S1C7: Nuclear & Chemical Energies

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a) Nuclear forces and elementary particles

And we are back in the realm of the unfathomably small, among subatomic particles and even further down the scale, dealing with elementary particles. In Section 1.d we spent some time defining the nature of the strong and weak interactions; you may want to refresh your memory and refer to these. In case you do not, think of the strong interaction as what glues some elementary particles to form the nucleons and also keeps those nucleons together, thus forming the atomic nucleus, despite the repulsive electromagnetic forces acting on electrically charged particles like the proton.

We then introduced the notion of elementary particles and force carriers in Section 1.e and this is where we must return to make sense of nuclear forces. It gets quite complex, the word esoteric may even be appropriate, but I don’t think this needs to be the case. So, let’s take a crack at it and remember we are dealing with hypotheses that are on the whole very hard to observe and even test so even trying to disprove them is a tough act.

Deep down, as I am now fond of saying, it is all forces. The view I share is one where even the most “elementary particles” are essentially force fields that tend to aggregate, because of their interaction, into more complex sub-atomic particles. This means any particle should be thought of as being point-like and its volume is merely a theoretical artefact of our mind, including the electron and its “orbit”. The fact that we observe particle-like behaviours doesn’t prove they are particles, and in fact the concept of wave-particle duality in quantum mechanics supports this statement – we will cover this topic in due course, in Section 9.b [link].

The ultimate force carrier mediating the strong force is called a gluon; in the Standard Model of Elementary Particles (the theory currently dominating the field of particle physics), it forms part of the boson family and has no mass. Gluons pull together quarks to form composite particles such as protons and neutrons falling under the family of hadrons. By the way, if you need a refresher, you can revert to Section 1.e which included a coloured grouping of elementary particles according to the Standard model.

At least a couple of things are special about quarks: firstly, they are subject to all four fundamental interactions – so they do have a mass, and secondly, they are described as “fundamental constituents of matter”. This is somehow problematic if we do not think matter really is a thing. Instead, what would make more sense, in my personal opinion, is that quarks are a combination of force carriers, which is why they interact with all of the forces.

The same issue arises with the electron, of the lepton family. It has mass but is not subject to the strong interaction. Leptons are stamped as elementary particles, I would think it is more probable they are, like quarks, a combination of force carriers that doesn’t include the gluon. Take this with a heavy dose of salt, this opinion is highly speculative.

Marching on. How do we go from hadrons, and specifically nucleons, to the atomic nucleus? The answer is that we now rely on mesons, another strong force carrier made up of quarks and antiquarks bound together by the strong interaction. Again, the mesons are described as a particle and as force carriers, at the same time. I have to say this bothers me and since mesons are made of quarks held together by gluons then really, looking through, it seems gluons remain the force carrier for mesons as well.

In any case, atoms and their constituting parts are held together by the strong force, it is the one interaction dominating the three others at this scale of 10^-15m – the unit for this is 1 femtometre. The strong force is about 100 times stronger than the electromagnetic force and about one million times stronger than the weak force. For those interested in diving into the deep end, I am including a link to the Wikipedia entry for quarks at the end of this chapter, from there you can make your way to the leptons and bosons.

b) Mass and binding energy

One of the experimental giveaways of the strong nuclear force is the fact that the mass of an atomic nucleus is less than the aggregate of the masses of its constituting nucleons. For example, the mass of helium-4, the most commonplace isotope of Helium (chemical element with atomic number 2), is less than the mass of two protons plus two neutrons. How is that a giveaway?

It comes down to mass-energy equivalence, the principle captured in Einstein’s iconic E=mc² formula. The core idea is to equate mass with energy, more specifically when considering a system in its rest frame. However, as the formula p=mv reminds us, velocity is a key variable when computing momentum and, likewise, the amount of energy of a given mass will vary on account of the relative speed at which the object with such mass is moving – which is a function of the frame of reference. This is why we talk of rest mass, rest frame, relativistic mass, and relativistic energy. If you re-read the various laws of motion described in Section 6.d with the mass-energy equivalence formula at the back of your mind you will immediately notice the same underlying logic.

When two nucleons interact with each other through the strong force, the creation of bonds liberates energy, and this decrease in total energy within the system can be observed by a drop in the mass of the fused nucleus; a quantity known as “mass defect” as relates to the nucleons. Remember, it is mass-energy equivalence, it is not a conversion from one into the other and there is no causal relationship between the release of energy and a lowering of the mass, those are two sides of the same coin. This energy release is what powers the nuclear fusion within stars and the creation of heavier elements out of the original hydrogen atoms comprising only one proton. Why exactly is there a release of energy? The answer lies in quantum electrodynamics and would be too technical for me to convey succinctly so suffice to say that in the process of reaching a lower energy state, a photon is emitted out of the combined systems. Hence the star light.

The opposite of fusion is fission, the splitting apart of the atom’s nucleus. This was the basis of the first atomic bomb, which indicates the process also liberates energy. A bit of a head scratcher, isn’t it? We should be expecting fission to be endothermic, not exothermic. Or if fission releases energy, then we should expect fusion to require energy. How can we reconcile this two seemingly opposite dynamics?

The answer lies in context, in the details so to speak. Given the same set of systems, the maths would as expected work out with the two reactions having two opposite energetic outcomes. The corollary is that if fission and fusion can both release energy, this can only happen because the value of at least one variable has been modified. In this case, what changes is the type of nucleus. As we have just seen, fusion takes place with lighter elements such as hydrogen and helium whereas fission is carried out on heavy nuclei like uranium and plutonium. In fission, the potential energy of the resulting nucleus is much lower compared to the level of the starting configuration and the energy differential takes the shape of kinetic energy, in the form of particles ejected at high speed, and the emission of gamma ray photons.

Whether or not the fusion of 2 elements into a new one or the reverse fission reaction requires or releases energy depends on the maths of the binding energy involved in each system. Binding energy is the quantum of energy required to disassemble the nucleus into its constituting nucleons. If the binding energy of the systems after the reaction is higher than the binding energy at the start, then we have a more stable system with lower potential energy at the end and energy would have exited the system in a quantum equal to the difference in binding energy between the starting system and the one at the end. Correspondingly, it would take energy from outside the system to reverse this reaction.

The main forces involved in the computation of net binding energy are the repulsive electromagnetic interaction and the attractive strong force. If we were to plot this, the line grows from helium until iron (atomic number 26) and reaches its peak with isotope Iron-56 (comprising 26 protons and 30 neutrons) before decreasing as we move further into the periodic table of elements, the domain where fission is exothermic. This is why the fusion of stars end at Iron-56 and they die with an iron core.

A last comment regarding the difference in energy levels between fusion and fission. The energy released by the splitting of a plutonium or uranium nucleus is much higher than that emitted during the fusion of hydrogen atoms and yet the H bomb which relies on fusion is much more powerful than the fission-based A-bomb. The primary reason behind this is fuel density, a function of the large volume occupied by heavy elements with over 200 nucleons compared to hydrogen-2 (deuterium). In short, there are over 100 times more reactions taking place per gram of fuel in the case of the H bomb, which more than compensates for the difference in energy released on a per-reaction basis.

c) The weak interaction and radioactive decay

On the face of it, the weak interaction is arguably not as potent as the strong interaction, yet it plays a crucial role in the makeup and identity of chemical elements in the universe. According to the Standard Model theory, it is mediated by bosons called the W and Z bosons responsible for changes in the nature of quarks. To be precise, there are two W bosons, one with a positive charge W⁺ and one with a negative charge W^–, whereas the Z boson has zero charge. Since quarks are the basis of composite particles such as the proton, changes in the nature of quarks translates into changes in the nature of the composite particles. Bosons can thus cause a neutron to become a proton, and vice versa, with emission of other particles to account for conservation of energy and charge. Ultimately this results in the changing in the constitution of an atom’s nucleus, a real nuclear transmutation turning one chemical element into another.

Open a parenthesis. Here, I would like to reiterate a personal doubt already expressed in section a) regarding the nature of quarks as elementary particles. Instead, if we think of them as consisting of a combination of smaller force fields, then it is easier to see how a boson could change the type of quark we are dealing with, perhaps acting the same way an input of energy can facilitate a chemical reaction. Close the parenthesis.

The phenomenon described above is called radioactive beta decay and is different from the gamma rays emitted during nuclear fission. The dynamic responsible for this goes back to nucleus stability and the minimization of binding energy. In nuclear physics, the set of atom nuclei with the same total number of nucleons is called isobaric nuclides (a nuclide refers to a specific nucleus with Z atoms and N neutrons). The concept of isobaric nuclides should not be mistaken with isotopes. Isotopes have the same atomic number, meaning they have the same number of protons but a different number of neutrons so the total number of nucleons differ. On the contrary, isobaric nuclides will by definition not have the same number of protons and belong to different elements. Among every set of isobaric nuclides, one combination will exhibit the lowest mass defect, being the difference between actual mass and mass number – disconcertingly, the term mass excess is also used in lieu of mass defect. The configuration with the smallest mass defect is the one with the lowest binding energy and the weak interaction can trigger the change towards this more stable configuration but not the other way since it requires a fair bit of energy. There are two possible scenarios, the first one is the morphing of a neutron into a proton (thus increasing the atomic number by one) accompanied by the emission of an electron and an electron antineutrino; this is termed β⁻ decay. The other is called β⁺ decay and consists in a proton becoming a neutron together with the emission of a positron and an electron neutrino.

At our current level of knowledge, radioactive decay appears to be random, however it obeys a specific distribution, meaning that when dealing with millions of unstable nuclei, we have a pretty precise estimate of how long it would take for 50% of those nuclei to undergo decay; this is called half-life and this statistically consistent phenomenon is very handy for dating substances if we know their original concentration in a particular nuclide. This is how carbon-14, which decays into nitrogen-14, is used to derive the age of fossils. Its half-life is approximately 5700 years, implying that every 5700 years half the carbon-14 contained into a fossil will disappear and after 11400 years there will only be a quarter left, and so forth. You had probably already heard about Carbon 14, now you know the physics behind it.

d) Energy in chemical reactions

The idea of more stable configurations can be carried over from the atomic nucleus to the inter-atomic level, the domain of molecules and chemistry. We have already covered a fair bit on this theme, in particular Section 2.f on chemical reactions so I invite you to read through it if you have not done so previously.

You may recall there are several types of bonds, the most prevalent being covalent bonds where two atoms or molecules are sharing a pair of electrons and ionic bonds where atoms with opposite electrical charges are drawn to each other. As a reminder, an ion is an atom or molecule with a net negative charge because it is missing one or more electrons or it has captured some extra ones. In a chemical reaction, the nature and the strength of the chemical bonds will be altered and this change either releases or requires energy. Specifically, when adding a reactant with weak bonds, this compound has a higher amount of potential energy and is therefore comparatively less stable than one with a strong bond configuration and lower potential energy. The amount of energy required or released in a reaction can be computed as the differential in energy stored in chemical bonds before and after.

Note that unlike in fission, fusion and beta decay, we do not end up with different elements but with different chemical compounds or isotopes. This is because the process of chemical reactions does not impact the nucleus of the atoms. Instead, it consists in a redistribution of the electrons and their pairing so the fundamental interaction at play is electromagnetism. No surprise then that some reactions can convert chemical energy into electrical energy, or the other way around; these are called electrochemical reactions.

e) Electrochemical reactions

The electrochemical reaction you are probably the most familiar with is the electric battery and to understand how it works we need to go back to the concepts of oxidation and redox briefly explained in Section 2.f. Essentially, oxidation is the loss of an electron and redox is the reduction in oxidation, i.e. an electron gain. In an electrochemical cell, there is an anode where oxidation takes place and the electrons flow from there via conductive materials such as a copper wire onto the cathode where the reduction occurs. This difference of voltage between the anode and cathode creates an electric current across the wire that can then be used to do work on a light bulb (where some of the energy will be transformed into heat) or some other equipment. The chemical reaction was always about electrons, now their relocation and reconfiguration is simply being harnessed to do work. This source of energy is called electromotive force. I am including a link to the Wikipedia entry for electrochemical cell if you want the complete details, including the requirement to close the circuit with an ionic conduction path between the electrolytes at each of the cathode and anode.

When direct electrical current (i.e. one directional, it would not work with alternating current) is applied to and work is done on the system, then it is possible to design a circuit such that the electrons will be made to travel the other way thus spurring electrochemical reactions that would not occur spontaneously otherwise because they are endothermic and thus require the supply of external energy. This is the basis of electrolysis, the process of separation of elements via electricity. One of the most ubiquitous application of electrolysis is the manufacture of aluminium; it involves processing bauxite into alumina, an aluminium oxide (Al₂O₃), and the presence of a carbon cathode. As part of the electrochemical reaction, the alumina is broken down, yielding the metallic Al while the oxygen and carbon combine, mostly in the form of CO₂. And yes, this means the carbon cathode is consumed over time and yes, the process is highly energy intensive, in fact more than 4 times the already elevated level needed for steel manufacturing, which is why aluminium producing plants are almost always located in close proximity to power plants.

Another technological area seeing increasing interest and commercial development is the electrolysis of water (H₂O) to produce hydrogen (H₂) with oxygen as a by-product (O₂). Hydrogen can indeed be used as a fuel powering energy intensive application such as steel, glass and cement manufacturing and could also be adopted more widely in the transport industry in the next couple of decades. I will spend more time on the production of hydrogen as a fuel in a future series.

f) Electrochemical gradients and photosynthesis

If the battery and electrolysis are man-made processes, nature on its own has found a way to exploit the imbalance between electrical charges and the concentration of ions . When a solution has a high concentration of certain ions, the starting system will automatically evolve towards one with a lower potential energy (and higher entropy), a phenomenon called molecular diffusion. In addition, a high concentration of ions results in a localized electrical charge and electromagnetic interaction ensures those ions tend to travel towards areas with opposite charges. All that is needed to take advantage of this is to create a channel where the flow of ions can do work, the same way the electric current does work in a voltaic battery.

This is one of the many uses of organic membranes (refer to Section 2.a and Section 2.d): they can ensure the preservation of the difference in chemical concentration between the solutions on each side and of the difference in electric charge across the membrane. Those are called respectively the chemical gradient and the electrical gradient and together they form an electrochemical gradient creating a flow of ions through porous channels in the membrane.

Electrochemical gradients are essential in the oxidation of nutrients and production of ATP but for once I would like to focus on the kingdom of plants, our very distant cousins, since the gradient powers photosynthesis, their main energy source and also the origin of a significant proportion of the oxygen we breathe. The big picture is relatively straightforward: photosynthesis uses energy from sunlight to fuel the metabolism of plants and converts carbon dioxide into carbohydrates such as starches and cellulose (refer to Section 4.b), releasing oxygen as by-product. However, this is such a fantastic example of the chance ingenuity of evolution that we should not be content with the big picture. What we want is understand and be impressed. Let’s strap in.

In plants and some algae, the first step in photosynthesis involves chlorophyll pigments located in chloroplasts, a type of organelle within cell membranes. Just like the mitochondria, they are thought to have partnered with eukaryotic cells in an endosymbiotic relationship: living inside the cell without being destroyed by it because it turned out to be a good thing in terms of natural selection for both entities. Chlorophyll molecules are able to absorb photons (with specific wavelengths) that are used to provide the energy required for the splitting of water molecules, yielding in the process oxygen molecules, hydrogen ions (essentially, lone protons) and free electrons: 2xH₂O becomes O₂+ 4H⁺ + 4e^–. The absorption of photons is itself a complex process made possible by the “photosynthetic reaction centre”, a mechanism I will not expand on but you may want to look into on your own. Note that this is the part of the process which releases O₂ into the atmosphere.

The second step is not dependent on light and involves the freed-up electrons. Those go through a series of redox reactions, moving along from electron donors to electron acceptor molecules in what is termed an “electron transport chain”. This and the issuance of proton cations (H⁺) creates a proton gradient across a membrane which is channelled through a protein conveniently called proton pump. It is analogous to the electrochemical gradient used to power ATP synthesis except that in this instance the force is proton-motive rather than electromotive.

In addition, the energy level of the circulating electrons is further boosted by another light-dependent reaction before their involvement in the redox reaction of NADP⁺ into NADPH, thus returning the electron to a molecular home. NADPH is used in several anabolic pathways and, alongside ATP, H⁺ and CO_2, in the creation of carbohydrate. This is why green plants remove CO₂ from the atmosphere and are so crucial in the carbon fixation process.

It is hard to imagine the number of mutations, trials and errors, it took to get to such complex and tremendously useful processes although it must be said that with each intermediary step there would have been some functional gains so we are dealing with incremental evolutionary paths exploration, not an out-of-the-blue wonder.

g) Trivia – Gluons

Gluons come in six flavours, across three generations: up and down, charm and strange, top and bottom. They have mass, fractional electric charge (-1/3 or +2/3 for quarks and +1/3 or -2/3 for antiquarks, the antiparticle of quarks), and spin (+⁠1/2⁠ or -1/2), which we’ll learn more about in the next chapter.

And when you think it cannot get more confusing, it does. In the theory of quantum chromodynamics (QCD), gluons mediate the strong interaction and impart another property to quarks that make them susceptible to this force; it is called colour charge and comes in a palette of three, namely red, green and blue – no relationship with everyday colours. As for antiquarks, their colour charge is of course a choice of antired, antigreen and antiblue.

Fun and perplexing. And the non-integer electric charge is one more sign, in my opinion, that we are dealing with combinations rather than elementary particles.