2.17 eV?
Monday, March 23, 2009
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Applications of photoelectric
effect
Photoelectrons
generated by
the light
• Photographic light meters
• CCD arrays to capture the image in digital
cameras –
+
+
+
Incident light releases electrons in each pixel,
the number of electrons is proportional to the
light intensity. Electrons are trapped in a pixel
by positive electrodes.
Reading out the number of trapped electrons in
each pixel gives the distribution of light intensity.
Red, blue, green filters for colours.
Monday, March 23, 2009
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Blackbody Radiation (Planck)
• Energy is “quantized” – can take on only certain values
• Light is emitted and absorbed as bundles of energy – photons
• Planck’s constant determines the energy of the photons, E = hf
Photoelectric Effect (Einstein)
Photon: E = hf
Electron: KEmax = hf – W0
e
e
Surface of metal
• The energy of the light beam is concentrated in photons of energy hf
• A single photon can eject an electron from the surface, but only if the
photon has sufficient energy, hf > work function, W0
Monday, March 23, 2009
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