Chapter 10 of Understanding Chemical Bonding: The development of A level students' understanding of the concept of chemical bonding
Learners' alternative conceptions of electrostatics forces
§10.0: The significance of learners’ notions of electrostatics
As progression was found to be related to the adoption of electrostatic principles as the basis of explaining bonding phenomena, learners' notions about electrostatic forces are of central importance to the research. In this research the colearners exhibited beliefs about the interactions of charged particles which are inconsistent with Coulombic electrostatics, and may therefore act as impediments to the learning of the curriculum science model.
It was found in this study that most of the chemistry learners interviewed exhibited notions about the interactions between charged particles which were in some sense inconsistent with curriculum science. The following features were found amongst one or more of the colearners in the study,
- an interpretation of charge as a deviation from full electron shells, rather than a deviation from electrical neutrality.
- apparent confusion of force with charge.
- apparent confusion about force and energy.
- systems were considered to be in equilibrium without forces being
balanced; or to be non-equilibrium systems when forces would
cancel. - forces were associated with one body, not seen as an interaction
between bodies. • forces were seen to act from one charged particle onto another, without reciprocity (as required by Newton's third law). The 'reaction' forces might be absent (or considered as negligible), of the wrong sign (i.e. an attraction paired with a repulsion), or wrong magnitude (i.e. the greatest force acting on the smaller particle). - nuclei were considered to give rise to a fixed amount of attraction – depending upon charge – which would be shared amongst the electrons available to receive it.
These alternatives to conventional electrostatic principles were found to varying extents (for example the 'deviation charges' notion was only elicited from Annie, but the notion of the effects of a charge being shared was more common.) Some learners were found to apply different variants of physical principles in contexts that were equivalent from a curriculum science perspective. Similarly the meanings that learners appeared to give to words such as 'force' and 'attraction' did not always match the curriculum science definitions. These aspects will be considered, and evidence presented from the data base.
§10.1: Ignorance of electrostatic forces
The case of Annie has been discussed in an earlier chapter (chapter 7), and her alternative conception of charge, deviation charges was described (§7.2.2). Although Annie saw charge as a deviation from noble gas electronic structure, and therefore classed neutral atoms as charged, she believed that there would be a force between two particles that were charged in her scheme. For example, a sodium atom and a chlorine atom "would probably get held together by just forces" (A1.256). The force was, "the attraction from the plus to the minus because like chlorine's minus an electron and sodium is over an electron" (A1.260). The force was seen to be a direct consequence of the deviation from a stable electronic structure, that is (in her interpretation) the lack of, or abundance of, electrons (see appendix 31, §A31.1.1). So for Annie it was not electrostatic charges, but deviation charges which gave rise to a force. Although Annie's deviation charge conception was unique amongst the co- learners in the research, Kabul also commenced A level chemistry apparently ignorant of electrostatic forces.
focal figure 2
Kabul thought there was a force involved in holding the atoms in focal figure 2 together. However, he was unable to suggest what physicists might consider to be the basic forces. He recalled that "there is force like gravitational force" but he did not think that this was involved in holding atoms together (K1.B165). That force was different as "gravitational force is due to the force of gravity. But … [the force between two atoms] is an attraction force" (K1.B165). Kabul thought that gravity was "not an attraction, it just pulls everything downwards" (K1.B165). Kabul knew about the tides, and they were due to "the attraction from the moon", but he had "no idea" what kind of attraction that might be – except that it was not the same attraction holding the atoms (in focal figure 2) together, and (three centuries after Newton proposed Universal Gravitation) nor did he think it was the same kind of attraction that makes an apple fall from a tree (K1.B191). As well as these three types of force Kabul suggested that there were "lots of forces", and they all had to be treated separately (K1.B191).
§10.1.1: Learners may confuse force with charge
An example of a colearner who appeared to have an alternative meaning of the word force was Jagdish. In her first interview she suggested that "the proton … has a stronger force so there is a kind of positive force … at the nucleus" (J1.A076), an utterance which suggested that Jagdish did not always use the curriculum science distinction between 'force' and 'charge'. Her utterance seems to imply either that force is charge, or that it is a property of charge (rather than arising between several charges). The notion of force being designated to charged particles is discussed further below (§10.3.4).
In her second interview there were other utterances which suggested that Jagdish was not using the conventional idiom of curriculum science. The discussion had turned to electricity and in order to find out what Jagdish meant by the term she was asked about 'anti-iron' which she thought would contain delocalised positrons. Jagdish would not commit to whether electricity would be possible, but one would "have some sort of erm, force like electricity" (J2.A206). She was asked about a radioactive substance giving out a stream of alpha particles, and she thought that this was "maybe not electricity as we know it, but … it would, be a force though … it is a force, but I, you wouldn't call it electricity" (J2.A224). Jagdish said she had used the term electric current at G.C.S.E., where it was defined as a "flow of electrons" (J2.A240). In this sense a flow of alpha particles was "not electricity, but it is a current", and Jagdish went on to suggest "it is a force, because it's charged … so there must be a force" (J2.A240). When it was suggested to Jagdish that perhaps the definition she had been given (i.e. that to be a current there had to be a flow of electrons) did not cover all cases, she seemed to accept this this readily, as "it's all energy though, isn't it, I mean like a flow of electric current, or a flow of alpha particles? It's all energy. It's all some sort of energy" (J2.A240). It would seem that for Jagdish an electric current, electricity, was not a phenomenon that was related to force and energy, but rather that electricity was a force, and was energy: She did not apply the distinct meanings that scientists give to these terms. In particular she seemed to think that the presence of charge implied a force, where the curriculum science view would be that the force arises from the interaction of different charges (c.f. §10.4 and §10.5).
focal figure 1
focal figure 2
In Quorat's first interview she did not seem to consider that an attraction counted as a force,
I: Are there any forces in, in number 1, would there be any forces, or interactions?Q: No.
I: No?
Q: No, it's just the electrons attracted to the positive nucleus, that's why they're kept together.
I: Right, but there's no force though?
Q: No.
I: They're just attracted?
Q: Mm.
Q1.A226
Later in the interview Quorat referred to "the force of the nucleus" as if it is a property of the protons. So in focal figure 2, representing the hydrogen molecule, the strength of the force depends upon "the force of the nucleus" which is due to "the positive protons" (Q1.A381). She explains that "the more positive it is, … the more the force it will put onto the electrons, so the more they'll be attracted to the nucleus" (Q1.A380). In focal figure 1, the force on the electrons depended on two factors, "how further [sic] away the electrons are from the nucleus, the distance" and what Quorat called "the force of the nucleus, how positive it is" (Q1.A386, c.f. §10.5).
In Tajinder's second interview he suggested that in metals "one of the forces might be positive and negative forces that hold them together" (T2.A207). Tajinder repeated that there were "positive and negative forces" which were "not the same". However he did not appear to mean the convention that repulsive forces are given a positive sign, and attractions a negative sign, rather, he was confusing force with charge, so that "two positive forces repel one another, and so do two negative forces repel one another, but opposite forces attract one another" (T2.A207).
So in the present study, as in the literature reviewed in chapter 3 (§3.1.3), learners do not always use the term force in its curriculum science sense.
§10.1.2: Learners may confuse force with energy
Another finding of the present study that reflects the existing literature is that learners did not always seem to clearly differentiate the concepts of 'force' and 'energy'.
So in her third interview Carol seems to conflate force and energy when she describes "that Coulomb's, thing" (C3.689), that "the further they are away the less … kind of energy they have against the other one" (C3.691). In Mike's first interview he explained the attraction between an electron and a nucleus as "positive-negative energy attracting … positive energy coming from the, the nucleus, and negative energy from the electron" (M1.A163)'. When he was asked about force he suggested that he "knew some of the forces, [e.g.] kinetic, potential" (M1.A163), i.e. labels that in curriculum science refer to energy, not force.
Potential energy is important because energy changes met in chemistry usually involve changes in electrostatic potential. Kabul did not seem to commence his study of chemistry with a concept of potential energy, although later he seemed to incorporate this notion into his concept of force (see appendix 31, §A31.1.2). Kabul recognised only "kinetic" energy in the earth-moon system (K3.B045), that is he did not recognise any potential energy in this situation. Similarly, Kabul thought that the only energy present in the solar system was "kinetic energy" "located on the planets" (K3.B109). However, at one point Kabul appeared to conflate the concepts of the force between two charges and a tacit appreciation of electrical potential energy, when he suggested that the force between two opposite charges would be greater than between two similar charges as "once they've repelled each other, there won't be anything" (K3.B209), whereas as the opposite charges moved together the force "gets bigger" (K3.B219).
Tajinder did recognise potential energy from early in his course, but associated this with one body (e.g. a falling apple) rather than an interactions between bodies. Further the potential energy was not associated with configuration per se: Tajinder only recognised the potential energy when it was converted due to movement (see appendix 31, §A31.1.3).
§10.2: Newtonian mechanics: inertia, equilibrium and reciprocity
Although Newtonian mechanics is not a requirement of the A level chemistry syllabus, the use of the concepts of force and energy means that the Newtonian framework is implicit. As was discussed in the literature section (§3.1.3), this is an area where it is known that many people, including those who have studied the topic formally, find curriculum science counter-intuitive, and where it would seem inappropriate to assume chemistry students share the implicit assumptions under- pinning the taught explanatory models of the subject.
In the present research many examples were found of colearners making statements which were inconsistent with these aspects of curriculum science. First I will present some examples relating to newton-1 and newton-2 (Newton's first and second laws of motion), which allow us to make the following inferences, amongst others:
- object remaining stationary ⟹ zero resultant force ⟹ forces are balanced
- unbalanced force ⟹ non-zero resultant force ⟹ object not remaining stationary
This chain of inference is important if students are to appreciate how unbalanced forces can bring about changes in configuration at the molecular level during chemical reactions, and why species may be stable. However, colearners in the present study did not always draw these inferences.
§10.2.1: Applications of an impetus notion
Although the research interviews were largely spent discussing focal figures intended to elicit students' ideas about bonding, some of the colearners spent time discussing some focal figures concerned with force and motion (reproduced in appendix 13). Kabul and Tajinder both demonstrated that they held the type of impetus notions commonly reported in the literature (§3.1.3).
Kabul (see appendix 31, §A31.2.1) thought that an object subject to an applied force would not continue to accelerate, but that the speed "will settle out on a particular value, if it's a constant force". Kabul knew an apple would fall down due to the force of gravity. Even when there was no other force acting on the apple he thought it would fall at constant velocity: again he did not expect acceleration.
When asked about an object thrown by hand Kabul thought that it would also be subject to a force from the hand until it reached its highest point, but as it fell back down it would have used up all its force – or at least would not have enough left to overcome gravity. Kabul believed "the resultant force is zero" where the object "may just stop … for an instant, when it has reached its maximum height". When it reached the ground the object was stationary, and therefore Kabul did not think any forces were acting. On the ground gravity was negligible.
When Tajinder was asked to consider the same situation of a ball being thrown in the air, he also demonstrated an impetus conception (see appendix 31, §A31.2.2). So according to Tajinder on the way up "the force of which it was thrown in the air is stronger than the force of gravity". Tajinder saw the apogee as a point where force, rather than momentum, is momentarily zero, so "the force that it gained from being thrown up in the air, is like erm cancelled out by the force of gravity".
Neither Kabul nor Tajinder studied A level physics, and both held impetus notions that were counter to the tacit Newtonian framework underlying chemistry, and which – had they not been colearners in this study – could well have gone undiagnosed and remained unchallenged during their course.
§10.3: Equilibrium
Chemical structures, such as atoms, molecules and lattices, are understood to be stable as a result of the equilibrium of forces acting on their constituent particles.
Chemical processes may be understood to occur when this equilibrium is disturbed: that is bonds are broken and formed as a consequence of unbalanced forces acting. In organic chemistry the electrostatic nature of such forces is reflected in the terminology: electrophile, nucleophile, electron-rich etc. Again, however, this research suggests that the underlying assumption is not always shared by learners.
§10.3.1: Equilibrium without forces being balanced
When colearners were shown diagrams of stable systems (objects stationary on the ground, or on a table) they did not always recognise that there was an equilibrium of forces acting. Rather, several of the students took the view that the downward force due to gravity was the larger, or only force acting (see appendix 31, §A31.3.1). Two alternative notions were uncovered. One view was that no upward force was needed, as the object was supported instead, or simply that the object could not fall any lower as the ground was in the way. The other view was the downward force had to be greater to hold the object down: if it the forces had been balanced there would have been nothing stopping the object from floating away.
Colearners' failure to apply the curriculum science notions of equilibrium were also elicited in systems more central to the present thesis, that is chemical systems.
Application to the atomic nucleus. In Carol's third interview she suggested that the attraction holding the nucleus together had to be greater than any repulsions "otherwise it wouldn't be there. It wouldn't exist" (C3.71). In a similar vein, in Edward's first interview he explained that from an electrostatic perspective "the protons repel each other … in the nucleus" but he was able to explain the nuclear stability as "the force of repulsion, is less than the, gluing action of the neutrons" (E1.142), which suggested a non-equilibrium configuration.
Application to atomic structure. In Jagdish's third interview she was able to describe the interactions within an atom in terms of electrostatic charges. However, Jagdish thought that "the attractions are more stronger [sic] than the repulsions, and that's what's holding it together" (J3.A293). Later in the interview she reiterated that "the attractions from the nucleus, pulling in the electrons" were stronger than the repulsions (J3.A460). However the electrons did not fall into the nucleus as although "they're being attracted, … the attraction isn't … that strong" (J3.A463). Later she reiterates again that inside the atom "the attractions" are strongest (J3.A506).
Application to molecules. In the research it was found that a number of colearners thought that in a stable molecule the attractive forces must be larger than the repulsive forces (see appendix 31, §A31.3.2). One rationale for this (Edward, Lovesh) was that if the forces holding the molecule together were not stronger, then it would not be held together – a similar argument to that used in the case of objects on the ground (above). Other colearners (Jagdish, Kabul, Quorat) argued from an analysis of the components of the molecule that there would be more attraction than repulsion – although as such an analysis should not support the premise, this would seem to be a rationalisation of the students' beliefs.
Umar suggested that there was not a balance of forces, although in this case he did not suggest that the electrostatic repulsion was overcome by a larger attraction, but apparently by the effect of the full shells explanatory principle (which is discussed in chapter 11, §11.2), so that "there's repulsion between the two nuclei but the tendency of each of the nuclei to gain an electron to fill its outer shell is greater than the repulsion between the nuclei" (U4.A553).
Application to molecular shape. In the second term of her second year Jagdish was recorded (on audio tape) on two occasions discussing some examination questions with another colearner. One of the questions she was asked to discuss with Tajinder was about the shapes of molecules, and Jagdish started off by stating that "lone-pair – lone-pair repulsion is greater than lone-pair – bond-pair which is greater than bond- pair – bond-pair" (JT1.A079), whereas the actual molecular shape occurs when there is an equilibrium of forces (it is the angles for which 'lone-pair – lone-pair is greater than lone-pair – bond-pair which is greater than bond-pair – bond-pair'). The following day, in discussing another question about shapes of molecules with another colearner (Noor), Jagdish answers her own rhetorical question in the same terms, "okay what's the valence shell electron pair repulsion theory? Lone-pair – lone-pair repulsion is stronger than lone-pair – bond-pair, stronger than bond-pair – bond-pair" (JN1.A317).
In his end-of-first-year examination Kabul used the valence shell electron pair repulsion theory to explain the shapes of a number of molecules. However when discussing the case of ammonia he wrote that "as the repulsion betwn [between] Lone Pair : Bonding Pair > Bonding Pair : Bonding Pair a pyramidal structure is favoured" (A1 examination response, June 1993), i.e. the same mistake that Jagdish had made.
Application to ionic lattices. Carol explained, in her third interview, that whilst there were repulsions "between like charges" (C3.674) in sodium chloride, the structure does not fall apart because they have "gotta be less" (C3.676) than the attractions.
focal figure 5
Similarly, Jagdish thought that in the structure,
"there are repulsions, but they're not as great as the attractions, … there are some repulsions between the negative and this negative, that's why you … have alternate layers … [so that] they're not close enough to erm actually repel each other a great amount, so … to split the molecule [sic]."
J3.B263
For Jagdish the ions are "just stable in that configuration", in which "the attractions are stronger" (J3.B263).
In his first interview Kabul accepted that there was an "attraction force" (K1.A295) between two ions that were bonded, but he did not think there was any force between ions of similar charge (K1.A344). So at the start of the course Kabul's scheme included attractions, but apparently not repulsions. Later in the fourth interview Kabul was discussing focal figure 5, where he recognised there would be attractions and repulsions, but he thought "the forces of attraction is [sic] greater" (K4.A535).
In Umar's final interview, near the end of his A level course, he suggested that in sodium chloride (focal figure 5) the forces were not balanced, as "there are attractions between the sodium ions and the chloride ions, and, these attractions are more than the repulsions between the individual chloride ions and the sodium plus ions" (U4.A549).
Application to metallic structures. As I have just reported, when Kabul was discussing focal figure 5, he thought that "the forces of attraction is [sic] greater". However in response to questioning he changed this position, to accept that the forces had "balanced out themselves". However, Kabul did not transfer this argument to the metallic case, so when he was then asked about focal figure 6, Kabul suggested "the attraction is greater" than the repulsions (see appendix 31, §A31.3.3).
focal figure 6
focal figure 80
When Tajinder was shown focal figure 80 (meant to represent a metallic structure) his immediate analysis was that "the attractions seem [sic] to be stronger" (T1.B357).
Application to a simple molecular solid. In his third interview Tajinder seemed to suggest that, in a similar way, the van der Waals interactions in solid neon led to a non-equilibrium situation,
"when you have the neon nucleus it's attracting … all its electron towards it, but then once you get another neon atom it will attract the electrons from the other neon atom, and … I think the attraction of the nucleus is greater than the repulsion of the electrons."
T3.A557
Again Tajinder failed to appreciate the balance of forces in a stable structure.
§10.3.2: Equilibrium due to forces acting on different bodies
Another type of error that some colearners made during the study was to consider an equilibrium of forces possible when two forces acting on different bodies were equal.
So Quorat thought that the force on the earth from a falling apple could not be equal to the force acting on the earth else the "apple would stay where it was" (see appendix 31, §A31.3.4), whilst Tajinder suggested that the force upwards on the earth had to equal "the force of gravity" or else the earth would collapse (see appendix 31, §A31.3.5). In these two cases the colearners came to opposite conclusions by considering the effect of an equilibrium of forces (the force acting on the apple, the force acting on the earth) as if both forces acted on a single body.
Tajinder's alternative application of equilibrium was also seen in a number of other contexts (see appendix 31, §A31.3.6). So he considered the earth moon system to be stable because the earth was attracting the moon, which was balanced by the moon repelling the earth. He thought that if the moon had been larger than the earth then it would have repelled the earth away to a more distant equilibrium position. When considering a planet orbiting a star Tajinder thought there would be a balance between an attraction on the planet from the sun, and a repulsion from the planets to the sun. It is not possible to know the extent to which Tajinder's answers were based on long-held views about celestial mechanics rather than the ad hoc creation of an explanatory scheme constructed in the interview context. However, in either case, Tajinder did not seem to realise that his answers contravened fundamental principles of curriculum science.
§10.4: Reciprocity of force
In this section learners' alternative notions to newton-3 are considered. In the research it was found that forces were seen to act from one charged particle onto another, without the reciprocity (as required by newton-3). The 'reaction' forces might be absent, considered as negligible, of the wrong sign (i.e. an attraction paired with a repulsion), or wrong magnitude (i.e. the greatest force acting on the smaller particle).
§10.4.1: Designated forces
The term designated forces, from the work of Watts reported in chapter 3 (§3.1.3), is used where forces are associated with one body, rather than seen as an interaction between bodies. In this research it was found that learners often referred to forces as though they were a property of one body. This was considered to be significant because it is a perspective which logically allows the learner to make newton-3 errors, and to assume that a particular charge gives rise to a certain amount of force (alternative notions discussed below, §10.2.5, §10.3.)
For example Annie interpreted diagrams meant to represent the electron density distributions in bonds as force fields. She appeared to have a notion similar to the curriculum science concept of electric field strength, but not distinguished from force, so that "the force" or "the pull" from one atomic nucleus might not reach the adjacent atoms. She referred to the "electrostatic forces coming out from the … nucleus of the atom, which pulls the electrons in" (A3.6). For Annie this force originated "from the nucleus, … protons in the nucleus, make up a plus charge, which would draw the electrons in, by … electrostatic forces" (A3.8). Even at the end of her course she referred to how the nucleus would "contain the force … to pull the electrons towards it" (see appendix 31, §A31.4.1).
In Carol's first interview she referred to how an "aluminium [ion] has got more of an attractive force" than a potassium ion (C1.445), as though the force was associated with one species, rather than being an interaction. In the second interview she referred to the lithium iodide bond being polar because "one of them has got more … attractive force, over the other one" (C2.277), in contravention to newton-3, as she was designating forces to single bodies, rather than to the interacting system.
Tajinder referred to a single central attraction from the nucleus of an atom to the electrons. When Tajinder was asked about the repulsions in the system he did not construe force to be an interaction between two bodies, asking if he should count the repulsion between two electrons twice – once in each direction. He suggested ionisation energy was "to do with … how much force the atom has at attracting that electron". This is another example of a force being designated to one part of an interacting system (see appendix 31, §A31.4.2).
§10.4.2: The paired force is absent
During the study a number of examples of learners not recognising the presence of a 'reaction force' were elicited. Some of these examples originated in the context of macroscopic situations, and some in the context of atomic and molecular interactions.
When asked about an apple falling to the ground both Kabul and Noor thought there would be no force acting on the earth (see appendix 31, §A31.4.3). Noor thought that gravity only acted on the smaller body, so "the apple gets pulled by the earth, because it's, it's, it's of a greater mass, it's larger in size than the apple is".
Kabul did not recognise an attractive force acting on the earth in the cases of objects resting on the ground. When a 'massive object' rested on a table Kabul identified a downward force on the table from the object, but not the 'reaction' force (see appendix 31, §A31.4.4).
focal figure 1
focal figure 63
When in her last interview Annie suggested that a nucleus would attract an electron more than vice versa (see below), by way of an analogy the – presumed more familiar – Earth-Sun system was introduced into the discussion. However it transpired that Annie was "not really very up on astronomy" (A4.255). Annie "suppose[d] there must be" (A4.261) a force from the Sun to the Earth, although she had "never really thought about it" (A4.263), and did "not really" (A4.267) think that the Earth attracts the sun, "due to size" because "if you look at the size of the earth compared to the sun, it's such a dot, there's not really any way that the earth's going to attract, the sun" (A4.267).
Similarly, when Kabul considered focal figure 63 which represented a simple solar system, he thought there would be a force acting, that "just attracts the planets towards the sun" (K3.B066), but the sun would not experience any force (K3.B071), another example of his failure to apply newton-3. When discussing focal figure 1 in the fourth interview, near the end of the first year of the course, Kabul agreed that there was a force on the outermost electron due to the charge on the nucleus (K4.A132), but he did not think there was any force on the nucleus, due to the electron (K4.A143). Kabul agreed this was a one-way process, (K4.A143), yet another example of what I am labelling a newton-3 error.
Kabul was asked about the case of the hydrogen atom (where the electron and nucleus have charge of equal magnitude), where he suggested that there was a force acting on the electron, and "theoretically there should be" a force acting on the nucleus, but he did not think there was (K4.A202). This was followed by laughter from Kabul, and after a pause – while Kabul thinks about the problem for about seventeen seconds – he accepts "all right there will be, there will be a force on nucleus also" (K4.A202), and "in that case it would be equal" (K4.A210). Presumably Kabul had metacognitive awareness that he could not justify his belief, that his 'intuition' and 'learning' were in contradiction.
In Lovesh's third interview, near the end of his first year, he was asked about the forces between the constituent particles in an atom. The extract below shows how he was immediately able to discuss the force acting on an electron, but is nonplused by a question about the force acting on the nucleus.
Although Lovesh eventually decides the nucleus is attracted to the electrons, it is as if the question about the force acting on the nucleus is totally incomprehensible – perhaps something Lovesh has never considered. Indeed the question is asked four times before Lovesh offers an opinion. Apparently, reciprocity of forces is not an intuitive notion for this colearner.
I: Do you think there's any force on that electron holding it in that position, keeping it in the atom?L: Yes, the nucleus attracts all the electrons as well as [i.e. not just] the one, the valence electron.
I: I see. So is there an equal force on all the electrons?
L: No. The valence electron, there is less force because the distance between the nucleus and the electron is greater than the other shells.
••
I: Right, is there any force on the nucleus there, do you think?
• • • • • [pause, c.5s]
L: What do you mean?
I: Well, this electron apparently experiences a force from the nucleus,
L: Yeah.
I: is there any force on the nucleus, does it experience [sic] any force, or any forces?
• • • • [pause, c.4s]
L: Erm.
• • • [pause, c.3s]
L: Don't know.
I: For example, er, does this electron attract the nucleus, as well as being attracted by it?
• • • • • • • • [pause, c.8s]
L: I don't understand what you mean {laugh}
I: Okay. Is this is this electron attracted by the nucleus?
L: Yeah.
I: Is this electron attracted by the nucleus?
L: Yeah.
I: Is this nucleus attracted by this outer electron?
• • • • • • • [pause, c.7s]
L: I think so, yeah.
I: What about by this inner electron, is it attracted by that one?
• • • • [pause, c.4s]
L: Yeah it's, I think it's attracted by all of them.
L3.A189
Quorat was another colearner who knew electrons were attracted towards the nucleus, but did not think this was reciprocated. In Quorat's first interview for the research she discussed the hydrogen molecule (focal figure 2), and initially did not think there was any force acting on the nuclei,
I: Is there any force on the nuclei?
Q: It's positive. But there's no, no outer force acting on it.
I: No outer force?
Q: No.
I: So the only force, … in that diagram, the force from the nuclei to the electrons?
Q: Well yeah, there's, it's just a positive nucleus that, that's attracting the electrons.
I: So both those electrons are attracted by both positive nuclei?
Q: Yeah.
I: Yeah?
Q: Mm.
I: But there's no force on the nuclei?
Q: No.
I: The force is acting on the electrons?
Q: Uh hm.
I: So, the electrons don't put [sic] a force on the nucleus, it works the other way round?
Q: Yeah.
Q1.A159
So Quorat did not think the force was a reciprocal interaction. Yet, when she started to think about why the molecule did not fall apart, she changed her mind,
"The electrons are pushed apart, but because that electron, this electron is attracted to that [nucleus], and that one to that, like they're both attracted, both the electrons are attracted to both the nucleuses [sic], so therefore they are kept together. … That means that, really there is a force of the electrons that is keep¬ that is acting on the nucleus."
Q1.A177
However, when a little later in the interview Quorat considered focal figure 1 she she thought that in the sodium atom, all the electrons were attracted to the nucleus (Q1.A230), but this was not reciprocated,
I: So all of those are attracted to the nucleus.
Q: Uh hm.
I: Is the nucleus attracted to anything?
Q: No.
…
I: … there's no force on the nucleus itself?
Q: No.
Q1.A230
Two other examples that were elicited were where Annie suggested that in lithium iodide the iodine was pulling the lithium more than vice versa (see appendix 31, §A31.4.5), and when – at the end of his course – Kabul described hydrogen bonding in hydrogen fluoride as a one way action of the fluorine on one molecule attracting the hydrogen on another, as the charge on the hydrogen was "too small to attract" the seven valence electrons of the fluorine (see appendix 31, §A31.4.6).
§10.4.3: The paired force has the wrong direction
In Tajinder's second interview he described how in the earth-moon system there would be "a gravitational force from the earth which is pulling the moon, towards it, … and there's also a force from the moon which is repelling the earth away from itself" (T2.B344). Similarly in a solar system he thought that the sun would attract the planets, but was being repelled by them (see appendix 31, §A31.4.7). It seems clear that for Tajinder, at this point in his course, the 'reaction' to an attraction could be a repulsion.
This type of 'error' was also found in the interviews with other colearners. In Annie's first interview she was asked if she knew how the protons and neutrons in the nucleus were held together. She suggested that "forces from the outer ring" (A1.27) were "pushing them" (A1.29). In her second interview Annie suggested there could be some kind of symmetry: "something to do with, 'cause the nucleus pulls in the electrons, so [I don't know] if the electron forces actually help bind the nucleus, in any way" (A2.8). Annie's comments here were tentative, as she was quite clear that she did not know what held the nucleus together, but her suggestion would have required an attraction (on electrons from the nucleus) to have been paired by a repulsion (on the nucleus from the electrons.) At the end of the third interview Annie was asked if the atomic nucleus was attracted by the atomic electrons. Annie thought "no, but, saying that I'll probably go home and somebody's probably discovered that it is" and went on to report that "obviously the electrons … may sort of control what's actually happening in the nucleus. Sort of … holding the neutrons and the protons together" (A3.491). Although Annie's comments were tentative, her idea recurred at three stages of her course, and it demonstrated that she did not see a difficulty in this type of violation of newton-3.
Carol also attempted to use electrostatic interactions to explain nuclear binding, in her second interview. She knew some explanation was needed as "you would think that a nucleus wouldn't, wouldn't be there really because, it's all protons and they [should] repel, 'cause they're the same charge" (C2.33). Carol thought the protons would repel "but, there's another force, might be to do with electrons around the outside that holds it together … acting from outside" (C2.40-4).
In appendix 3 there is a description of a questionnaire which was written to diagnose some of the aspects of learners' explanation elicited in this study: the truth about ionisation energy diagnostic instrument. This questionnaire was presented to over one hundred A level chemistry students who had studied the topic of ionisation energies. The students were shown focal figure 1, and asked to suggest whether various statements relating to the figure were true or false (see the appendix for details). It was found that 60% of respondents agreed that "electrons do not fall into the nucleus as the force attracting the electrons towards the nucleus is balanced by the force repelling the nucleus from the electrons", a statement which not only has an attraction paired with a repulsion, but also suggests an equilibrium due to forces acting on different bodies (as discussed above, §10.3.2). If the findings from this small scale and unrepresentative survey may be taken as indicative, then it would seem that the beliefs of the colearners in the interview study about the relative directions of 'action-reaction' forces may be shared by a significant proportion of A level chemistry students.
§10.4.4: The paired force has the wrong magnitude
In §10.4.2, above, several examples were presented where colearners suggested that a larger body will exert a force on smaller body, but not vice versa. There were also many examples in the research of colearners acknowledging the reciprocal nature of forces between bodies, but believing that the larger body exerted the larger force. So in Tajinder's second interview he recognised that in the context of a falling apple there would be a gravitational force pulling the apple downwards, and an upwards force on the Earth. However, Tajinder thought that "the force pulling the apple downwards" was the larger force (T2.B110).
Similarly Quorat thought that the Earth exerted a larger force on objects than they would exert on it. Quorat justified her belief that the force on the smaller object is greater by, in the case of a falling object, the fact that the object falls and does not stay still; and conversely in the case of an object on the ground, that the object stays still and does not float away (see appendix 31, §A31.4.8).
Quorat applied similar ideas to astronomical systems so the Earth exerted more force on the moon (than vice versa), and the sun exerted more force on the planets (than vice versa) (see appendix 31, §A31.4.9).
Tajinder also thought that the relative sizes of the two forces were related to the relative sizes of the earth and moon, so in his scheme, as long as the earth was larger than the moon "the earth would still have the gravity, and it would pull, the moon towards it", whereas if the moon were bigger then "the force of the moon repelling the earth would be larger than the attraction", and if the earth and the moon were the same size "the forces between the two would be equal" (T2.B374).
Both Tajinder and Quorat applied similar ideas in the context of electrostatic forces, and thought that the force between two electrically charged bodies would be greater on the body with the smaller charge (see appendix 31, §A31.4.10). When colearners were asked about atomic systems it was common to find the suggestions that although the nucleus experienced a force due to an electron, this was much less than the force experienced by the electron due to the nucleus (see appendix 31, §A31.4.11). So Quorat reports "the force due to the nucleus on the electrons is greater", and Kabul went further, suggesting that "even if there is some force [on the nucleus] it's just negligible". The rationale behind this view seemed to be that a nucleus was larger than an electron, either in terms of mass ("the nucleus is a larger mass than the electron", Noor; electrostatic force on the nucleus is "negligible, because the electron has such a small mass", whereas "the pull is greater towards the nucleus because it's so much bigger", Jagdish), or in terms of the charge ("the nucleus is attracting the electron, more than the electron is attracting the nucleus, because the nucleus will have a greater charge", Paminder). The literature reviewed in chapter 3 (§3.1.3) suggests that the apparent distinction may not be too significant as learners commonly fail to clearly distinguish between the basic categories of physics. The importance assigned to the magnitude was made explicit by Kabul who claimed that "a small charge of minus one … can't attract … plus eleven, as plus eleven can attract minus one".
In two cases the general 'rule' that the nucleus attracted the electrons more was carried over to the case where there was equal charge on the positive nucleus and negative electron (i.e. the hydrogen atom). In Annie's final interview she suggested that the force on the nucleus would be less than the force on the electrons, and extended this to the case of hydrogen, where "although they they're of similar charge, it seems to be convention that that's the way that … the force goes" (A4.245). Annie also demonstrated that she thought the larger component of a system would exert more force in the context of lithium iodide and potassium fluoride (see appendix 31, §A31.4.12).
In the other case Quorat thought that "the force on the negative" would be a larger, although she could not give any reason, and admitted that she was not sure. (Q2.B439).
In her third interview near the end of the academic year Quorat made a similar comment about the hydrogen molecule (focal figure 2) where she thought that "the electrons will probably tend to pull the nucleus towards themselves, but because the nucleus is much bigger, it can pull the electron towards itself" (Q3.A151). When questioned, Quorat accepted that, in this particular case, the force on the electron from a nucleus, and the force on the nucleus from the electron were "about the same", but in general she thought that "it depends on … what charge the nucleus has, … if the overall core charge of the nucleus is greater, then it will have a greater force" (Q3.A151).
Quorat's language implies designated forces (as discussed above, §10.4.1). Such a belief appears to imply that the charged particles will experience a different size force, as the force is not seen as arising from the mutual interaction, but is associated with one charge as agent, and another as subject,
I: So if you had an atom where the core charge was, let's say, plus seven,
Q: Mm.
I: and there was an electron in the outer shell being attracted to that core,
Q: Yeah.
I: is the core also being attracted to the electron?
Q: Yeah.
I: Which is stronger?
Q: The attraction of the electron towards the nucleus.
I: Is that a greater force?
Q: Yeah.
Q3.A151
In appendix 3 there is a description of a questionnaire which was written to diagnose some of the aspects of learners' explanation elicited in this study: the truth about ionisation energy diagnostic instrument. This questionnaire was presented to over one hundred A level chemistry students who had studied the topic of ionisation energies. The students were shown focal figure 1, and asked to suggest whether various statements relating to the figure were true or false (see the appendix for details).
53% of the respondents made the newton-3 error of agreeing with the statement "the force on an innermost electron from the nucleus is greater than the force on the nucleus from an innermost electron", and 41% agreed that "the force pulling the outermost electron towards the nucleus is greater than the force pulling the nucleus towards the outermost electron". 35% of the respondents thought the statement "the force on an innermost electron from the nucleus is equal to the force on the nucleus from an innermost electron" was false. If the findings from this small scale and unrepresentative survey may be taken as indicative, then it would seem that the beliefs of the colearners in the interview study about the relative sizes of 'action-reaction' forces in the atom may be shared by a significant proportion of A level chemistry students.
§10.5: The notion of 'conservation of force'
I:Right, so what are you saying about the amount of force that the nucleus can give out?
T: It's, it's erm, spread over the number of electron there are. That's what I'm saying.
…
I:So if you've got an extra electron, the nucleus can't just give out extra force?
T: Not if the charge hasn't gone up by one.
I:Right, so a certain charge on the nucleus, implies there's a certain amount of force available,
T: Yeah.
I:And if you increase the number of electrons, you therefore … decrease the amount of force each one gets?
T: Erm, yeah.
I:Kind of 'conservation of force principle'
T: Yeah.
T7.A559
In this study it was found that nuclei were often considered to give rise to a fixed amount of attraction – depending upon charge – which would be shared amongst the electrons available to receive it. In the segment of transcript quoted in the motto above I suggested to colearner Tajinder that he was using a 'conservation of force principle' and he concurred. I have retained this term.
§10.5.1: The conservation of force explanatory principle
The notion of conservation of force was commonly used as an explanatory principle by the colearners in the research. The idea of the nuclear force being used up arose in the final interview with Annie, where her understanding of the shielding concept was being probed. Rather than explaining the effect of core electrons as being to repel the valence electrons, and thus partly counter the effect of the nuclear force, Annie thought,
"they'll cut down the amount that it's being pulled towards the nucleus because it's being sort of, they're being pulled in before. So, the actual pull on the outer electron will be less than what's in between"
A4.511
Annie agreed with my interpretation of her comments, that the nucleus has a certain pulling power, and that because it's using some of that up, pulling in the core electrons, by the time it gets to the valence shell, it hasn't got much left (A4.516).
focal figure 68
focal figure 75
Tajinder appeared to hold similar notions. In his second interview, he considered focal figure 68, and recognised that there would be a stronger force of attraction in focal figure 68 part (b), than in part (a), because the distance between the positive and negative particles is smaller (T2.B515). However, when he was subsequently shown focal figure 75 he thought that all the electrons would be attracted equally (T2.C056). It would seem that Tajinder's recognition that charge separation is important was not elicited in the more complex atom-like structure where the nucleus was attracting many electrons. (The difference could be related to a number of factors: the larger number of charged particles, the atom-like configuration, or the identification of the constituents as electrons and a nucleus rather than abstract charged particles.)
In his fourth interview Tajinder compared the metallic bonding in lithium and sodium. His explanation of the difference in melting temperatures included a reference to the shielding electrons in sodium containing the force, that in sodium "there's more surrounding electrons to like contain the force because they [nuclei] attract them electrons." Tajinder though that in sodium "those ten electrons … sort of block out … like equal out the core charge" (T4.A289). It would appear that in an atom-like system the nucleus is assumed to have some sort of inherent attracting power, which may be considered to be used-up electron by electron.
In Mike's first interview he made a fairly explicit statement of the conservation of force explanatory principal. He explained that he thought that the size of the nucleus-electron attraction depended upon, "whether there was enough electrons to fulfil the attraction of the positive. … a single proton attracts a single electron, a one-on- one basis, … when you've got two electrons to one proton, they're both attracted, but not as much" (M1.A257).
focal figure 2
In Kabul's fourth interview he also gave an explicit example of the application of the conservation of force explanatory principle. He was discussing focal figure 2, where both electrons were being attracted to both nuclei. He thought that in the molecule the force on an electron due to one nucleus, when compared to the force it would have experienced in a single hydrogen atom, was less: "it will experience less force now, because the nucleus [is] attracted to a cloud of two electrons, so the force, you know, divides" (K4.A283). So Kabul thought there was "less force going towards that electron" although the total force due to the nucleus was "the same". There was the same amount of force as before, but in the molecule it was shared amongst two electrons (K4.A293).
Umar applied a similar logic to considering the force acting in a hydrogen molecule. He thought that in a single hydrogen atom there would be a force between the nucleus and electron, and "it will be an attraction, of plus one" (U3.B341). When he compared this with the force acting between one nucleus and one electron in the molecule he thought there would be less force in the molecule than the atom as "the single one [the atom] would have more effect on the single electron because one plus can be for the one minus electron, but here in this [the molecule], in where it's bonded, like, the nucleus, the same charge, one plus, is acting on two electrons, each of one minus, so it'd be less" (U3.B347). To make sure that I had understood Umar's meaning, I spelt out my interpretation for him,
I: …if I try and paraphrase what you're telling me, you tell me if I've sort of got this right > or not, >
U: < Mm. <
I: erm, [U]. Erm, in this covalent bond the electrons are being shared, between the two atoms
U: Yeah.
I: But in a sense also, this nucleus is in a sense being shared by these two electrons.
U: Yeah.
I: And therefore it's got less force available to give either of them in¬ independently,
U: Yeah.
I: even though the total force might still be the same?
U: Yeah.
I: Because it's only got a one plus charge and it has to kind of share that between the two electrons.
U: Yeah.
Whereas in a single atom that one-plus charge was all available to one electron.
U: Yeah.
U3.B357
§10.5.2: Applications of the conservation of force explanatory principle to ionic size
Some of the colearners seemed to apply a similar principle when explaining why cationic radii are smaller than atomic radii. For example, in a test answer Jagdish suggested that "because the core charge of the Al [aluminium ion] has less electrons to pull in, it can pull in more tightly" (assessment response, March 1993). Similarly, in her end-of-first-year-examination, Jagdish explained the greater size of the fluorine anion compared to the atom partly in terms of "more repulsion", but she also suggested "because of the extra electron … the core charge cannot pull on the electrons as tightly". Lovesh's explanation for why the fluoride ion was larger than the potassium ion was partly in terms of the repulsion between electrons in the fluoride ion, but also in terms of the increased attraction acting on the potassium electrons – that potassium had "lost an electron and so the effective nuclear charge … attracts the electrons in more closer" (L4.A371).
Both of these examples from colearners are ambiguous, in that they could be read as just clumsy phrasing. However the following two explanations of changes in radius on forming an ion (from incidental data collected from other students) are more explicit in their use of conservation of force as an explanatory principle,
"the radius will become smaller when an electron is taken away from outer shell because the nucleus's attraction will have more effect ie/ it's force will be distributed amongst less atoms [sic, electrons]."
End-of-first-year examination response, June 1994.
"As the ion has an extra electron in its valent shell means the core charge, which remains the same, has to spread its attractive forces equally to each electron thus resulting in less attractive forces on each valent electron and larger atomic radius."
End-of-first-year examination response, June 1994
§10.5.3: Applications of the conservation of force explanatory principle to ionisation energy
The topic that provided the richest evidence of colearners applying a conservation of force explanatory principle was patterns in ionisation energies (an important part of the study of periodic trends in chemistry). It was in an attempt to understand this topic that Tajinder used his conservation of force explanatory principle when he was discussing atomic energy levels during interviews in his first year (see appendix 31, §A31.5.1). In his sixth interview he considered how the energy levels of electrons in the helium atom, and helium cation might compare. Tajinder thought that the energy level would be different "because in the ion, the two proton's are only attracting one electron, but in [the atom] they're they've got two electrons to attract, so therefore like sort of their attraction is like spread out over two instead of one". In the following interview he repeated his idea, that "the protons only have … one electron to attract, in helium ion, [whereas in] helium atom they've got two electrons to attract". So the force from the nucleus was "spread over the number of electron there are". It was explained to Tajinder that force was not conserved in this way, but that the ionisation energy of the atom would be less due to repulsion between the two electrons. Tajinder accepted this at the time, but later, when the second and third ionisations of lithium were considered, his initial tendency was still to think in terms of force conservation.
Similar reasoning was applied to this topic by other colearners. For example when Rhea attempted to explain the pattern in the successive ionisation energies of magnesium in an assessment, her response included two phrases that seemed to imply she was applying the conservation of force principle,
"Then once that shell [the L shell] has been emptied, again you have to break into another shell, but by this time you have an ion with +10 charge, holding 2 electrons. so the nucleus has the two protons keeping the electron attracted to the nucleus, and also a spare 10 protons left over from the 10 electrons removed. to hold the 2 electrons very tightly so as well as having to break in to a new shell of electrons, it has to break into a shell with a +6 charge for each electron that is to be removed. so alot [sic] of ionisation energy is required to remove the final two electrons."
Response to assessment question, March 1993
Rhea seems to have thought that each proton gives rise to a certain amount of force, sufficient to attract one electron under normal conditions. Thus the removal of ten electrons gives an ion which has "10 spare protons", which can be redistributed to give "a +6 charge for each electron".
In response to the same question Jagdish wrote that
"there is a slight increase in I.E. [ionisation energy] when the second electron is removed because although the core charge doesn't change, because there is one less electron the positive nuclear charge can pull on the electrons a little more, slightly decreasing the atomic radius [therefore] more energy is needed to remove it".
Response to assessment question, March 1993
She also wrote that when electrons were removed from the second shell
"there is a slight increase in energy needed because again although at the same energy level the core charge can pull in more tightly each time an electron is removed and reduce the radius"
Response to assessment question, March 1993
Jagdish's answers seem to imply that having fewer electrons to attract is itself a cause of greater attraction to the nucleus.
In Tajinder's fifth interview he attempted to explain the difference in first ionisation energies for beryllium and magnesium. His explanation was complex, and included valid electrostatic considerations, but part of his reasoning was that "there's more electrons in the magnesium atom, … and therefore the core hasn't got as much attraction to the outermost electrons because there's more electrons to attract, and therefore the amount of energy you need is less than beryllium" (T5.A085).
Another suggestion of this notion may be detected in Kabul's discussion with Mike about ionisation energies, when Kabul comments that "as we start removing the electrons, you know the net nuclear charge acting on the remaining electrons will increase" (KM1.29). In his final interview Kabul explained that when the outermost electron was removed from a sodium atom the force acting on the remaining electrons "would be more compared to before" (K6.A132), "because there are eleven protons in the nucleus, you know, holding ten electrons, so there would be more force, but before there were, you know, eleven protons and eleven electrons, so the force divides" (K6.A136).
If a second electron was removed, the force on those remaining increased again (K6.A139), and if all but one electron was removed the force on that one electron would be "much more", indeed Kabul thought it would be "probably more than" twice as much, and perhaps ten, eleven or twelve times as much (K6.A143). He thought he could work out the force on an electron using "Coulomb's law, and … measure the distance, and … just bung it in the formula and you know the force" (K6.A153). Kabul thought he could carry out the calculation for the electron when in a sodium atom, and repeat the calculation for the situation when it was the only electron, and he would get a bigger answer (K6.A161). It would appear that even when Kabul had available the appropriate curriculum science tools to analyse such a situation, his preexisting intuitions about force and charge took precedence in his thinking.
Lovesh also retained the conservation of force explanatory principle through his course, and in his final interview he suggested that if the outer electron was removed from a sodium atom the other electrons would "be attracted even more" (L4.A130). His reasoning was based on the amount of positive charge in the nucleus compared to the number of electrons being attracted "because now the … number of electrons is less than the number of protons, so there's overall more positive charge in the middle so that attracts them even more" (L4.A130).
Umar also seemed to apply the conservation of force explanatory principle in his explanations of ionisation energy throughout his course (see appendix 31, §A31.5.2). So Umar's response to an assessment question on ionisation energies shortly after being taught about the topic suggested he also thought in terms of nuclear charge being shared between the electrons. Umar had drawn an appropriate diagram for the successive ionisations of magnesium, but his explanation of this pattern included both points which would be judged valid from a curriculum science perspective, and several references to the core charge being shared amongst the electrons present. In all there are four references to the increasing share of core charge that a smaller number of electrons experience (the 3s1 electron "has slightly more nuclear charge action[sic] on it once the 3s2 electron has been removed"; "as once each previous electron is removed there is greater attraction by the nuclear charge on the remaining electrons, so the same nuclear charge is pulling on less no. of electrons"; "there is a greater core charge pulling on less electrons"; "once the [1s2 electron has been removed] there is increased core charge attraction to the 1s1 electron").
Near the end of the first year of his course Umar suggested that because an anion had more electrons than protons "each electron's got less charge on it overall from the core charge" (U3.A212). In a neutral atom the "charge on the nucleus to [a specific] electron" would be "plus one", because "effectively it's like one plus to each electron", however if an electron were removed then "the same positive charge is acting on a less number of electrons". In a Na9+ ion "there's an eleven plus charge, on two electrons" and so "effectively five and a half, positive to one minus electron", and in the Na10+ ion "they'd be eleven plus on the one electron" and so a "much stronger force". In the end-of-first-year examination Umar wrote that "once the 1st electron is removed [from a magnesium atom] there is increased pull from the nucleus on the 2nd electron as it is the only one in that shell" (A1 examination response, June 1993). Even at the end of his A level course Umar explained increasing successive ionisation energies as due to "the same nuclear charge pulling on less electrons so there's a greater electrostatic force … each time". So when a sodium atom was ionised,
"they'll be ten electrons and eleven-plus nuclear charge so they'll be attracted more, because the same positive charge pulling on less electrons, so, it's more on each electron [as] the amount of energy [sic] that that nuclear charge used in pulling that outer electron which is one, po¬ one plus, is like distributed across the other remaining electrons, that same energy"
U4.A089
So according to Umar's understanding, when one electron was removed from the sodium atom the nucleus "just attracts [the remaining electrons] more. What it would have used to attract the [eleven] electrons it uses to attract the remaining ten" (U4.A102). If a second electron was removed "then there'll be the same nuclear charge pulling on the remaining nine electrons so it'd be stronger even more" (U4.A110). Each time an electron was removed "there's a stronger nuclear charge on the electrons" (U4.A115), until when only one electron remained "it'd be attracted much more stronger, 'cause there'd be plus-eleven charge pulling on only one electron" (U4.A120).
§10.5.4: The conservation of force explanatory principle as a common notion
Incidental data collected from other chemistry students includes explanations that are similar to those from the colearners in this study, and suggest that the conservation of force explanatory principle may be more widely applied. The following examples concern the ionisation of magnesium, and are quite explicit in suggesting that the force of the nucleus is shared amongst the electrons present,
"When an electron is removed the effective core charge is shared out between 1 less electron therefore increasing the energy needed to remove another electron."
End of first year examination response, June 1994
"The loss of one electron has meant the remaining electrons receive the lost electron[']s share of the attraction to the centre so the valence shell is pulled more tightly in to the centre. This requires more energy to free the second electron from the valence shell hence the rise in ionisation energy."
End of first year examination response, June 1994
"Once the first electron is removed, the nuclear charge is no longer shared amongst two valence electrons, but one. There is a stronger attraction which means more energy is needed to remove it."
End of first year examination response, June 1994
In appendix 3 there is a description of a questionnaire which was written to diagnose some of the aspects of learners' explanations elicited in this study: the truth about ionisation energy diagnostic instrument. This questionnaire was presented to over one hundred A level chemistry students who had studied the topic of ionisation energies. The students were shown focal figure 1 (representing a sodium atom), and asked to suggest whether various statements relating to the figure were true or false (see the appendix for details).
Most of the respondents, 72%, agreed that "the eleven protons in the nucleus give rise to a certain amount of attractive force that is available to be shared between the electrons" was true. Almost as many, 69% of respondents, agreed that "if one electron was removed from the atom the other electrons will each receive part of its attraction from the nucleus", and a similar proportion, 70%, agreed that "the third ionisation energy is greater than the second as there are less electrons in the shell to share the attraction from the nucleus". An even greater proportion, 79%, agreed that "after the atom is ionised, it then requires more energy to remove a second electron because once the first electron is removed the remaining electrons receive an extra share of the attraction from the nucleus". 74% of respondents agreed with the statement "the force attracting the electrons in the first shell towards the nucleus would be much greater if the other two shells of electrons were removed". If the findings from this small scale and unrepresentative survey may be taken as indicative, then it would seem that the conservation of force explanatory principle may be shared by a significant proportion of A level chemistry students.
The present research may be seen to suggest that learners studying A level chemistry may not only designate forces to specific charged particles, but may see the magnitude of the designated force as being proportional to the particle's charge, and therefore being shared amongst whatever oppositely charged particles are construed as being attracted.
