How much damage can eight neutrons do?

Scientific literacy and desk accessories in science fiction

Keith S. Taber


Is the principle of conservation of mass that is taught in school science falsified all the time?


I am not really a serious sci-fi buff, but I liked Star Trek (perhaps in part because it was the first television programme I got to see in colour 1) and I did enjoy Blakes7 when it was broadcast by the BBC (from 1978-1981).



Blakes7 was made with the same kind of low budget production values of Dr Who of the time. Given that space scenes in early episodes involved what seemed to be a flat image of a spacecraft moving across a star field with no sense of depth or perspective (for later series someone had built a model), and in one early episode the crew were clearly given angle-poise lamps to control the craft, it was certainly not a case of 'no expense spared'. So, it was never quite clear if the BBC budget had also fallen short of a possessive apostrophe in the show title credits or Blakes7 was to be read in some other way.

After all, it was not made explicit who was part of Blake's 7 if that was what the title meant, and no one referred to "Blake's 7" in the script (perhaps reflecting how the doctor in Dr Who was not actually called Dr Who?).


The Blakes7 team on the flight desk of the Liberator – which was the most advanced spaceship in the galaxy (and was, for plot purposes, conveniently found drifting in space without a crew) – at least until they forgot to clean the hull once too often and it corroded away while they were on an away mission.

Blake's group was formed from a kind of prison break and so Blake was something of a 'rough-hero' – but not as much as his sometime unofficial lieutenant, sometime friend, sometime apparent rival, Avon, who seemed to be ruled by self-interest (at least until the script regularly required some act of selfless heroism from him). 'Rough-heroes' are fictional characters presented in the hero role but who have some traits that the audience are likely to find morally questionable if not repugnant.

As well as Blake (a rebel condemned as a traitor, having 'recovered' from brainwashing-supported rehabilitation to rebel again) and Avon (a hacker convicted of a massive computer fraud intended to make himself extremely rich) the rest of the original team were a smuggler, a murderer and a petty thief, to which was added a terrorist (or freedom fighter if you prefer) picked up on an early mission. That aside, they seemed an entirely reasonable and decent bunch, and they set out to rid the galaxy of 'The Federation's tyrannical oppression. At least, that was Blake's aspiration even if most of his companions seemed to see this as a stop-gap activity till they had decided on something with more of a long-term future.

At the end of one season, where the fight with the Federation was temporarily put aside to deal with an intergalactic incursion, Blake went AWOL (well, intergalactic wars can be very disruptive) and was assumed dead/injured/lost/captured/?… for much of the remaining run without affecting the nature of the stories too much.

Among its positive aspects for its time were strong (if not exactly model) roles for women. The main villain, Servalan, was a woman – Supreme Commander of the Federation security forces (and later Federation president).


As the ruthless Supreme Commander of the Federation security forces, Servalan got to wear whatever she liked (a Kid Creole, or Mel and Kim, look comes to mind here) and could insist her staff wore hats that would not upstage hers

In Blake's original team (i.e., 7?), his pilot is a woman. (Reflecting other SciFi series, the spacecraft used by Blakes7 require n crew members to operate effectively, where n is an integer that varies between 0 and 6 depending on the specific plot requirements of an episode.) In a later series, after Avon has taken over the role of 'ipso facto leader-among-equals', the group recruits a female advanced weapons designer/technologist and a female sharpshooter.


The Blakes7 team later in the run. (Presumably they are checking the monitor and having a quick recount.) Was Soolin (played by Glynis Barber, far right) styled as a subtle reference to the 'Seven Samurai'?

When I saw Blakes7 was getting a rerun recently I re-watched the series I had not seen since it was first aired. Despite very silly special effects, dodgy story-lines, and morally questionable choices (the series would make a great focus for a philosophy class) the interactions between the main characters made it an enjoyable watch.

But, it is not science

Of course, the problem with science fiction is that it is fiction, not science. Star Trek may have prided itself on seeking to at least make the science sound feasible, but that is something of an outlier in the genre.

Egrorian and his young assistant Pinder (unfortunately prematurely aged somewhat by a laboratory mishap) show Avon and Vila around their lab.

This is clear, for example, in an episode called 'Orbit' where Avon discuses the tachyon funnel, an 'ultimate weapon', with Egrorian, a renegade scientist. Tachyons are hypothetical particles that travel faster than the speed of light. The theory of special relatively suggests the speed of light is the theoretical maximum speed anything can have, but some other theories suggest tachyons may exist in some circumstances. As always in science, theories that are widely accepted as our current best understanding of some aspect of nature (e.g., relativity) are still open to modification or replacement if new evidence is found that suggests this is indicated.

In the Blakes7 universe, there seemed to be a surprisingly high frequency of genius scientists/engineers who had successfully absconded from the tyrannical and paranoid Federation with sufficient resources to build private research facilities on various obscure deserted planets. Although these bases are secret and hidden away, and the scientists concerned have normally been missing for years or even decades, it usually transpires that the Blakes7 crew and the Federation manage to locate any particular renegade scientist during the same episode.

This is part of the exchange between this particular flawed genius scientist and our flawed and reluctant 'rough hero', Kerr Avon:

Egrorian: You've heard of Hoffal's radiation?

Avon: No.

Ah… Hoffal had a unique mind. Over a century ago he predicted most of the properties that would be found in neutron material.

Neutron material?

Material from a neutron star. That is a… a giant sun which has collapsed and become so tightly compressed that its electrons and protons combine, making neutrons.

I don't need a lecture in astrophysics. [But presumably the scriptwriter felt the audience would need to be told this.]

When neutrons are subjected to intense magnetic force, they form Hoffal's radiation. Poor Pinder [Egrorian's lab. assistant] was subjected for less than a millionth of a second. He aged 50 years in as many seconds. …

So neutrons are part of the tachyon funnel.

Um, eight of them … form the core of the accelerator. 

From the script of 'Orbit' (c) 1981 by the British Broadcasting Corporation – made available 'for research purposes'

Now, for anyone with any kind of science background such dialogue stretches credibility. Chadwick discovered the neutron in everyday matter in 1932, so the neutron's properties could be explored without having to obtain samples from a neutron star – which would certainly be challenging. When bound in nuclei, neutrons (which are electrically neutral, thus the name, and so not usually affected by magnetic fields) are stable.

Thinking at the scale of a neutron

However, any suspension of disbelief (which fiction demands, of course) was stretched past breaking point at the end of this exchange. Not only were the generally inert neutrons the basis of a weapon that could destroy whole worlds – but the core of the accelerator was formed of, not a neutron star, nor a tonne of 'neutron matter', but eight neutrons (i.e., one for each member of Blake's 7 with just a few left over?)

That is, the intensely destructive beam of radiation that could destroy a planet from a distant solar system was generated by subjecting to a magnetic field: a core equivalent to (the arguably less interesting) half of a single oxygen atomic nucleus.


Warning – keep this away from strong magnetic fields if you value your planet! (Image by Gerd Altmann from Pixabay )

Now free neutrons (that is, outside of an atomic nuclei – or neutron star) are unstable, and decay on a timescale of around a quarter of an hour (that is, the half-life is of this order – following the exponential decay familiar with other kinds of radioactivity), to give a proton, an electron and a neutrino. The energy 'released' in this process is significant on the scale of a subatomic particle: 782 343 eV or nearly eight hundred thousand eV.

Eight hundred thousand seems a very large number, but the unit here is electron volt, a unit used for processes at this submicroscopic scale. (An eV is the amount of work that is done when one single electron is moved though a potential difference of 1v – this is about 1.6 x10-19 J). In the more familiar units of joules, this is about 1.25 x 10-13 J. That is,

0.000 000 000 000 125 J

To boil enough water at room temperature to make a single cup of tea would require about 67 200 J. 2 So, if the energy from decaying neutrons were used to boil the water, it would require the decay of about

538 000 000 000 000 000 neutrons.3

That is just to make one cup of tea, so imagine how many more neutrons would have to decay to provide the means to destroy a planet. Certainly, one would imagine,

more than 8.

E=mc2

Now since Einstein (special relativity, again), mass and energy have been considered to have an equivalence. It is commonly thought that mass can be converted to energy and the equation E=mc2 tells you how much of one would be converted to the other: how many J per kg or kg per J. (Spoiler alert – this is not quite right.)

In that way of thinking, the energy released by a free neutron when it decays is due to a tiny part of the neutrino's mass being converted to energy.

The neutron's mass defect

The mass (or so called 'rest mass') of a neutrino is about 1.67 x 10-27 kg. In the usual mode of decay the neutrino gives rise to a proton (which is nearly, but not quite, as heavy as a neutron), an electron (which is much lighter), and a neutrino (which is considered to have zero rest mass.)


Before decayRest mass / 10-31 kgAfter decayRest mass / 10-31 kg
neutron16 749.3proton16 726.2
electron9.1
neutrino
total16 749.316 735.3
[rest] mass defect in neutrino decay

So, it seems like some mass has disappeared. (And this is the mass sometimes said to have been converted into the released energy.) This might lead us to ask the question of whether Hoffal's discovery was a way to completely annihilate neutrons, so that instead of a tiny proportion of their mass being converted to energy as in neutron decay – all of it was.

Mass as latent energy?

However, when considered from the perspective of special relativity, it is not that mass is being converted to energy in processes such as neutron decay, but rather that mass and energy are considered as being different aspects of something more unified -'mass-energy' if you like. Energy in a sense carries mass, and mass in a sense is a manifestation of energy. The table above may mislead because it only refers to 'rest mass' and that does not tell us all we need to know.

When the neutron decays, the products move apart, so have kinetic energy. According to the principle of mass-energy equivalence there is always a mass equivalence of any energy. So, in relativity, a moving object has more mass than when it is at rest. That is, the 'mass defect' table shows what the mass would be if we compared a motionless neutron with motionless products, not the actual products.

The theory of special relativity boldly asserts that mass and energy are not the independent quantities they were once thought to be. Rather, they are two measures of a single quantity. Since that single quantity does not have its own name, it is called mass-energy, and the relationship between its two measures is known as mass-energy equivalence. We may regard c2 as a conversion factor that enables us to calculate one measurement from the other. Every mass has an energy-equivalent and every energy has a mass-equivalent. If a body emits energy to its surroundings it also emits a quantity of mass equivalent to that energy. The surroundings acquire both the energy and mass in the process.

Treptow, 2005, p.1636

So, rather than thinking mass has been converted to energy, it may be more appropriate to think that the mass of a neutron has a certain (latent) energy associated with it, and that, after decay, most of this energy is divided between products (according to their rest masses), but a small proportion has been converted to kinetic energy (which can be considered to have a mass equivalence).

So, whenever any process involves some kind of energy change, there is an associated change in the equivalent masses. Every time you boil the kettle, or go up in an elevator, there is a tiny increase of mass involved – the hot water is heavier than when it was cold; you are heavier than when you were at a lower level. When you lie down or burn some natural gas, there is a tiny reduction in mass (you weigh less lying down; the products of the chemical reaction weigh less than the reactants).

How much heavier is hot water?

Only in nuclear processes does the energy change involved become large enough for any change in mass to be considered significant. In other processes, the changes are so small, they are insignificant. The water we boiled earlier to make a cup of tea required 67 200J of energy, and at the end of the process the water would not just be hotter, but also heavier by about

0.000 000 000 000 747 kg

0r about 0.000 000 000 75 g. That is easy to calculate 4, but not so easy to notice.

Is mass conserved in chemical reactions?

On this basis, we might suggest that the principle of conservation of mass that is taught in school science is falsified all the time – or at least needs to be understood differently from how it is usually presented.


Type of reactionMass change
endothermicmass of products > mass of reactants
exothermicmass of products < mass of reactants
If we just consider the masses of the substances then mass is not conserved in chemical change

Yet, the discrepancies really are tiny – so tiny that in school examinations candidates are expected to pretend there is no difference. But, strictly, when (as an example) copper carbonate is heated in a crucible and decomposes to give copper oxide and carbon dioxide there is a mass decrease even if you could capture all the CO2. But it would not be measurable with our usual laboratory equipment – so, as far as chemistry is concerned, mass is conserved. 'To all intense and purposes' (even if not absolutely true) mass is always conserved in chemical reactions.

Mass is conserved overall

But actually, according to current scientific thinking, mass is always conserved (not just very nearly conserved), as long as we make sure we consider all relevant factors. The energy that allowed us to boil the kettle or be lifted in an elevator must have been provided from some source (which has lost mass by the same extent). In an exothermic chemical reaction there is an extremely slight difference of mass between the reactants and products, but the surroundings have been warmed and so have got (ever so slightly) heavier.


Type of reactionMass change
endothermicenergy (and equivalent mass) from the surroundings
exothermicenergy (and equivalent mass) to the surroundings
If we just consider the masses of the substances then mass does not seem to be conserved in chemical change


As Einstein himself expressed it,

"The inertial mass of a system of bodies can even be regarded as a measure of its energy. The law of the conservation of the mass of a system becomes identical with the law of the conservation of energy, and is only valid provided that the system neither takes up nor sends out energy."

Einstein, 1917/2015, p.59

Annihilate the neutrons!

So, if we read about how in particle accelerators, particles are accelerated to immense speeds, and collided, and so converted to pure energy we should be suspicious. The particles may well have been destroyed – but something else has now acquired the mass (and not just the rest mass of the annihilated particles, but also the mass associated with their high kinetic energy).

So, we cannot convert all of the mass of a neutron into energy – only reconfigure and redistribute its mass-energy. But we can still ask: what if all the mass of the neutron were to be converted into some kind of radiation that carried away all of its mass as high energy rays (perhaps Hoffal's radiation?)

Perhaps the genius scientist Hoffal, with his "unique mind", had found a way to do this (hm, with a magnetic field?) Even if that does not seem very feasible, it does give us a theoretical limit to the energy that could be produced by a process that converted a neutron into radiation.6 Each neutron has a rest mass of about

1.67 x 10-27 kg

now the conversion factor is c2 (where c is the speed of light, which is near enough 3 x 108 ms-1, so c2 =(3×108ms-1)2 , i.e., about 1017m2s-2), so that mass is equivalent to about 1.50 x 10-10 J 5 or,

0.000 000 000 150 J

Now that is a lot more energy than the 1.25 x 10-13 J released in the decay of a neutron,

0.000 000 000 150 000 J

>

0.000 000 000 000 125 J

and now we could in theory boil the water to make our cup of tea with many fewer neutrons. Indeed, we could do this by annihilating 'only' about 7

448 000 000 000 000 neutrons

This is a lot less neutrons than before, i.e.,

448 000 000 000 000 neutrons

< 538 000 000 000 000 000 neutrons

but it seems fair to say that it remains the case that the number of neutrons needed (now 'only' about 448 million million) is still a good deal more than 8.

448 000 000 000 000 neutrons

> 8 neutrons

So, if over 400 million million neutrons would need to be completely annihilated to make a single cup of tea, how much damage can 8 neutrons do to a distant planet?

A common learning difficulty

In any reasonable scenario we might imagine 8 neutrons would not be significant. This is worth emphasising as it reflates to a common learning difficulty. Quanticles such as atoms, atomic nuclei, neutrons and the like are tiny. Not tiny like specs of dust or grains of salt, but tiny on a scale where specs of dust and grains of salt themselves seem gigantic. The scales involved in considering electronic charge (i.e., 10-19C) or neutron mass (10-27 kg) can reasonably said to be unimaginatively small – no one can readily visualise the shift in scale going from the familiar scale of objects we normally think of as 'small', to the scale of individual molecules or subatomic particles.

Students therefore commonly form alternative conceptions of these types of entities (atoms, electrons, etc.) being too small to see, but yet not being so far beyond reach. And it is not just learners who struggle here. I have even heard someone on a national news programme put forward as an 'expert' make a very similar suggestion to Egrorian, in this case that a "couple of molecules" could be a serious threat to public health after the use of chemical nerve agent. This is a preposterous suggestion to a chemist, but was, I am sure, made in good faith by the international chemical weapons expert.

It is this type of conceptual difficulty which allows scriptwriters to refer to 8 neutrons as being of some significance without expecting the audience to simply laugh at the suggestion (even if some of us do).

It also explains how science fiction writers get away with such plot devices given that many in their audiences will readily accept that a few especially malicious molecules or naughty neutrons is a genuine threat to life.8 But that still does not justify using angle-poise lamps as futuristic spacecraft joysticks.


Jenna pilots the most advanced spacecraft in the galaxy

Works cited:
  • Einstein, A. (1917/2015). Relativity. The special and the general theory. (100th Anniversary ed.). Princeton: Princeton Univerity Press.
  • Treptow, R. S. (2005). E = mc2 for the Chemist: When Is Mass Conserved? Journal of Chemical Education, 82(11), 1636. doi:10.1021/ed082p1636

Notes:

1 To explain: For younger readers, television was first broadcast in monochrome (black and white – in effect shades of grey). My family first got a television after I started primary school – the justification for this luxury was that the teachers sometimes suggested programmes we might watch.

Colour television did not arrive in the UK till 1967, and initially it was only used for selected broadcasts. The first colour sets were too expensive for many families, so most people initially stayed with monochrome. This led to the infamous 'helpful' statement offered by the commentator of the weekly half-hour snooker coverage: "And for those of you who are watching in black and white, the pink [ball] is next to the green". (While this is well known as a famous example of misspeaking, a commentator's blooper, those of a more suspicious mind might bear in mind the BBC chose snooker for broadcast in part because it might encourage more people to watch in colour.)

Snooker – not ideal viewing on 'black and white' television (Image by MasterTux from Pixabay )

My father had a part-time weekend job supervising washing machine rental collections (I kid you not, many people only rented such appliances in those days), to supplement income from his full time job, and this meant on Monday evenings after his day job he had to visit his part-time boss and report and they would go throughout the paperwork to ensure things tallied. I would go with him, and was allowed to watch television whilst they did this – it coincided with Star Trek, and the boss had a colour set!


2 Assuming water had to be heated from 20ËšC to 100ËšC, and the cup took 200 ml (200 cm3) of tea then the calculation is 4.2 x 80 x 200

4.2 J g-1K-1 is the approximate specific heat capacity of water.

Changing these parameters (perhaps you have a small tea cup and I use a mug?) will change the precise value.


3 That is the energy needed divided by the energy released by each neutron: 67200 J ÷ 1.25 x 10-13 J/neutron = 537 600 000 000 000 000 neutrons


4 E=mc2

so m = E/c2 = 67 200 ÷ (3.00 x 108)2 = 7.47 x 10-13


5 E=mc2 = 1.67 x 10-27 x (3.00 x 108)2 = 1.50 x 10-10


6 Well, we could imagine that somehow Hoffal had devised a process where the neutrons somehow redirect energy provided to initially generate the magnetic field, and perhaps the weapon was actually an enormous field generator producing a massive magnetic field that the funnel somehow converted into a beam (of tachyons?) that could pass across vast amounts of space without being absorbed by space dust, remaining highly collimated, and intense enough to destroy a world.

So, perhaps the neutrons are analogous to the core of a laser.

I somehow think it would still need more than 8 of them.


7 That is the energy needed divided by the energy released by each neutron: 67200 J ÷ 1.50 x 10-10 J/neutron = 4.48 x 1014 neutrons


8 Of course molecules are not actually malicious and neutrons cannot be naughty as they are inanimate entities. I am not anthropomorphising, just alliterating.


How much damage can a couple of molecules do?

Just how dangerous is Novichok?

Keith S. Taber


"We are only talking about molecules here…

There might be a couple of molecules left in the Salisbury area. . ."

Expert interviewed on national news

The subject of chemical weapons is not to be taken lightly, and is currently in the news in relation to the Russian invasion of Ukraine, and the concern that the limited progress made by the Russian invaders may lead to the use of chemical or biological weapons to supplement the deadly enough effects of projectiles and explosives.

Organophosphorus nerve agents (OPNA) were used in Syria in 2013 (Pita, & Domingo, 2014), and the Russians have used such nerve agents in illicit activities – as in the case of the poisoning of Sergey Skripal and his daughter Yulia in Salisbury. Skripal had been a Russian military intelligence officer who had acted for the British (i.e., as a double agent), and was convicted of treason – but later came to the UK in a prisoner swap and settled in Salisbury (renown among Russian secret agents for its cathedral). 1

Salisbury, England – a town that featured in the news when it was the site of a Russian 'hit' on a former spy (Image by falco from Pixabay )

These substances are very nasty,

OPNAs are odorless and colorless [and] act by blocking the binding site of acetylcholinesterase, inhibiting the breakdown of acetylcholine… The resulting buildup of acetylcholine leads to the inhibition of neural communication to muscles and glands and can lead to increased saliva and tear production, diarrhea, vomiting, muscle tremors, confusion, paralysis and even death

Kammer, et al., 2019, p.119

So, a substance that occurs normally in cells, but is kept in check by an enzyme that breaks it down, starts to accumulate because the enzyme is inactivated when molecules of the toxin bind with the enzyme molecules stopping them binding with acetylcholine molecules. Enzymes are protein based molecules which rely for their activity on complex shapes (as discussed in 'How is a well-planned curriculum like a protein?' .)


Acetylcholine is a neurotransmitter. It allows signals to pass across synapses. It is important then that acetylcholine concentrations are controlled for nerves to function (Image source: Wikipedia).


Acetylcholinesterase is a protein based enzyme that has an active site (red) that can bind and break up acetylcholine molecules (which takes about 80 microseconds per molecule). The neurotransmitter molecule is broken down into two precursors that are then available to be synthesised back into acetylcholine when appropriate. 2

Toxins (e.g., green, blue) that bind to the enzyme's active site block it from breaking down acetylcholine.

(Image source: RCSB Protein Data Bank)


A need to clear up after the release of chemical agents

The effects of these agents can be horrific – but, so of course, can the effects of 'conventional' weapons on those subjected to aggression. One reason that chemical and biological weapons are banned from use in war is their uncontrollable nature – once an agent is released in an environment it may remain active for some time – and so hurt or kill civilians or even personnel from the side using those weapons if they move into the attacked areas. The gases used in the 1912-1918 'world' war, were sometimes blown back towards those using them when the wind changed direction.


Image by Eugen Visan from Pixabay 

This is why, when small amounts of nerve agents were used in the U.K. by covert Russian agents to attack their targets, there was so much care put into tracing and decontaminating any residues in the environment. This is a specialised task, and it is right that the public are warned to keep clear of areas of suspected contamination. Very small quantities of some agents can be very harmful – depending upon what we mean by such relative terms as 'small'. Indeed, two police officers sent to the scene of the crime became ill. But what does 'very small quantities' mean in terms of molecules?

A recent posting discussed the plot of a Blakes7 television show episode where a weapon capable of destroying whole planets incorporated eight neutrons as a core component. This seemed ridiculous: how much damage can eight neutrons do?

But, I also pointed out that, sadly, not all those who watched this programme would find such a claim as comical as I did. Presumably, the train of thought suggested by the plot was that a weapon based on eight neutrons is a lot more scary than a single neutron design, and neutrons are found in super-dense neutron stars (which would instantly crush anyone getting too near), so they are clearly very dangerous entities!

A common enough misconception

This type of thinking reflects a common learning difficulty. Quanticles such as atoms, atomic nuclei, neutrons and the like are tiny. Not tiny like specs of dust or grains of salt, but tiny on a scale where specs of dust and grains of salt themselves seem gigantic. The scales involves in considering electronic charge (i.e., 10-19C) or neutron mass (10-27 kg) can reasonably be said to be unimaginatively small – no one can readily visualise the shift in scale going from the familiar scale of objects we normally experience as small (e.g., salt grains), to the scale of individual molecules or subatomic particles.

People therefore commonly form alternative conceptions of these types of entities (atoms, electrons, etc.) being too small to see, but yet not being so far beyond reach. It perhaps does not help that it is sometimes said that atoms can now be 'seen' with the most powerful microscopes. The instruments concerned are microscopes only by analogy with familiar optical microscopes, and they produce images, but these are more like computer simulations than magnified images seen through the light microscope. 3

It is this type of difficulty which allows scriptwriters to refer to eight neutrons as being of some significance without expecting the audience to simply laugh at the suggestion (even if some of us do).

An expert opinion

Although television viewers might have trouble grasping the insignificance of a handful of neutrons (or atoms or molecules), one would expect experts to be very clear about the vast difference in scale between us (people for example) and them (nanoscopic entities of the molecular realm). Yet experts may sometimes be stretched beyond their expertise without themselves apparently being aware of this – as when a highly qualified and experienced medical expert agreed with an attorney that the brain sends out signals to the body faster than the speed of light. If a scientific expert in a high profile murder trial can confidently make statements that are scientifically ridiculous then this underlines just how challenging some key scientific ideas are.

For any of us, knowing what we do not know, recognising when we are moving outside out of areas where we have a good understanding, is challenging. Part of the reason that student alternative conceptions are so relevant to science learning is that a person's misunderstanding can seem subjectively to be just as well supported, sensible, coherent and reasonable as a correct understanding. Where a teacher themself has an alternative conception (which sometimes happens, of course) they can teach this with as much enthusiasm and confidence as anything they understand canonically. Expertise always has limitations.

A chemical weapons expert

I therefore should not have been as surprised as I was when I heard a news broadcast featuring an expert who was considered to know about chemical weapons refer to the potential danger of "a couple of molecules". This was in relation to the poisoning by Russian agents of the Salisbury residents,

"During an interview on a BBC Radio 4 news programme (July 5th, 2018), Hamish de Bretton-Gordon, who brands himself as one of the world's leading chemical weapons experts, warned listeners that there may be risks to the public due to residue from the original incident in the area. Whilst that may have been the case, his suggestion that "we are only talking about molecules here. . .There might be a couple of molecules left in the Salisbury area. . ." seemed to suggest that even someone presented to the public as a chemistry expert might completely fail to appreciate the submicroscopic scale of individual molecules in relation to the macroscopic scale of a human being."

Taber, 2019, p.130
Chemical weapons expert ≠ chemistry expert

Now Colonel de Bretton-Gordon is a visiting fellow at  Magdalene College Cambridge, and the College website describes him as "a world-leading expert in Chemical and Biological weapons". I am sure he is, and I would not seek to underplay the importance of decontamination after the use of such agents; but if someone who has such expertise would assume that a couple of molecules of any substance posed a realistic threat to a human being with its something like 30 000 000 000 000 cells, each containing something like 40 000 000 molecules of protein (to just refer to one class of cellular components), then it just underlines how difficult it is to appreciate the gulf in scale between molecules and men.

Regarding samples of nerve agents, they may be deadly even in small quantities, but that still means a lot of molecules.

Novichok cocktails

The attacks in Salisbury (from which the intended victims recovered, but another person died in nearby Amesbury apparently having come into contact with material assumed to have been discarded by the criminals), were reported to have used 'Novichok', a label given to group of compounds.

"Based on analyses carried out by the British "Defence Science and Technology Laboratory" in Porton Down it was concluded that the Skripals were poisoned by a nerve agent of the so-called Novichok group. Novichok … is the name of a group of nerve agents developed and produced by Russia in the last stage of the Cold War."

Carlsen, 2019, p.1

Testing of toxins is often based on the LD50 – which means finding the dose that has an even chance of being lethal. This is not an actual amount, as clearly the amount of material that is needed to kill a large adult will be more than that to kill a small child, but the amount of the toxin needed per unit mass of victim. Although no doubt these chemicals have been directly tested on some poor test specimens of non-consenting small mammals, such information is not in the public domain.

Indeed, being based on state secrets, there is limited public data on Novichok and related agents. Carlsen (2019) estimates the LD50 for oral administration of 9 compounds in the Novichok group and some closely related agents to vary between 0.1 to 96.16 mg/kg.

Carlsen suggest the most toxic of these compounds is one known as VX. VX was actually first developed by British Scientists, although almost equivalent nerve agents were later developed elsewhere, including Russia.


'Chemical structures of V-agents.'
(Figure 2 from Nepovimova & Kuca, 2018 – subject to http://creativecommons.org/licenses/BY-NC-ND/4.0/)
n.b. This figure shows more than a couple of molecules of nerve agent – so might this be a lethal dose?


Carlsen then argues that the actual compounds in Novachok are probably less toxic than XV, which might explain…

"…why did the Skripals not die following expose to such high potent agents; just compare to the killing of Kim Jong-nam on February 13, 2017 in Kuala Lumpur International Airport, where he was attacked by the highly toxic VX, and died shortly after."

Carlsen, 2019, p1

So, for the most sensitive agent, known as XV (LD50 c. 0.1 mg/kg), a person of 50 kg mass would it is estimated have a 50% chance of being killed by an oral dose of 0.1 x 50 mg. That is 5 mg or 0.005 g by mouth. A single drop of water is said to have a volume of about 0.05 ml, and so a mass of about 0.05 g. So, a tenth of a drop of this toxin can kill. That is a very small amount. So, if as little as 0.005 g of a nerve agent will potentially kill you then that is clearly a very toxic substance.

The molecular structure of XV is given in the figure above taken from Nepovimova and Kuca (2018). These three structures shown appear to be isomeric – that is the three molecules are structural isomers. They would have the same empirical formula (and the same molecular mass).

Chemical shorthand

This type of structural formula is often used for complex organic molecules as it is easy for experts to read. It is one of many special types of representation used in chemistry. It is based on the assumption that most organic compounds can be understood as if substituted hydrocarbons. (They may or may not be derived that way – this is jut a formalism used as a thinking tool.) Hydrocarbons comprise chains of carbon atomic cores bonded to each other, and with their other valencies 'satisfied' by being bonded to hydrogen atomic cores. These compounds can easily be represented by lines where each line shows the bond between two carbon atomic cores. The hydrogen centres are not shown at all, but are implicit in the figure (they must be there to 'satisfy' the rules of valency – i.e., carbon centres in a stable structures nearly always have four bonds ).

Anything other than carbon and hydrogen is shown with elemental symbols, and in most organic compounds these other atomic centres take up on a minority of positions in the structure. So, for compounds, such as the 'VX' compounds, these kinds of structural representations are a kind of hybrid, with some atomic centres shown by their elemental symbols – but others having to be inferred.

From the point of view of the novice learner, this form of abstract representation is challenging as carbon and hydrogen centres need to be actively read into the structure (whereas an expert has learnt to do this automatically). But for the expert this type of representation is useful as complex organic molecules can contain hundreds or thousands of atomic centres (e.g., the acetylcholinesterase molecule, as represented above) and structural formulae that show all the atomic centres with elemental symbols would get very crowded.

So, below I have annotated the first version of XV:


The VX compound seems to have a molecular mass of 267

This makes the figure much more busy, but helps me count up the numbers of different types of atomic centres present and therefore work out the molecular mass – which, if I had not made a mistake, is 267. I am working here with the nearest whole numbers, so not being very precise, but this is good enough for my present purposes. That means that the molecule has a mass of 267 atomic mass units, and so (by one of the most powerful 'tricks' in chemistry) a mole of this compound, the actual substance, would have a mass of 267g.

The trick is that chemists have chosen their conversion factor between molecules and moles, the Avogadro constant of c. 6.02 x 1023, such that adding up atomic masses in a molecule gives a number that directly scales to grammes for the macroscopic quantity of choice: the mole. 5

So, if one had 267 g of this nerve agent, that would mean approximately 6.02 x 1023 molecules. Of course here we are talking about a much smaller amount – just 0.005 g (0.005/267, about 0.000 02 moles) – and so many fewer molecules. Indeed we can easily work out 0.005 g contains something like

(0.005 / 267) x 6.02 x 1o23 = 11 273 408 239 700 374 000 = 1×1019 (1 s.f.)

That is about

10 000 000 000 000 000 000 molecules

So, because of the vast gulf in scale between the amount of material we can readily see and manipulate, and the individual quanticle such as a molecule, even when we are talking about a tiny amount of material, a tenth of a drop, this still represent a very, very large number of molecules. This is something chemistry experts are very aware of, but most people (even experts in related fields) may not fully appreciate.

The calculation here is approximate, and based on various estimates and assumptions. It may typically take about 10 000 000 000 000 000 000 molecules of the most toxic Novichok-like agent to be likely to kill someone – or this estimate could be seriously wrong. Perhaps it takes a lot more, or perhaps many fewer, molecules than this.

But even if this estimate is out by several orders of magnitude and it 'only' takes a few thousand million million molecules of XV for a potential lethal dose, that can in no way be reasonably described as "a couple of molecules".

It takes very special equipment to detect individual quanticles. The human retina is in its own way very sophisticated, and comes quite close to being able to detect individual photons – but that is pretty exceptional. As a rule of thumb, when anyone tells us that a few molecules or a few atoms or a few ions or a few electrons or a few neutrons or a few gamma rays or… can produce any macroscopic effect (that we can see, feel, or notice) we should be VERY skeptical.


Work cited:

Notes:

1 Two men claiming to be the suspects whose photographs had been circulated by the British Police, and claimed by the authorities here to be Russian military intelligence officers, appeared on Russian television to explain they were tourists who had visited Salisbury sightseeing because of the Cathedral.

2 According to the RCSB Protein Data Bank website

"Acetylcholinesterase is found in the synapse between nerve cells and muscle cells. It waits patiently and springs into action soon after a signal is passed, breaking down the acetylcholine into its two component parts, acetic acid and choline."

Molecule of the month: Acetylcholinesterase

Of course, it does not 'wait patiently': that is anthropomorphism.


3 We might think it is easy to decide if we are directly observing something, or not. But perhaps not:

"If a chemist heats some white powder, and sees it turns yellow, then this seems a pretty clear example of direct observation. But what if the chemist was rightly conscious of the importance of safe working, and undertook the manipulation in a fume cupboard, observing the phenomenon through the glass screen. That would not seem to undermine our idea of direct observation – as we believe that the glass will not make any difference to what we see. Well, at least, assuming that suitable plane glass of the kind normally used in fume cupboards has been used, and not, say a decorative multicoloured glass screen more like the windows found in many churches. Assuming, also, that there is not bright sunlight passing through a window and reflecting off the glass door of the fume cupboard to obscure the chemist's view of the powder being heated. So, assuming some basic things we could reasonably expect about fume cupboards, in conjunction with favourable viewing conditions, and taking into account our knowledge of the effect of plane glass, we would likely not consider the glass screen as an impediment to something akin to direct observation.

Might we start to question an instance of direct observation if instead of looking at the phenomenon through plane glass, there was clear, colourless convex glass between the chemist and the powder being heated? This might distort the image, but should not change the colours observed. If the glass in question was in the form of spectacle lenses, without which the chemist could not readily focus on the powder, then even if – technically – the observations were mediated by an instrument, this instrument corrects for a defect of vision such that our chemist would feel that direct observation is not compromised by, but rather requires, the glasses.

If we are happy to consider the bespectacled chemist is still observing the phenomenon rather than some instrumental indication of it, then we would presumably feel much the same about an observation being made with a magnifying glass, which is basically the same technical fix as the spectacles. So, might we consider observation down a microscope as direct observation? Early microscopes were little more than magnifying glasses mounted in stands. Modern compound microscopes use more than one lens. A system of lenses (and some additional illumination, usually) reveals details not possible to the naked eye – just as the use of convex spectacles allow the longsighted chemist to focus on objects that are too close to see clearly when unaided.

If the chemist is looking down the microscope at crystal structures in a polished slice of mineral, then, it may become easier to distinguish the different grains present by using a Polaroid filter to selectively filter some of the light reaching the eye from the observed sample. This seems a little further from what we might normally think of as direct observation. Yet, this is surely analogous to someone putting on Polaroid sunglasses to help obtain clear vision when driving towards the setting sun, or donning Polaroid glasses to help when observing the living things at the bottom of a seaside rock pool on a sunny day when strong reflections from the surface prevent clear vision of what is beneath.

A further step might be the use of an electron microscope, where the visual image observed has been produced by processing the data from sensors collecting reflections from an electron beam impacting on the sample. Here, conceptually, we have a more obvious discontinuity although the perceptual process (certainly if the image is of some salt crystal surface) may make this seem no different to looking down a powerful optical microscope. An analogy here might be using night-vision goggles that allow someone to see objects in conditions where it would be too dark to see them directly. I have a camera my late wife bought me that is designed for catching images of wildlife and that switches in low light conditions to detecting infrared. I have a picture of a local cat that triggered an image when the camera was left set up in the garden overnight. The cat looks different from how it would appear in day-light, but I still see a cat in the image (where if the camera had taken a normal image I would not have been able to detect the cat as the image would have appeared like the proverbial picture of a 'black cat in a coal cellar'). Someone using night-vision goggles considers that they see the fox, or the escaped convict, not that they see an image produced by electronic circuits.

If we accept that we can see the cat in the photograph, and the surface details of crystal grains in the electron microscope image, then can we actually see atoms in the STM [scanning tunneling microscope] image? There is no cat in or on my image, it is just a pattern of pixels that my brain determines to represent a cat. I never saw the cat directly (I was presumably asleep) so I have no direct evidence there really was a cat if I do not accept the photograph taken using infrared sensors. I believe there are cats in the world, and have seen uninvited cats in my garden in daylight, and think the camera imaged one of them at night. So it seems reasonable I am seeing a cat in the image, and therefore I might wonder if it is reasonable to doubt that I can also see atoms in an STM image.

One could shift further from simple sensory experience. News media might give the impression that physicists have seen the Higgs boson in data collected at CERN. This might lead us to ask: did they see it with their eyes? Or through spectacles? Or using a microscope? Or with night-vision goggles? Of course, they actually used particle detectors.

Feyerabend suggests that if we look at cloud chamber photographs, we do not doubt that we have a 'direct' method of detecting elementary particles …. Perhaps, but CERN were not using something like a very large cloud chamber where they could see the trails of condensation left in the 'wake' of a passing alpha particle, and that could be photographed for posterity. The detection of the Higgs involved very sophisticated detectors, complex theory about the particle cascades a Higgs particle interaction might cause, and very complex simulations to allow for all kinds of issues relating to how the performance of the detectors might vary (for example as they age) and how a signal that might be close to random noise could be identified…. No one was looking at a detector hoping to see the telltale pattern that would clearly be left by a Higgs, and only a Higgs. In one sense, to borrow a phrase, 'there's nothing to see'. Interpreting the data considered to provide evidence of the Higgs was less like using a sophisticated microscope, and more like taking a mixture of many highly complex organic substances, and – without any attempt to separate them – running a mass spectrum, and hoping to make sense of the pattern of peaks obtained.

Taber, 2019, pp.158-160

4 That is not to suggest that one should automatically assume that one molecule of a toxin can only ever damage one protein molecule somewhere in one body cell. After all, one of the reasons that CFCs (chlorofluorocarbons, which used to be used as propellants in all kinds of spray cans for example) were so damaging to the ozone 'layer' was because they could initiate a chain reaction.

In reactions that involve free radicals, each propagation step can produce another free radical to continue the reaction. Eventually two free radicals are likely to interact to terminate the process – but that might only be after a great many cycles, and the removal of a great many ozone molecules from the stratosphere. However, even if one free radical initiated the destruction of many molecules of ozone, that would still be a very small quantity of ozone, as molecules are so tiny. The problem was of course that a vast number of CFC molecules were being released.


5 So one mole of hydrogen gas, H2, is 2g, and so forth.

The cell nucleus is probably bigger than an atomic nucleus

A cell is about ten times larger than an atom

Keith S. Taber

Dividing cell image by  ar130405 from Pixabay

Bert was a participant in the Understanding Science Project. Bert was interviewed in Y10 and asked about the topics he had been studying, which included circulation in biology, static electricity in physics, and oxidation in chemistry.

He talked about protons, electrons and atoms in both chemistry and physics, and was asked if this could also link with biology. Bert suggested that the nucleus comes up in chemistry (in the context of atomic structure) and physics (in the context of static electricity), and in biology in the context of cells (see 'The nucleus is the brain of the cell'). From the perspective of the science teacher, there is little basis for confusing the nucleus of an atom with that of a cell: obviously a cell is a complex entity with many components, each of which has itself a complex supra-molecular structure – so clearly the atomic nucleus is on a scale many orders of magnitude smaller than a cell nucleus.

However, the expert perspective is based on relating a lot of knowledge that the novice may not yet have, or at least, may not yet be coordinating. In Bert's case, he was only just starting to coordinate these ideas, as became clear when Bert was asked about the relative sizes of atomic and cell nuclei:

Which do you think is bigger, an atom or a cell, or are they both about the same size?

I'd say a cell.

A correct, but hardly confident and definitive, response. I followed up:

Which do you think is bigger, an atom or a cell, or are they both about the same size?

I'd say a cell.

So which do you think is bigger, the nucleus of a cell or the nucleus of an atom, or do you think they're both about the same size?

I think they're both about, well I should, oh. (Laughs) I'd say the one in the cell is probably bigger.

Why do you think that?

Well it's a cell, I'd have thought it was bigger than the atom. And you know, if the nucleus is kind of the main part of it, then it would probably be about, it would be the • same sort of – If the atom was brought to the size of the cell then the nucleus would be the same size I would have thought. So if the atom is smaller then the nucleus is a lot smaller.

I see, so you are sort of like scaling it, accordingly?

Yeah.

I see. So any idea roughly, just very roughly, how much bigger a cell is than an atom?

Erm oh, it's, they're both really microscopic so, I couldn't really say how much bigger they are than each other.

So it seems that Bert would "have thought [the cell] was bigger than the atom", but he did not seem entirely certain of this, whereas from the scientific perspective the difference in scale is considered vast and highly significant. Although cells are generally microscopic entries, they are more like familiar macroscopic objects that we can handle in everyday life than quanticles such as atoms which do not behave like familiar objects. (So, there is sense in which it is meaningless to talk about the size of atoms as they have no edges or surfaces but rather fade away to infinity.)

Erm oh, it's, they're both really microscopic so, I couldn't really say how much bigger they are than each other.

Mm. No, okay. So if I said a cell was ten times bigger than an atom, a hundred times bigger than an atom, a thousand times bigger than an atom?

I wouldn't say that, I'd say, I'd probably go with the first one you said, ten times bigger.

So roughly ten times bigger than an atom. So a nucleus of a cell you'd expect to be roughly ten times bigger than the nucleus of an atom?

Yeah.

But you're not really sure?

Well no, there are a lot more parts in a cell than there is in an atom. So I'd say the nucleus is… if they're both brought to the same size again, I'd say the nucleus of the atom would be bigger than the cell. But I could be totally wrong.

Oh I see, so you've got two arguments there. That because they, because they both have a nucleus in the middle, that in terms of scale, if the cell is quite a bit bigger than the atom, you'd expect the nucleus of the cell would be quite a bit bigger than the atom. But an atom is quite a simple structure, whereas a cell has a lot more things in it, it's a lot more complex.

Yeah.

So maybe there's not so much room for the nucleus of the cell as there is for an atom because you've got to fit so much more in.

Yeah.

Is that what you're thinking?

Yeah.

Bert's thinking here is quite reasonable, within the limits of his knowledge. He suggests that a cell nucleus will be larger than an atomic nucleus, because a cell is larger than an atom. However, he only think the cell nucleus will be about ten times the size of the atomic nucleus as he suspects the cell is only about ten times the size of an atom – after all they are both "really microscopic".

However, he also points out that a cell seems to have a more a lot more components to be fitted in, which would suggest that perhaps there is less space to fit the nucleus, so perhaps it would not be as much as ten times bigger than the atomic nucleus.

So Bert is able to consider a situation where there may be several factors at work (the size of the cell versus the size of the atom; the multitude of cellular components versus the sparsity of atoms) and appreciate how they would operate in an opposite sense within his argument so one could compensate for the other. (This type of thinking is needed a lot in studying science. One example is comparisons of ionisation enthalpies between different atoms and ions. I also recall physics objective examination questions that asked students to compare, say, the conductance of two wires with different resistivity, length and area.)

It is not reasonable to expect Bert to know just how much larger a typical cell nucleus is to an atomic nucleus, however, it is likely the science teacher would expect Bert to be aware that the nucleus is one small part of the atom, which is a constituent of the molecules and ions that are the chemical basis for the organelles such as nuclei found in cells. Bert had told me "there are lots of atoms in you", but he did not seem to have understood the role those atoms played in the structure of all tissues. This would seem to be an example of a fragmentation learning impediment, where a learner has not made the connections between topics and ideas that a science teacher would have intended and expected.

Some particles are softer than others

Keith S. Taber

Image by Alexander Ignatov from Pixabay

Bill was a participant in the Understanding Science Project. Bill was a Year 7 student when he told me that previously, when he had been in primary school, "we did a lot about plants, and – inside them, how they produce their own food". As he had been talking to me about learning about particles (e.g. Gas particles try to spread out and move apart), I asked if there was any link between these two topics.

Okay. What about particles, we were just talking about particles, do you think that's got anything to do with particles?

Well in the plant, there is particles.

Are there?

'cause it's a solid.

Ah. So there'll be particles in that then?

Yeah.

Is it all solid, do you think?

Inside the stem is, 'cause going up the stem there would be water, so that's a liquid. And, it also uses oxygen, which is a gas, to make its food, so. I think so.

So it would be solids, liquids and gases?

Mm, I think some.

But they've all got some particle in them, they are all made up of particles.

Yeah.

Okay.

As Bill had talked to me earlier about there being particles in a gas when ice was melted, and then boiled, I wanted to see if he though the particles in different substances were the same:

Erm. Do you think that the particles in the – oxygen's a gas isn't it?

Yeah.

Do you think the particles in the oxygen gas, are the same as the particles in the steam that you said was a gas, in your experiment you did earlier?

Erm, I don't think so, no.

You think they'd be different sort of particles?

Yeah, they're different gases.

Okay. And in the solid part of the plant, do you think the particles that make up the solid part of the plant, are the same as the particles that make up this table, that's a solid?

Well, the particles, plants are soft, some plants are soft, and you, when you squeeze them they're, they feel soft and erm, but the table is hard so I think that the particles would be slightly different, but they would have, because they hold this different shape, and they would, they would be {pause} erm {pause} then they would, ob¬, then they would be softer as well.

So the softer, the plant which is softer, > > would have softer particles?

< Yeah. < I think so yeah

And the harder wood, made of harder particles?

I think so.

Here Bill offered evidence of a very common alternative conception about the particle theory. A key feature of particle theory is that chemists use particle models to explain the properties of substances macroscopically (what can be observed directly) in terms of the very different nature and properties of conjectured 'particles' (quanticles) at a submicroscopic level.

Yet after learning about these 'particles', students commonly 'explain' macroscopic properties of substances and materials by suggesting that the particles of which they are made up themselves have the property to be explained – being hard, sharp, colourless, conducting, etc.