A4-132
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. See Figure A4-1 for combined results of Correctness Analysis.
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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.
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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.
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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)
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 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.
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.
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.
Question 1 - Photoelectric Effect
Class and Overall Tick-box Distributions for Parts A and B
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.
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.
Question 1 - Photoelectric Effect
Interpretation of the Bird on a Wire Model
Correct Interpretations
Category / Representative Examples of Responses / (n)%
1 / Understand WAVE = Shake / ... it would be like starting to shake the bird off the wire. (sid 017) / (92)
45
2 / Understand Particle = Throw / ... balls you throw at the bird. (sid 229) / (121)
59
3 / Intensity Wave = Amplitude / ... Increasing the intensity corresponds to shaking the wire with greater amplitude. (sid 302) / (26)
13
4 / Intensity Particle = Amount of Projectiles / ... greater intensity means more stones... (sid 311) / (72)
35
5 / Frequency Wave = Number of shakes per Second / The frequency of light corresponds to the number of peaks which the bird counts per second. (sid 145) / (37)
18
6 / Frequency Particle = Energy of Projectiles / The particle model requires the stones to have a high energy... (sid 121) / (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.
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.
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. It was found that 14% (29/205) clearly stated that Frequency = Intensity. 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
Category / Representative Examples of Responses / (n)%
1 / Frequency = Intensity / Explicit Response (11) 5
Higher intensity means higher frequency... (sid 220)
Implicit Response (18) 9
By increasing the intensity the number of waves increase... (sid 417 ) / (29)
14
2 / Frequency = Amplitude / Explicit Response (1) 0.5
... the frequency will provide an increase to the amplitude... (sid 133)
Implicit Response (5) 2.5
... the height of the wave is frequency ... (sid 304) / (6)
3
Table A4-3 : Representative examples of alternate interpretations of terms associated with the ‘bird on a wire’ analogy.
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).
Figure A4-5 : The histogram shows the context in which the students chose to present their responses.
Question 1 - Photoelectric Effect
Context of Presentation
Category / Representative Examples of Responses / (n)%
1 / 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) / (93)
45
2 / ADDRESSING ONLY Photons/Electrons / Electrons are ejected when the right amount of quantum energy is being absorbed by the photoelectric material. (sid 211 ) / (40)
20
3 / ADDRESSING BOTH Categories / 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) / (70)
34
Table A4-4 : Representative examples of student responses in the context analysis