Download appendix 3 - University of Sydney

Please cite as:
Fletcher, P.R., (1997) Master of Science Thesis - How Students Learn Quantum
Mechanics (School of Physics, University of Sydney)
APPENDIX 3
PRIMARY SURVEY INSTRUMENT
This Appendix contains a copy of the primary survey instrument which was
administered to 231 first year physics students at the University of Sydney in 1995.
Presented in this Appendix are:
•
the Physics 1/1A Quantum Mechanics Concept Quiz questions,
•
the Answer Booklet, and
•
the “Official” Answers.
When the quiz was distributed to the students it appeared in two different
formats. One of these is included here. The other format consisted of a simple
renumbering of the items. Questions 1 and 2 were renumbered 3 and 4 and vice
versa. This was done to promote an even distribution of responses.
A3-105
A3-106
PHYSICS 1/1A :: QUANTUM PHYSICS
LECTURE 10 :: CONCEPT QUIZ :: 1995
.
QUESTION 1
Monochromatic light (light of a single colour) may be considered either as a
continuous electromagnetic wave or as a stream of energy quanta (or photons). The
photoelectric effect is the emission of electrons from a metal surface when light is
shone onto the surface. The energy in the light is transferred to some of the electrons
in the metal surface and they are ejected. Two key observations are as follows:
1. For monochromatic light of sufficiently high frequency, the rate of electrons
ejected per second increases as the intensity of the light increases.
2. Electrons are ejected from the surface only when the frequency of the
monochromatic light is above a certain frequency; and for monochromatic light
below this frequency, no electrons are ejected no matter how great the intensity.
Picture in your mind the following model. Think of electrons in the metal surface as
being like birds sitting on a telegraph wire. The effect of light could be pictured in
two ways. If it is a classical electromagnetic wave then it would be like trying to
dislodge the birds by shaking the wire. But the effect of the stream of photons
(particles of light) would be like trying to knock the birds off the wire by throwing
stones at them.
Wave Model
Particle Model
Which of these models can account for the above observations?
PLEASE ANSWER THE QUESTIONS IN THE QUIZ ANSWER BOOKLET.
.
QUESTION 2
In 1927 Werner Heisenberg published his Uncertainty Principle, which included the
statement that all measurements have an associated uncertainty.
Consider a "measurement" involving catching a bus in a quantum mechanical world.
Your timetable says that the bus will arrive at 9:00 am. Heisenberg would say that
the time of arrival must have an associated uncertainty.
What does he mean by uncertainty?
PLEASE ANSWER THE QUESTIONS IN THE QUIZ ANSWER BOOKLET.
.
A3-107
.
QUESTION 3
In classical physics we say that something is a particle if it has well defined position,
velocity, mass, momentum and energy.
We also talk about another entity, a wave.
We know about water waves, surfing waves, radio waves, microwaves, sound waves
and light waves. In 1924 Louis de Broglie proposed that electrons and other
microscopic entities were also waves.
What do you mean when you say "something is a wave"?
PLEASE ANSWER THE QUESTIONS IN THE QUIZ ANSWER BOOKLET.
.
QUESTION 4
You are listening to a discussion about the structure of atoms. You listen carefully to
what Sue and Jim have to say and then they ask you for your opinion.
Sue:
The lecturer said that the spectral lines observed in excited atoms is strong
evidence that energy levels exist in atoms.
Jim:
In 1913, Niels Bohr proposed a model for the hydrogen atom that combined
the ideas of Max Planck's quantum theory, Albert Einstein's photoelectric
effect and Ernest Rutherford's atomic model.
Sue:
And... In 1924 Louis de Broglie proposed that electrons were also waves.
The lecturer said that it was then proposed that the missing piece of Bohr's
theory was that the electrons wavelength had to fit into the atom. Do you
know what she meant Jim?
Jim:
No. But I think it had something to do with the energy levels.
{ Sue and Jim turn to you and Sue asks }
Sue : I don't understand what she meant by energy levels and I don't understand
what she meant by the wavelength of an electron fitting into the atom. Do
you know?
You have been asked to join into the conversation.
Think carefully about the points Sue and Jim have been discussing, and
WRITE YOUR RESPONSES TO SUE'S QUESTIONS
IN THE QUIZ ANSWER BOOKLET.
.
A3-108
PHYSICS I :: QUANTUM PHYSICS
Physical / Technological - 1995
Concept Quiz
Answer Booklet
Student ID : _______________________________
PLEASE NOTE : This quiz is intended only for diagnostic purposes.
It will NOT be used for any kind of assessment.
We require your Student ID so that we may invite
sample groups to participate in further research
projects.
This Quiz Answer Booklet cover sheet will be
separated
and your Student ID encoded to ensure your privacy.
A3-109
QUESTION 1 - PHOTOELECTRIC EFFECT
Part A)
Consider the first key observation, that for monochromatic light of sufficiently high
frequency the number of electrons (birds) ejected per second increases as the
intensity of the light increases.
Please tick ONE of the following boxes
This key observation can be explained by
the wave model but not the particle model.
the particle model but not the wave model.
both the wave and particle model.
neither the wave nor the particle model.
In terms of the "bird on a wire" picture explain your answer in your own words
and/or diagrams.
____________________________________________________________________
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____________________________________________________________________
____________________________________________________________________
Part B)
Consider the second key observation, that electrons are only ejected from a metal
surface for frequencies of light above a certain frequency (eg. violet and ultraviolet)
and not for frequencies below (e.g. blue, yellow or red light).
Please tick ONE of the following boxes
This key observation can be explained by
the wave model but not the particle model.
the particle model but not the wave model.
both the wave and particle model.
neither the wave nor the particle model.
In terms of the "bird on a wire" picture explain your answer in your own words
and/or diagrams.
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
IF THERE IS INSUFFICIENT SPACE FOR YOUR ANSWER
PLEASE WRITE ON THE OTHER SIDE OF THIS PAGE
A3-110
QUESTION 1 - PHOTOELECTRIC EFFECT
ADDITIONAL SPACE
Part A)
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Part B)
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A3-111
QUESTION 2 - CATCHING THE QUANTUM
MECHANICAL BUS
Catching the quantum mechanical bus.
Please tick ONE of the following boxes
Consider the meaning of the word uncertainty in relation to a quantum mechanical
system. Which of the following statements describes most clearly what the word
"uncertainty" means in this context.
If you caught the same bus every day for one year, its arrival time would vary
even though on average it would arrive at 9:00 am.
not
You could never be sure exactly when the bus would arrive because it may
have left on time or may have been delayed in its journey.
Quantum mechanics says you can not predict results of an experiment, so
there can be no such thing as a time-table for a quantum mechanical bus.
it
Even if the bus arrived perfectly on time at 9:00 am you could never be sure
was on time because no watch is ABSOLUTELY accurate.
None of the above statements.
In your own words and/or diagrams support and explain your answer.
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____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
IF THERE IS INSUFFICIENT SPACE FOR YOUR ANSWER
PLEASE WRITE ON THE OTHER SIDE OF THIS PAGE
A3-112
QUESTION 2 - CATCHING THE QUANTUM MECHANICAL BUS
ADDITIONAL SPACE
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A3-113
QUESTION 3 - SOMETHING IS A WAVE
Please tick ONE of the following boxes, which states most clearly what you mean
when you say "something is a wave"
.
A wave is an entity that is not a particle.
A wave is an entity that does not show well defined position, velocity, mass,
momentum and energy.
Everything is a wave and what we call a particle is only a special localised
wave called a wave packet.
None of the above.
In your own words and/or diagrams support and explain your answer.
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
IF THERE IS INSUFFICIENT SPACE FOR YOUR ANSWER
PLEASE WRITE ON THE OTHER SIDE OF THIS PAGE
A3-114
QUESTION 3 - SOMETHING IS A WAVE
ADDITIONAL SPACE
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____________________________________________________________________
____________________________________________________________________
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A3-115
QUESTION 4 - STRUCTURE OF THE ATOM
Sue's and Jim's discussion about the structure of the atom.
Part A)
In your own words and/or diagrams explain what the lecturer meant by the
term "energy levels".
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
Part B)
In your own words and/or diagrams explain what the lecturer meant when she said
that the electron's wavelength had to "fit into the atom".
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
IF THERE IS INSUFFICIENT SPACE FOR YOUR ANSWER
PLEASE WRITE ON THE OTHER SIDE OF THIS PAGE
A3-116
QUESTION 4 - STRUCTURE OF THE ATOM
ADDITIONAL SPACE
Part A)
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
Part B)
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
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A3-117
OFFICIAL ANSWERS
PHYSICS 1 - QUANTUM PHYSICS - CONCEPT QUIZ - 1995
.
SOMETHING IS A WAVE
"None of the above" would be the most appropriate response.
A wave is a phenomenon by which a disturbance (energy) propagates through a
medium, without long-term change to the medium, and which exhibits properties
commonly associated with other things we call 'waves'.
•
•
•
•
•
it is usually non-localised
it can be described mathematically and would obey a 'wave equation'
when it is initiated by a periodic disturbance it will have wavelength, frequency
and amplitude
as it moves it exhibits reflection, refraction and absorption
MOST IMPORTANTLY (in the context of quantum physics) it obeys the
principle of superposition - it exhibits diffraction and interference
STRUCTURE OF THE ATOM
Part A - Energy Level
For any system made up of 'bits' there should be in principle lots of ways to put it
together and these constructions would be characterised by different energies. For
example, a planet in a solar system could exist at any distance from the sun, therefore
there are an infinite number of ways of constructing such a solar system. Whereas in
an atomic system we know that only some internal structures (energies) are allowed
in nature, these are called Energy Levels.
Part B - Electrons wavelength having to fit into the atom
If an electron is behaving like a wave inside an unchanging energy level then the
electron must be a standing wave. The characteristic of a standing wave, like for a
violin string or a column of air, is that the wavelength must 'fit into' the length of the
string or pipe. Therefore the circumference of the electron's orbit must be a whole
number of wavelengths.
CATCHING THE QUANTUM MECHANICAL BUS
Uncertainty in this context means "If you caught the same bus every day for one
year, its arrival time would vary even though on average it would arrive at 9:00
am".
The idea of uncertainty was proposed in response to the wave particle duality of
microscopic objects. Knowing where an object (the bus) will be at a particular time
is a particle-like measurement. But nature tells us that quantum mechanical objects
do not necessarily behave like particles. This means if you travelled back in time
and repeated your measurement of the object's position at the same time you would
not necessarily get the same answer. The results of such a measurement must be
uncertain.
Note that uncertainty has nothing to do with the inaccuracy of your measuring
instruments or lack of knowledge of what happened to the object earlier.
A3-118
PHOTOELECTRIC EFFECT
Firstly it is important that we understand what the terms frequency and intensity
mean in the context of the wave and particle models.
In the wave model
• frequency corresponds to how often the wire is shaken
• intensity corresponds to the amplitude of the shaking motion
In the particle model
• frequency corresponds to the energy of the projectiles being thrown at the bird by
the relation E = hf (Energy = Planks Constant x Frequency)
• intensity corresponds to the number of projectiles per second being thrown at the
bird
Part A - First key observation
"both the wave and particle models"
Consider the first key observation, that for monochromatic light of sufficiently high
frequency the number of electrons (birds) ejected per second increases as the
intensity of the light increases.
The wave model says for birds on the wire
• Increasing the intensity corresponds to shaking the wire with an increased
amplitude.
• If you increase the amplitude, a bird is more likely to be dislodged from the wire.
The particle model says for birds on the wire
• Increasing the intensity corresponds to throwing more projectiles at the bird.
• If you throw more projectiles a bird is more likely to be hit and knocked off the
wire.
Both models predict the experimental observations.
Part B - Second key observation
"the particle model and not the wave model"
Consider the second key observation, that electrons are only ejected from a metal
surface for frequencies of light above a certain frequency (e.g. violet and ultraviolet);
and for light below this frequency (e.g. blue, yellow or red light) no electrons are
ejected no matter how great the intensity.
The wave model says
• If you shake the wire at very low frequencies you will never dislodge the bird no
matter how great the amplitude (intensity).
• This is nonsense, if you shake the wire with a low frequency of once per second
but increase the amplitude to 10,000 kilometres I bet the bird comes off the wire.
• Therefore the wave model fails to explain the observation.
The particle model says
• If you throw low energy projectiles (corresponding to a low frequency) then no
matter how many you throw the bird will be able to hang on.
• But if the projectile has a higher energy (corresponding to a higher frequency)
then one direct hit will knock the bird off the wire.
Thus only the particle model correctly predicts the experimental observations.
A3-119
APPENDIX 3.....................................................................................................................................105
PRIMARY SURVEY INSTRUMENT ..............................................................................................105