Please cite as:
Fletcher, P.R., (1997) Master of Science Thesis - How Students Learn Quantum
Mechanics (School of Physics, University of Sydney)
APPENDIX 4
PHOTOELECTRIC EFFECT
THE BIRD ON A WIRE MODEL
This appendix contains the detailed analysis of Question 1 of the primary
instrument which was administered to 231 first year physics students at the
University of Sydney in 1995.
Question 1 was set utilising a multiple choice tick-box-and-explain response
format. The question was designed to evaluate a student’s ability to use a model to
explain the results of the photoelectric effect.
A4.1 RESULTS
Question 1 surveyed 231 first year physics, resulting in 224 tick-box
responses to both Part A & Part B and 205 written responses.
A4.2 RESULTS - CORRECTNESS TICK-BOX & WRITTEN RESPONSES
Of the student sample there were 224 tick-box responses (97%) to both Parts
A & B, 3 responses to only Part A and 16 responses to only Part B. The correctness
of the tick-box responses for Parts A & B was determined without any reference to
the written section of the response. The written responses were ‘marked’ to evaluate
the students’ ability to explain their answer to the question.
A response was
considered ‘correct’ if it explained correctly how both the wave and particle models
supported their response. The list of the points used to evaluate correctness follow.
A student’s written response was considered correct only if all the points were
addressed and the correct tick-box option was checked.
combined results of Correctness Analysis.
A4-119
See Figure A4-1 for
A4-120
_______________________________________
Part A - First key observation
Tick-box Answer 3 - "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.
Therefore BOTH models predict the experimental observations.
_______________________________________
Part B - Second key observation
Tick-box Answer 2 - "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 (eg. violet and ultraviolet); and for
light below this frequency (eg. 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.
Therefore ONLY the particle model predicts the experimental observation.
_______________________________________
A4-121
Example of a correct student response for Parts A & B.
Part A)
If the observation was based on particles then an increase in intensity
would be like increasing the number of stones being thrown, which
would knock more birds off. In the wave model, increasing the
intensity would increase amplitude, knocking more birds off. (sid 104)
Part B)
If the intensity was increased sufficiently at low frequency the wave
model predicts the bird will be shaken off. The particle model requires
the stones have to have high energy, or high frequency and so explains
the second observation. (sid 121)
Question 1 - Photoelectric Effect
Correctness Analysis
PART A) Multiple Choice
Correct
PART A) Written
Response Correct
PART B) Multiple Choice
Correct
PART B) Written
Response Correct
BOTH Multiple Choice
Correct
BOTH Written Responses
Correct
0
20
40
60
80
100
% of Responses
Figure A4-1 : The histogram shows the percentage of correct responses for the tick-box and
written responses.
The analysis of the tick-box responses showed that for Part A 39% (79/205)
and for Part B 43% (89/205) ticked the correct option (see Figure A4-1). Interestingly
the number of students that could support their response by detailing the issues of
A4-122
the models was extremely low. Only 6.8% (14/205) for Part A, 1% (2/205) for Part B
and 0.5% (1/205) for both Parts A & B. These results are disturbing considering the
importance of the Photoelectric Effect to the development and understanding of
quantum mechanics; and the fact that all the students had studied the effect in both
their secondary and tertiary physics studies.
A simple histogram showing the percentage of responses selecting each
option was constructed for each part to show the general distribution of multiple
choice responses (see Figures A4-2 and A4-3). The correct response option is coded
white while the incorrect are shaded.
Question 1 - Part A - Photoelectric Effect
% of Responses
Distribution of Tick-box Responses
50
45
40
35
30
25
20
15
10
5
0
Wave
NOT
Particle
Particle
NOT
Wave
BOTH
Wave &
Particle
NEITHER
Wave nor
Particle
No
Response
Figure A4-2 : The histogram shows the distribution of responses for the tick-box section of
Question 1 Part A. The unshaded bar identifies the correct response.
The most popular response 47% (107/224) felt that the increase in the rate of
electrons ejected due to increased intensity was solely explained by the particle
model. The second most popular response 34% (78/224) was that both the wave
and particle models (correct response) explained the observation.
A4-123
Question 1 - Part B - Photoelectric Effect
% of Responses
Distribution of Tick-box Responses
40
35
30
25
20
15
10
5
0
Wave
NOT
Particle
Particle
NOT
Wave
BOTH
Wave &
Particle
NEITHER
Wave nor
Particle
No
Response
Figure A4-3 : The histogram shows the distribution of responses for the tick-box section of
Question 1 Part A. The unshaded bar identifies the correct response.
In attempting to explain the observation that photoelectrons are only ejected
above a certain frequency, 36% (83/224) chose a wave model and 39% (89/224) a
particle model.
The tick-box results were further analysed to obtain an overall view of the
distribution of responses.
A matrix was constructed with the x-axis columns
containing the numbers of students selecting Part A options and the y-axis for Part B
options. Two separate matrices were constructed for each stream one showing the
number of responses and the other the percentage of responses (see Table A4-1 next
page). The final matrices in the table shows the distributions for the entire sample.
The intersection of the correct responses is highlighted by a box and the most
popular combination for both parts is bolded.
A4-124
Question 1 - Photoelectric Effect
Class and Overall Tick-box Distributions for Parts A and B
PHOTOELECTRIC EFFECT - Tables Comparing TICK BOXES for Part A and Part B
001 to 031
B\A NR
NR 2
1
0
2
0
3
0
4
0
2
Percentage Response
1
1
0
0
1
0
2
2
1
4
4
3
0
12
3
0
4
5
5
0
14
4
0
1
0
0
0
1
4
9
9
9
0
1
2
4
13
2
0
21
2
3
20
12
5
0
40
3
1
12
8
4
1
26
4
0
0
0
0
1
1
7
36
34
12
2
1
1
1
2
1
0
5
2
3
6
8
1
1
19
3
2
3
12
0
1
18
4
0
1
0
0
0
1
9
11
22
2
2
1
0
0
0
1
0
1
2
1
6
7
2
0
16
3
1
3
10
2
0
16
4
0
1
0
0
0
1
3
10
18
5
0
1
0
1
1
0
0
2
2
0
15
3
2
0
20
3
0
1
2
1
0
4
4
0
0
0
0
1
1
0
17
6
3
1
3
4
23
37
12
2
78
4
0
3
0
0
2
5
23
83
89
31
5
Total 31
B\A NR 1
2
3
4
NR 6.45 3.23 3.23 0
0 12.9
1
0
0 12.9 12.9 3.23 29
2
0
0 12.9 16.1 0 29
3
0 3.23 9.68 16.1 0 29
4
0
0
0
0
0
0
6.45 6.45 38.7 45.2 3.23 100 %
101 to 191
B\A NR
NR 1
1
0
2
1
3
1
4
0
3
B\A
NR
1
2
3
4
Total 91
NR
1.1
0
1.1
1.1
0
3.3
1
2.2
4.4
14.3
2.2
0
23.1
2
3.3
22
13.2
5.49
0
44
3
4
1.1 0 7.69
13.2 0 39.6
8.79 0 37.4
4.4 0 13.2
1.1 1.1 2.2
28.6 1.1 100 %
201 to 246
B\A NR
NR 3
1
0
2
0
3
0
4
0
3
Total 46
B\A NR 1
2
3
4
NR 6.52 2.17 6.52 4.35 0 19.6
1
0 2.17 13 6.52 2.17 23.9
2
0 4.35 17.4 26.1 0 47.8
3
0 2.17 2.17 0
0 4.35
4
0
0 2.17 2.17 0 4.35
6.52 10.9 41.3 39.1 2.17 100 %
Total 36
B\A NR 1
NR 2.78 0
1
0
0
2 2.78 0
3
0 2.78
4
0
0
5.56 2.78
Total 27
B\A NR 1
2
3
4
NR 0
0
0
0
0
1
0 3.7 55.6 3.7 0
2
0 3.7 11.1 7.41 0
3
0
0 7.41 3.7 0
4
0
0
0
0 3.7
0 7.41 74.1 14.8 3.7
301 to 336
B\A NR
NR 1
1
0
2
1
3
0
4
0
2
2
2.78
16.7
19.4
5.56
0
44.4
3
4
2.78 0 8.33
8.33 2.78 27.8
27.8 0 50
5.56 0 13.9
0
0
0
44.4 2.78 100 %
401 to 427
B\A NR
NR 0
1
0
2
0
3
0
4
0
0
0
63
22.2
11.1
3.7
100 %
OVERALL SUMMARY
B\A NR
NR 7
1
0
2
2
3
1
4
0
10
1
2
4
8
6 51
16 34
5 13
0
1
31 107
Chk 231
Total 231
B\A
NR
1
2
3
4
NR
3.03
0
0.87
0.43
0
4.33
1
1.73
2.6
6.93
2.16
0
13.4
2
3.46
22.1
14.7
5.63
0.43
46.3
3
4
1.73 0 9.96
9.96 1.3 35.9
16 0 38.5
5.19 0 13.4
0.87 0.87 2.16
33.8 2.16 100 %
Table A4-1 : The table shows the number (right column) and the percentage (left column)
combination distributions of the tick-box responses for Parts A and B. The boxes identify the
correct response combination and the bolded identifies the most popular response
combination.
A4-125
Analysis of the samples distribution revealed that the most popular
combination was Part A option 2 particle model not wave model and Part B option 1
the wave model not the particle model 22% (51/224). The correct 3&2 response option
scored 16% (37/224) closely followed by the 2&2 both being particle model not the
wave model with 15% (34/224) and the 3&1 option both the wave and particle model /
wave model but not particle model.
A4.2.1 Analysis of the Students Understanding of the Model
It is important that the student understood what the terms frequency and
intensity meant in the context of the wave and particle models.
The written
responses were read without considering the logic or correctness of their response.
Only the meanings that the students placed on the terms frequency and intensity were
considered. If the student’s response provided a ‘correct’ interpretation, a mark was
awarded. Other responses that articulated ‘incorrect’ interpretations were recorded.
The correct meanings of the terms frequency and intensity in relation to each of the
models follow.
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 = Planck’s Constant x Frequency)

intensity corresponds to the number of projectiles per second being thrown
at the bird
The categories used to code the students’ written responses in terms of the
correct interpretation of frequency and intensity are in presented in Table A4-2.
A4-126
Question 1 - Photoelectric Effect
Interpretation of the Bird on a Wire Model
Correct Interpretations
Category
Representative Examples of Responses
1
Understand WAVE = Shake
2
Understand Particle = Throw
... it would be like starting to shake the
bird off the wire. (sid 017)
... balls you throw at the bird. (sid 229)
3
Intensity Wave = Amplitude
4
Intensity Particle = Amount
of Projectiles
5
Frequency Wave = Number of
shakes per Second
6
Frequency Particle = Energy
of Projectiles
... Increasing the intensity corresponds to
shaking the wire with greater amplitude.
(sid 302)
... greater intensity means more stones...
(sid 311)
The frequency of light corresponds to
the number of peaks which the bird
counts per second. (sid 145)
The particle model requires the stones to
have a high energy... (sid 121)
(n)
%
(92)
45
(121)
59
(26)
13
(72)
35
(37)
18
(21)
10
Table A4-2 : Representative examples and distributions of student responses which correctly
interpreted the terms and concepts associated with the ‘bird on a wire’ analogy.
The percentages of responses falling into each of the interpretation categories
are graphically presented in Figure A4-4.
A4-127
Question 1 - Photoelectric Effect
Interpretation of the Bird on a Wire Model
Understand WAVE =
Shake
Understand Particle =
Throw
Intensity Wave =
Amplitude
Intensity Particle =
Amount of Projectiles
Frequency Wave = Num
shakes per Second
Frequency Particle =
Energy of Projectiles
0
20
40
60
80
100
% of Response
Figure A4-4 : Representative examples and distributions of student responses which correctly
interpreted the terms and concepts associated with the “bird on a wire” analogy. (Graphical
representation of Table A4-2).
The analysis of the first two categories that dealt with the understanding of
what was basically meant by the wave and particle models. Interestingly only
around half the responses explicitly stated in words what was presented to them in
the pictures of the bird on a wire.
The student interpretation of the term intensity rated 13% (26/205) for the
Intensity Wave = Amplitude and 35% (72/205) for the Intensity Particle = Amount of
Projectiles. The student interpretation of the term frequency rated 18% (35/205) for
the Frequency Wave = Number shakes per second and 10% (21/205) for the Frequency
Particles = Energy of Projectiles.
A4-128
These extremely poor scores are disturbing considering the students have
recently completed a module on the properties of waves. Higher scores in the
interpretations of the terms frequency and intensity in relation to waves would have
been expected.
The results in Table A4-3 which tabulate the alternate interpretations
presented in responses provides an unexpected clue into the nature of the students’
difficulty with interpreting the models. The students appear to be having trouble
clearly delineating the terms frequency and intensity.
(29/205) clearly stated that Frequency = Intensity.
It was found that 14%
This was a considered
conservative because only responses that clearly stated the relationship were
counted.
Another ~35% of the responses hinted toward belief that intensity is
linked to frequency. Also revealed to a smaller extent 3% (6/205) clearly stated that
Frequency = Amplitude and another ~5% hinted toward this belief.
In the process of coding the student interpretations to the meaning of the
terms frequency and intensity two alternate views were revealed (see Table A4-3).
These interpretations are contrary to the accepted physical concepts.
Question 1 - Photoelectric Effect
Interpretation of Bird on a Wire Model - Other Interpretations of the Terms
1
2
Category
Representative Examples of Responses
Frequency = Intensity
Explicit Response (11) 5
Higher intensity means higher
frequency... (sid 220)
Frequency = Amplitude
(n)
%
(29)
Implicit Response (18) 9
By increasing the intensity the number
of waves increase... (sid 417 )
14
Explicit Response (1) 0.5
... the frequency will provide an increase
to the amplitude... (sid 133)
(6)
Implicit Response (5) 2.5
... the height of the wave is frequency ...
(sid 304)
3
Table A4-3 : Representative examples of alternate interpretations of terms associated with the
‘bird on a wire’ analogy.
A4-129
A4.2.2 Context
Question 1 was set in a format requiring the response to be presented in
terms of the ‘birds on a wire’. The written responses were analysed and three
categories became evident. Responses that only addressed the bird model addressing
only the bird, responses that did not mention the bird model at all addressing only
photons/electrons and responses that addressed both addressing both categories (see
Figure A4-5 and Table A4-4 for details).
Question 1 - Photoelectric Effect
% of Responses
Context of Presentation
50
45
40
35
30
25
20
15
10
5
0
ADDRESSING
ONLY THE BIRD
ADDRESSING
ONLY
Photons/Electrons
ADDRESSING
BOTH Categories
Figure A4-5 : The histogram shows the context in which the students chose to present their
responses.
A4-130
Question 1 - Photoelectric Effect
Context of Presentation
1
2
3
Category
Representative Examples of Responses
ADDRESSING ONLY THE
BIRD
In terms of the bird on the wire both
models can be accepted for observation 1
as when intensity increases bird loses its
balance and then gets pegged in the
head by a particle, but this bird will only
fall if the balls are thrown hard enough.
(sid 209)
Electrons are ejected when the right
amount of quantum energy is being
absorbed by the photoelectric material.
(sid 211 )
The particles can be more selective in
dislodging the birds (electrons) than the
shaking of the wire. Only photons of a
certain energy can dislodge the birds
(electrons). (sid 410)
ADDRESSING ONLY
Photons/Electrons
ADDRESSING BOTH
Categories
Table A4-4 : Representative examples of student responses in the context analysis
(n)
%
(93)
45
(40)
20
(70)
34
PART A Written Respnse Correct
Part B Tick CORRECT
PART B Written Response Correct
Both Ticks CORRECT
Both Written Responses Correct
Understand WAVE = Shake
Understand Particle = Throw
Intensity Wave = Amplitude
Intensity Particle = Amount of Projectiles
Frequency Wave = Num shakes per Second
Frequency Particle = Energy of Projectiles
Frequency = Intensity (explicit)
Frequency = Intensity (implicit)
Frequency = Amplitude (explicit)
Frequency = Amplitute (implicit)
Did response include Mathematics
Did response address BIRD
Did response address ELECTRONS/PHOTONS
0 - 31
31
3
28
28
100
15
54
3
11
9
32
0
0
5
18
0
0
4
14
6
21
3
11
5
18
3
11
1
3.6
2
7.1
4
14
0
0
1
3.6
2
7.1
24
86
16
57
101 - 191
91
9
82
82
100
26
32
4
4.9
34
41
1
1.2
8
9.8
0
0
42
51
55
67
11
13
32
39
13
16
7
8.5
5
6.1
7
8.5
1
1.2
2
2.4
9
11
64
78
44
54
201 - 246
46
7
39
39
100
18
46
2
5.1
22
56
0
0
12
31
0
0
14
36
17
44
3
7.7
9
23
5
13
4
10
1
2.6
1
2.6
0
0
1
2.6
5
13
27
69
21
54
301 - 336
36
4
32
32
100
16
50
5
16
18
56
1
3.1
10
31
1
3.1
20
63
26
81
9
28
17
53
11
34
7
22
2
6.3
3
9.4
0
0
1
3.1
5
16
28
88
12
38
401 - 427
27
3
24
24
100
4
17
0
0
6
25
0
0
2
8.3
0
0
12
50
17
71
0
0
9
38
5
21
2
8.3
1
4.2
1
4.2
0
0
0
0
2
8.3
20
83
17
71
OVERALL SUMMARY
231
Tot 205
26
% 100
205
79
39
14
6.8
89
43
2
1
37
18
1
0.5
92
45
121
59
26
13
72
35
37
18
21
10
11
5.4
16
7.8
1
0.5
5
2.4
23
11
163 110
80 54
Table A4-5 : Tabular summary of analysis showing class and overall results.
CONTEXT
MIS-INTERPRETATION OF BIRD MODEL
INTERPRETATION OF BIRD MODEL
CORRECTNESS
Written Response
MULTIPLE CHOICE
Part A Tick CORRECT
TICKED BOXES
A4-131
Question 1 - Photoelectric Effect
Results Summary
A4-132
APPENDIX 4 ........................................................................................................................................... 119
PHOTOELECTRIC EFFECT .................................................................................................................. 119
THE BIRD ON A WIRE MODEL ............................................................................................................ 119
A4.1 RESULTS ...................................................................................................................................... 119
A4.2 RESULTS - CORRECTNESS TICK-BOX & WRITTEN RESPONSES ......................................... 119
A4.2.1 Analysis of the Students Understanding of the Model ........................................................................... 125
A4.2.2 Context ................................................................................................................................................... 129
FIGURE A4-1 : THE HISTOGRAM SHOWS THE PERCENTAGE OF CORRECT RESPONSES FOR THE TICK-BOX
AND WRITTEN RESPONSES. ................................................................................................................. 121
FIGURE A4-2 : THE HISTOGRAM SHOWS THE DISTRIBUTION OF RESPONSES FOR THE TICK-BOX SECTION OF
QUESTION 1 PART A. THE UNSHADED BAR IDENTIFIES THE CORRECT RESPONSE. ............................. 122
FIGURE A4-3 : THE HISTOGRAM SHOWS THE DISTRIBUTION OF RESPONSES FOR THE TICK-BOX SECTION OF
QUESTION 1 PART A. THE UNSHADED BAR IDENTIFIES THE CORRECT RESPONSE. ............................. 123
FIGURE A4-4 : REPRESENTATIVE EXAMPLES AND DISTRIBUTIONS OF STUDENT RESPONSES WHICH
CORRECTLY INTERPRETED THE TERMS AND CONCEPTS ASSOCIATED WITH THE “BIRD ON A WIRE”
ANALOGY. (GRAPHICAL REPRESENTATION OF TABLE A4-2). ............................................................ 127
FIGURE A4-5 : THE HISTOGRAM SHOWS THE CONTEXT IN WHICH THE STUDENTS CHOSE TO PRESENT
THEIR RESPONSES. ............................................................................................................................. 129
TABLE A4-1 : THE TABLE SHOWS THE NUMBER (RIGHT COLUMN) AND THE PERCENTAGE (LEFT COLUMN)
COMBINATION DISTRIBUTIONS OF THE TICK-BOX RESPONSES FOR PARTS A AND B. THE BOXES
IDENTIFY THE CORRECT RESPONSE COMBINATION AND THE BOLDED IDENTIFIES THE MOST POPULAR
RESPONSE COMBINATION. .................................................................................................................. 124
TABLE A4-2 : REPRESENTATIVE EXAMPLES AND DISTRIBUTIONS OF STUDENT RESPONSES WHICH
CORRECTLY INTERPRETED THE TERMS AND CONCEPTS ASSOCIATED WITH THE ‘BIRD ON A WIRE’
ANALOGY. ......................................................................................................................................... 126
TABLE A4-3 : REPRESENTATIVE EXAMPLES OF ALTERNATE INTERPRETATIONS OF TERMS ASSOCIATED
WITH THE ‘BIRD ON A WIRE’ ANALOGY. ............................................................................................. 128
TABLE A4-4 : REPRESENTATIVE EXAMPLES OF STUDENT RESPONSES IN THE CONTEXT ANALYSIS .............. 130
TABLE A4-5 : TABULAR SUMMARY OF ANALYSIS SHOWING CLASS AND OVERALL RESULTS. ...................... 131