The quantum understanding of pre-university physics students

The quantum understanding of pre-university physics students Gren Ireson Department of Education, Loughborough University, Loughborough, Leicestershire LE11 3TU, UK Students in England and Wales wishing to read for a physics-based degree will, in all but the more exceptional situations, be required to follow the two-year GCE Advanced-level physics course. This course includes, in its mandatory core, material that addresses the topic of quantum phenomena. Over the years journals such as this have published teaching strategies, for example Lawrence (1996), but few studies addressing what students understand of quantum phenomena can be found. This paper aims to address just this problem. The GCE Advanced-level course is the main route into an undergraduate course of study in England and Wales. In physics this course contains a E-mail: g.p.ireson@lboro.ac.uk mandatory core of material addressing quantum phenomena. The examining groups form a syllabus of study then interpret this core material. The examination syllabus followed by the students in this study was the Northern Examination and Assessment Board (NEAB 1997), which specifies: Electromagnetic spectrum The continuous nature of the spectrum Photon model of electromagnetic radiation The Planck constant E = hf The photoelectric effect Work function, φ Photoelectric equation hf = φ + E K Collisions of electrons with atoms The electronvolt Ionization, excitation Line spectra (e.g. of atomic hydrogen) Energy levels, photon emission hf = E 1 E 2 Phys. Educ. 35(1) January 2000 15

Wave particle duality Particle diffraction De Broglie wavelength λ = h/p Studies into students understanding of quantum phenomena have been carried out within a European context (Fischler and Lichtfeldt 1992, Petri and Nieddrer 1998) and within a UK context (Mashhadi 1996). These studies have presented findings which demonstrate that clusters of understanding exist amongst students of this age, and that their understanding is closely linked to the use of models. It is the belief of this author that before we, as physics educators, develop either a syllabus or a teaching strategy we need to start with an understanding of how students think. Teachers and tutors need to spend a good deal more time asking what students think. Teachers and tutors need to spend a good deal less time relating their own well formed thoughts. It is not the teacher who should be rehearsing the problem, it is the student. (Monk 1994) Given that quantum phenomena are often counterintuitive to everyday thinking or mechanistic reasoning then, I argue, understanding students thinking is all the more important. Drawing on both the findings and methodology of the above-mentioned studies the aim of this paper is to present findings that offer insights into students understanding of quantum phenomena. Methodology During 1998 a questionnaire of 40 items, using a five-point scale from strongly agree to strongly disagree, was presented to 342 students, across six institutions, following a GCE Advanced-level physics course. Approximately half of the sample (N = 190) had yet to study quantum phenomena. Of the 40 items on the questionnaire 29 directly addressed ideas related to quantum phenomena and the remaining 11 addressed ideas related to models. Only those items relating to quantum phenomena are dealt with in this paper. These are listed in full in figure 1. The analytical technique of cluster analysis was used to analyse the returned questionnaires. Cluster analysis is concerned with allocating individuals or items to a group in such a way that each member of the group is more like members in the same group than those outside the group. In this study the items from the questionnaires were clustered. This allowed the clusters to be interpreted as groups of students who hold similar ideas regarding quantum phenomena. A statistical test of significance, the Kruskal Wallis H test, was used to ascertain if differences in thinking, amongst the students, were evident after following a course of study that addressed quantum phenomena. The test statistic is the chisquare (χ 2 ) distribution with n 1 degrees of freedom. A significant difference in this study is one in which the post-study group shows a greater tendency to respond in the manner of the currently accepted understanding. The three levels of significance refer to the possibility of the differences being due to chance: 0.01, one in a hundred; 0.05, five in a hundred; and 0.10, one in ten. This allows greater confidence to be attached to those showing significance at the 0.01 level. Findings For the pre-study, cluster analysis generated four clusters for the 29 items addressing quantum phenomena. For the post-study group the number of clusters was reduced to three. These clusters can be seen in figures 2(a) and (b). The Kruskal Wallis H test pointed to differences between the pre- and post-study groups on the items shown in figure 3. Discussion The clusters in the pre-study group (figure 2(a)) can be labelled: 1. Structure and mental image of entities [B16 Electrons move along wave orbits around the nucleus; B08 An atom cannot be visualized]. 2. Mechanistic thinking (definite trajectory) [ Electrons move around the nucleus in definite orbits with a high velocity; B30 If a container has a few gas molecules in it and we know their instantaneous positions and velocities then we can use Newtonian mechanics to predict exactly how they will behave as time goes by]. 16 Phys. Educ. 35(1) January 2000

Item Number B01 B02 B03 B04 B06 B07 B08 B12 B13 B15 B16 B18 B26 B27 B28 B30 B31 B33 B35 B36 The structure of the atom is similar to the way planets orbit the sun. It is possible to have a visual image of an electron. The energy of an atom can have any value. The atom is stable due to a balance between an attractive electric force and the movement of the electron. Coulomb s law, electromagnetism and Newtonian mechanics cannot explain why atoms are stable. The electron is always a particle. An atom cannot be visualized. Light always behaves as a wave. In passing through a gap electrons continue to move along straight-line paths. The photon is a sort of energy particle. Electrons are waves. When an electron jumps from a high orbital to a lower orbital, emitting a photon, the electron is not anywhere in between the two orbits. How one thinks of the nature of light depends on the experiment being carried out. Electrons move along wave orbits around the nucleus. The photon is a lump of energy that is transferred to or from the electromagnetic field. Electrons consist of smeared charge clouds which surround the nucleus. Nobody knows the position accurately of an electron in orbit around the nucleus because it is very small and moves very fast. It is possible for a single photon to constructively and destructively interfere with itself. Since electrons are identical it is not possible to distinguish between them. Electrons move around the nucleus in definite orbits with a high velocity. When a beam of electrons produces a diffraction pattern it is because the electrons themselves are undergoing constructive and destructive interference. Electrons move randomly around the nucleus within a certain region or at a certain distance. Whether one labels an electron a particle or wave depends on the particular experiment being carried out. If a container has a few gas molecules in it and we know their instantaneous positions and velocities then we can use Newtonian mechanics to predict exactly how they will behave as time goes by. During the emission of light from atoms the electrons follow a definite path as they move from one energy level to another. Individual electrons are fired towards a very narrow slit. On the other side is a photographic plate. What happens is that the electrons strike the plate one by one and gradually build up a diffraction pattern. Electrons are fixed in their shells. Orbits of electrons are not exactly determined. The photon is a small, spherical entity. Figure 1. Matching significant change to syllabus items. 3. Quantum thinking [B12 The photon is a sort of energy particle ; B15 How one thinks of the nature of light depends on the experiment being carried out]. 4. Conflicting mechanistic thinking [B35 Electrons are fixed in their shells; Light always behaves as a wave; B13 Electrons are waves]. Both cluster two and cluster four point to confusion in the minds of the students. In cluster two B01 [The structure of the atom is similar to the way planets orbit the sun] is grouped with B06 [Coulomb s law, electromagnetism and Newtonian mechanics cannot explain why atoms are stable]. Whilst in cluster four [In passing through a gap electrons continue to move along straight-line paths] is grouped with B13 [Electrons are waves]. These two pairs of statements demonstrate that students are failing to transfer ideas studied under one topic heading to another. Phys. Educ. 35(1) January 2000 17

Cluster 1 B16 B36 B04 B27 B08 Cluster 2 B01 B31 B06 B30 B07 Cluster 3 B12 B26 B28 B15 B18 B33 Cluster 4 B13 B35 B03 B02 Electrons move along wave orbits around the nucleus. Orbits of electrons are not exactly determined. The atom is stable due to a balance between an attractive electric force and the movement of the electron. It is possible for a single photon to constructively and destructively interfere with itself. Electrons consist of smeared charge clouds which surround the nucleus. Electrons move randomly around the nucleus within a certain region or at a certain distance. An atom cannot be visualized. The structure of the atom is similar to the way planets orbit the sun. Electrons move around the nucleus in definite orbits with a high velocity. During the emission of light from atoms the electrons follow a definite path as they move from one energy level to another. Coulomb s law, electromagnetism and Newtonian mechanics cannot explain why atoms are stable. If a container has a few gas molecules in it and we know their instantaneous positions and velocities then we can use Newtonian mechanics to predict exactly how they will behave as time goes by. Since electrons are identical it is not possible to distinguish between them. The electron is always a particle. The photon is a sort of energy particle. Nobody knows the position accurately of an electron in orbit around the nucleus because it is very small and moves very fast. When an electron jumps from a high orbital to a lower orbital, emitting a photon, the electron is not anywhere in between the two orbits. When a beam of electrons produces a diffraction pattern it is because the electrons themselves are undergoing constructive and destructive interference. Whether one labels an electron a particle or wave depends on the particular experiment being carried out. How one thinks of the nature of light depends on the experiment being carried out. The photon is a lump of energy that is transferred to or from the electromagnetic field. Individual electrons are fired towards a very narrow slit. On the other side is a photographic plate. What happens is that the electrons strike the plate one by one and gradually build up a diffraction pattern. Electrons are waves. Electrons are fixed in their shells. The energy of an atom can have any value. The photon is a small, spherical entity. In passing through a gap electrons continue to move along straight-line paths. It is possible to have a visual image of an electron. Light always behaves as a wave. Figure 2. (a) Clusters for the pre-study group. The clusters for the post-study group can be labelled: 1. Quantum thinking [B15 How one thinks of the nature of light depends on the experiment being carried out; B12 The photon is a sort of energy particle ]. 2. Conflicting quantum thinking [B01 The structure of the atom is similar to the way planets orbit the sun; It is possible for a single photon to constructively and destructively interfere with itself; B31 During the emission of light from atoms the elctrons follow a 18 Phys. Educ. 35(1) January 2000

Cluster 1 B15 B28 B12 B36 B16 B33 B03 B06 Cluster 2 B30 B01 B26 B31 B04 B18 B27 Cluster 3 B08 B13 B35 B02 B07 How one thinks of the nature of light depends on the experiment being carried out. Whether one labels an electron a particle or wave depends on the particular experiment being carried out. The photon is a sort of energy particle. Nobody knows the position accurately of an electron in orbit around the nucleus because it is very small and moves very fast. Orbits of electrons are not exactly determined. Electrons move along wave orbits around the nucleus. Individual electrons are fired towards a very narrow slit. On the other side is a photographic plate. What happens is that the electrons strike the plate one by one and gradually build up a diffraction pattern. Electrons consist of smeared charge clouds which surround the nucleus. The energy of an atom can have any value. Coulomb s law, electromagnetism and Newtonian mechanics cannot explain why atoms are stable. When an electron jumps from a high orbital to a lower orbital, emitting a photon, the electron is not anywhere in between the two orbits. It is possible for a single photon to constructively and destructively interfere with itself. Since electrons are identical it is not possible to distinguish between them. If a container has a few gas molecules in it and we know their instantaneous positions and velocities then we can use Newtonian mechanics to predict exactly how they will behave as time goes by. The structure of the atom is similar to the way planets orbit the sun. Electrons move around the nucleus in definite orbits with a high velocity. When a beam of electrons produces a diffraction pattern it is because the electrons themselves are undergoing constructive and destructive interference. During the emission of light from atoms the electrons follow a definite path as they move from one energy level to another. The atom is stable due to a balance between an attractive electric force and the movement of the electron. The photon is a lump of energy that is transferred to or from the electromagnetic field. Electrons move randomly around the nucleus within a certain region or at a certain distance. In passing through a gap electrons continue to move along straight-line paths. The photon is a small, spherical entity. An atom cannot be visualized. Electrons are waves. Electrons are fixed in their shells. It is possible to have a visual image of an electron. The electron is always a particle. Light always behaves as a wave. Figure 2. (b) Clusters for the post-study group. definite path as they move from one energy level to another]. 3. Conflicting mechanistic thinking [B13 Electrons are waves; B07 The electron is always a particle; The photon is a small, spherical entity]. Clusters two and three again point to confusion in the minds of the students. By considering those items showing significant difference at the 0.01 level the evidence suggests that teaching a module or unit on quantum phenomena can change, at the level of the Phys. Educ. 35(1) January 2000 19

Significance level 0.01 B08 0.05 B13 0.10 B12 Figure 3. Items showing a significant difference between the pre- and post-study groups. group, the way in which students think about quantum phenomena. However, only a minority of the significant changes can be traced back to statements in the syllabus; see figure 4. The majority of the changes must, therefore, be due to factors outside the direct teaching of the syllabus material. Implications for teaching and learning This study shows that some students cannot be considered to have an interpretation of quantum theory which even attempts to approximate to a non-classical interpretation of the formalized theory. This should not come as too much of a surprise since Planck and Einstein held a life-long disagreement as to the best interpretation (Selleri 1990). However, teachers in schools, colleges and, one could argue, universities need to be sensitive to the variety in the nature of their students thinking regarding quantum phenomena (i.e. from mechanistic to quantum modes of thought), and the possible groupings of conceptions that they may hold. In addition, course developers, examiners and textbook authors need to draw upon the available research to plan a sequence of instruction which allows the student to develop a conceptual framework for a subject that is often counterintuitive to commonsense or mechanistic reasoning. A way forward? In looking for a route through the minefield of quantum phenomena this author would suggest that all of those involved in physics education refer to the work of Fischler and Lichtfeldt (1992). In this work the recommended approach to the teaching of quantum physics is one in which: 1. Reference to classical physics is avoided. 2. Teaching of the photoelectric effect begins with electrons not photons. 3. Statistical interpretations of observed phenomena are used and dualistic descriptions avoided. 4. The Heisenberg uncertainty principle is introduced at an early stage for ensembles of quantum objects. 5. In the treatment of the hydrogen atom the Bohr model is avoided. Perhaps it is time for a reappraisal of both preuniversity and undergraduate physics in the light of this and other research into student understanding, but how can this be achieved? Taking the above route and given the syllabus being followed by the students in this study the following is offered. Significance level Syllabus 0.01 The photoelectric effect Wave-particle duality Energy levels, photon emission Energy levels, photon emission 0.05 B13 Wave-particle duality Photon emission Figure 4. Matching significant change to syllabus items. 20 Phys. Educ. 35(1) January 2000

The electron diffraction tube The diffraction pattern seen with the electron diffraction tube can be interpreted in terms of wavelength since its appearance is the same as that for light. The De Broglie wavelength, λ = h/p, can be arrived at by treating the electrons as classical objects before they are diffracted. The need for wave particle duality or matter waves can be avoided. Electrons can be treated as quantum objects. Russell Stannard (1994) uses this description in a manner aimed at 9 to 13 yearolds in his book Uncle Albert and the Quantum Quest. This text should, I feel, be set reading for A-level. The double slit experiment By using video clips it can be demonstrated that a beam of electrons produces an inteference pattern familiar to the students from work on light; hence electrons are not classical particles. By allowing only single electrons into the system a statistical distribution is revealed; hence electrons are not waves. Therefore electrons are quantum objects. The uncertainty principle this, I feel, should be limited to x ρ 1 h since it becomes 2 difficult to attach any meaning to the uncertainty of time of a particle or quantum object expressed in E t 1 2 h. The square-well potential for the hydrogen atom, which could lead to the two-dimensional Schrödinger equation. The meaning of quantum theory this need not be mathematical and may appeal to those students who appreciate the philosophical rather than the mathematical. Acknowledgment The author would like to thank Patrick Fullick, Southampton University, for his careful reading of a draft of this paper. Whilst his valued suggestions have been acted upon, any shortcomings remain the responsibility of the author. Received 15 April 1999, in final form 2 June 1999 PII: S0031-9120(00)03502-4 The Franck and Hertz experiment This experiment can be used to develop E = hf. Mercury atoms absorb energy in discrete amounts, E. This energy, when emitted as radiation, shows a relationship between the energy, E, and the frequency, f, which allows the Planck constant to be arrived at. This further allows the development of line spectra and energy levels in the atom; there is no mention of photons. The photoelectric effect The photoelectric effect can be intoduced by treating light as a quantum object. Rather than photons, it is possible to refer to quantum objects. This avoids the temptation of students to relate photons with classical particles. This would cover the requirements for the syllabus followed by students in this study. Further work could be added, if syllabus space could be found, using the quantum object approach to include: References Fischler H and Lichtfeldt M 1992 Modern physics and students conceptions Int. J. Sci. Educ. 14 181 90 Lawrence I 1996 Quantum physics in school Phys. Educ. 31 278 87 Mashhadi A 1996 Students conceptions of quantum physics Research in Science Education in Europe ed G Welford, J Osborne and P Scott (London: Falmer) pp 254 66 Monk M 1994 Mathematics in physics education: a case of more haste less speed Phys. Educ. 29 209 12 Northern Examinations and Assessment Board 1997 General Certificate of Education Syllabus for 1999 Physics (Manchester: NEAB) Petri J and Nieddrer H 1998 A learning pathway in high-school level quantum atomic physics Int. J. Sci. Educ. 20 1075 88 Selleri F 1990 Quantum Paradoxes and Physical Reality (Dordrecht: Kluwer Academic) Stannard R 1994 Uncle Albert and the Quantum Quest (London: Faber and Faber) Phys. Educ. 35(1) January 2000 21