[The below excerpt is from Chapter 3 of my book, Block by Block – The Historical and Theoretical Foundations of Thermodynamics.]

If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words?  … all things are made of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another.  In that one sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied. – Richard Feynman [1]

Forming the elements – review

Atoms weren’t there at the beginning.  The ingredients were but the early universe was too hot for them to combine.  It took a little over three minutes for the universe to cool enough (about 1 billion^oC) for protons and neutrons to combine (1:1) into deuterium nuclei.  Once this bottleneck was broken, the production of an array of two, three and four-particle nuclei soon followed.  These reactions bound almost all free neutrons into helium nuclei, thus preventing their disappearance from the universe on account of their short (~10 minute) half-life.   It would take another 300,000 years for the universe to cool further enough (3,000 ^oC) for the electrons to fall into stable orbits around these nuclei.

The mixture resulting from the Big Bang, largely atomic hydrogen (75 wt%) and helium-4 (25 wt%), became the raw materials to a second stage of reactions that took place inside the early stars due to the severe conditions present:  high temperature, high pressure and tremendous particle-spewing explosions.  The repeating star cycle of formation-collapse-explosion with increasingly heavier elemental starting materials led to the creation of the periodic table of elements at the universe-wide populations we observe today.  After each cycle was completed and after matter cooled, the electrons settled back into their orbits, one electron for each proton, thus preserving electrical balance.

Some staggering numbers

So what is an atom and what are its properties?  A seemingly simple question that becomes increasingly more complicated as one delves further.  Let’s start with the simple first.  An atom consists of protons, neutrons (except for the simplest atom, atomic hydrogen) and electrons.²  That’s it.  Just three fundamental building blocks behind the chemistry of the periodic table.  The protons and neutrons, collectively called nucleons, comprise the nucleus, giving the atom nearly all its mass, while the electrons move in orbit around the nucleus, giving the atom nearly all its volume.

As with The Big Bang, when discussing the atom, the numbers used are enormously far removed from 1, the number we’re most used to.  For example, the atom is 1-2 x 10^-8 centimeters in radius, a number so small that it’s difficult for us to grasp.  In a cubic centimeter of a solid, about the size of the end of your thumb joint, there are approximately 10²² atoms, a number so large that it’s also difficult to grasp.  How big is this number?  Well, if you spread this many peas across the continental United States, you would have a pile about 10 miles deep.

The sizes naturally get even smaller inside the atom.  It turns out that the nucleus has a radius of only 10^-13 centimeters, a hundred thousand times smaller than the atom itself.  In fact, much of an atom contains no mass.  Sticking with the peas, imagine placing a pea on the pitcher’s mound inside a baseball stadium.  The pea to the stadium is similar in size ratio as the nucleus to the orbiting electrons.³  And since the mass of the protons and neutrons far exceeds the mass of the electrons, nearly all of the weight of the atom is concentrated in a central region less than 0.0001% of the atom’s volume. 

Because the atom’s mass is concentrated in the infinitesimally small region of the nucleus, the density of the nucleus is huge.  About 3 x 10¹⁴ gm/cc.  One teaspoon of nuclear matter weighs as much as 50 billion tons.  The particles of nuclear matter, namely the proton, the neutron, and thus the nucleus, have this density.⁴

Strange behavior at small scales

The behavior of matter on a small scale… is different from anything that you are used to and is very strange indeed  – Richard Feynman⁵

While the atom may seem like a simple, quiet entity, to borrow a cliché, still waters run deep.  The strong proton-proton repulsive forces at play inside the nucleus lead to the high-speed motions of protons and neutrons relative to each other, and the electrons move around the nucleus in excess of about 1300 miles/sec, achieving quadrillions of rotations every second in a plane that itself is in motion, performing billions of full rotations per second.⁶  During each billionth of a second, the electron sweeps across the entire outer surface area of the atom. 

Such terms as orbit, particle and velocity are convenient terms for us to use.  But they’re not accurate, for at the small scales involved the strange world of quantum physics takes over and matter behaves unlike anything we’re used to.  The electron, for example, collides with other mass, just like a particle, and yet it has a wavelength and frequency, just like a wave.  It’s these wave-like characteristics that explain why the electron’s motion about the nucleus is like an orbit but really isn’t and also why the electron is pulled very strongly towards the proton but doesn’t crash into it as one would expect.  When working to understand or interpret such strange concepts, we often reach for words we’re familiar with to set up x-is-like-y analogies.  As Feynman wrote, “Because of the weakness of the human brain, we can’t think of something really new; so we argue by analogy with what we know.” ⁷  But at the small dimensions of the atomic world, such approaches break down and at times create confusion.  As we’ll see later, this topic about language comes up time and time again in science.  Nature does what she does, regardless of our way of thinking, and we struggle to describe her.  Unfortunately we can’t force her to conform to our words.  Now, having said all this, I have to stay with such inexact words like orbit and particle because they do fill a role and because I don’t have any other words to use.

The atomic building blocks and the interactions between them

In the following I address the science of the atom (Figure 3.1) by introducing the four relevant particles—proton, neutron, electron, photon—along with the interactions⁸ between them, but I don’t do this one-by-one.  While each individual particle and interaction is interesting, it’s really their participation in two larger structures that’s relevant to this book, the first such structure being the nucleus where the protons and neutrons reside, held together by the strong nuclear interaction and stabilized by proton:neutron ratio adjustments enabled by the weak interaction.  While the properties and behaviors of the nucleus aren’t critical to understanding the basic thermodynamic chemistry covered in this book, they did play a significant role in the historical steps leading to the discovery of the atom.

The second larger structure is the atom itself, comprised of electrons held in orbit around a positively charged nucleus by the electromagnetic interaction.  Free electrons together with other fundamental particles naturally played a significant role in the early moments of the Big Bang, but it’s the bound electrons that give us chemistry and thus most interests us now.  I’ll explain how the orbiting electrons create a seemingly hard (but comparatively massless) sphere around the nucleus, a sphere that can’t be penetrated by the orbiting electrons of neighboring (non-reacting) atoms, and how these properties create atomic volume.  I’ll then explain what it is about the orbiting electrons that leads to intermolecular forces.

I’ll conclude this section by introducing a final fundamental particle, the photon, which serves as the messenger of energy between atoms through its interaction with the orbiting electrons. 

While admittedly brief, I will periodically return to the following science background throughout the remainder of this book as a means of connecting the microscopic world with our macroscopic theories and equations.

The atom’s nucleus is comprised of both protons and neutrons.  Since the neutrons are neutral and the protons are positively charged, thus strongly repelling each other via the electromagnetic interaction, the question must be asked, what is holding the nucleus together?  How can it even exist?

Gravity and electromagnetism—like charges repel, unlike charges attract—represent two of the four fundamental interactions in nature.  Operating inside the nucleus is a third interaction acting between the protons and neutrons.  It’s this interaction that holds the nucleus together, a interaction that acts at very small distances and is much larger than the electromagnetic interaction.  It’s called the strong nuclear interaction.

The strong nuclear interaction

The strong interaction is attractive, pulling all of the nucleons towards each other—protons to protons, protons to neutrons, neutrons to neutrons.  It acts equally strongly between these particles and over very small distances, about the same size as the diameter of the particles themselves, and serves to counter the repulsive electromagnetic interaction between the protons.  It’s the presence of neutrons and the contributing attractive strong interactions they bring that makes possible atoms heavier than hydrogen.

The strong interaction falls off extremely rapidly with distance, much more so than the electromagnetic interaction, halving for each 10^-13 cm increment, which is about the diameter of a nucleon.  Because of this, the strong interaction is confined solely to the nucleus and plays no role in the interaction between the nucleus and the orbital electrons or neighboring atoms. 

Consider a proton at the surface of a nucleus.  The strong interaction holding it to the surface is greater than the combined electromagnetic repulsive interaction of the other protons in the nucleus.  If you tried to pull this single proton away from the surface, you’d need about the same force as that required to lift a 50-lb suitcase.⁹  However, as you continued to pull and eventually move the proton just a small distance away from the surface, on the order of the radius of the proton itself, the net force dramatically switches from attractive to repulsive, and once this switch occurs, the repulsive force is so large that the proton explodes away from the nucleus at extremely high velocities. This phenomenon—positively charged nucleus fragments separating from the remaining positively charge nucleus—is the source of the tremendous energy released in atomic fission.

The nucleus

For the elements with low atomic number, the nucleus contains about an equal number of protons and neutrons.  For example, carbon-12 has six neutrons and six protons.  With increasing atomic number however, a higher fraction of neutrons is required to hold the nucleus together.  Iron-56 has 26 protons and 30 neutrons, gold-197 has 79 protons and 118 neutrons and uranium-238 has 92 protons and 146 neutrons.  The reason for this shift is that each nucleon, whether proton or neutron, feels the strong attractive interaction only from its immediate neighbors, while each proton feels the repulsive interaction of all the other protons inside the nucleus.  Two protons on opposite sides of the nucleus aren’t attracting each other at all; the sole interaction acting between them is repulsive.  The increasing neutron:proton ratio with increasing atomic weight is needed to increase the attractive interactions inside the nucleus and so maintain stability.

This balancing act between protons and neutrons hits a breaking point at uranium-238, the heaviest naturally occurring element.¹⁰  Barely stable, this element is primed to explode given the least disturbance.  Its nucleus packs so much repulsive force from the 92 positively charged protons that even with so many additional neutrons the strong interaction is only just strong enough to hold the nucleus together.  If the nucleus is disturbed ever so slightly, it breaks apart—well, really it explodes apart—into two pieces that are each positively charged.  The strong electromagnetic repulsion between them causes them to fly apart at tremendous velocities.

Quarks – source of the strong interaction

The source of the strong interaction lies inside the protons and neutrons in the form of quarks.  The atom is somewhat like a Russian nesting doll.  Inside the atom is the nucleus.  Inside the nucleus are nucleons.  Inside the nucleons are quarks.  Some theorize that inside the quark are ‘strings.’  We won’t discuss this further other than to say that six types of quarks exist, of which two, one labeled ‘up’ and the other labeled ‘down’, are relevant to this discussion.  Each nucleon has three of these quarks, two up and one down for the proton and two down and one up for the neutron.  Being the actual source of the attractive strong interaction, these quarks only occur in tightly bound groups.  An interesting aspect of the quarks is that the attractive interaction between them counter intuitively increases with increasing distance, meaning that they can’t be pulled away from each other, further meaning that free quarks don’t exist.  Evidence of their existence is necessarily indirect.

Nuclear decay – alpha, beta and gamma

I introduce these three decay processes for two reasons, the first because each played a significant role in the discovery of the atom, and the second to introduce the weak interaction.  During beta decay, the weak interaction occurs within the quarks and thus operates at much shorter distances than even the strong interaction.  It allows quarks to exchange fundamental particles such that a down quark within a neutron changes to an up quark, thereby converting the neutron to a proton plus the emission of a beta ray (electron) plus a neutrino.¹¹

Beta Decay:  Neutron  –>   Proton + electron + anti-neutrino ¹²

The relative strength of the four fundamental interactions

Of the four fundamental interactions, I’m primarily interested in the electromagnetic interaction, because in the end it’s this interaction that governs the relationship between the electrons and protons and thus governs chemistry.  Here’s why.  First consider the four fundamental interactions along with their dramatically different (relative) strengths.

Strong interaction = 1                     acts inside nucleus; not relevant to this book’s thermodynamics

Electromagnetic interaction = 10^-2       the root cause of chemistry

Weak interaction = 10^-13                 acts inside nucleus; not relevant to this book’s thermodynamics

Gravitation interaction = 10^-38          conservation of mechanical energy – the lever & free fall

The strong and weak interactions act across very short distances, much less than the diameter of the very small nucleus where they operate.  While these interactions are critical to our world, serving to keep the nucleus intact, we don’t sense them in action.  This is left to the particle physicists who intentionally probe their inner workings.

Of the other two interactions, we are more familiar with gravitation.  We see direct evidence of gravity every second of every day.  It’s the dominant force shaping our universe, embedded in space, reaching beyond the atom all the way to the most distant stars.  It is the cause of motion in the lever and during free fall, the realization of which led early scientists to an early version of the conservation of mechanical energy.

While gravity is part of our everyday language, the electromagnetic interaction is more obscure.  We don’t think of it.  People on the street don’t talk about it.  It’s a more difficult concept to understand.  But, when all is said and done, it’s the electromagnetic interaction (and resulting forces) that makes our life so interesting.  Our body’s senses evolved to be triggered by this interaction.  It governs, either directly or indirectly, how we see, feel, hear, smell and touch.  It’s the electromagnetic relationship between electrons and protons and the associated separation of charges that governs the chemistry of the periodic table.  It’s a seemingly simple interaction that provides an abundance of wonderful and colorful complexity and beauty.

The electromagnetic interaction

The electromagnetic interaction originates from charges—opposite charges attract, like charges repel, acceleration generates photons—and overwhelms gravity as shown by their relative strengths above.  Put two grains of sand thirty meters apart from each other.  They can barely feel the attractive interaction of gravitation between them.  But if all of the mass in one of the grains were associated with a positive charge and all of the mass in the other grain were associated with a negative charge, the resultant attractive force between them would be three million tons.¹³   We don’t talk about the electromagnetic interaction because we live in a paired world of electrons and protons—it’s tough to keep them apart.  But this seemingly neutral world is an illusion.  It’s only neutral from a distance.  Like an Impressionist painting, an atom is smooth and continuous only from a distance.  Move up close and things start to get fuzzy as the neutrality disappears and the granularity shows itself.  It’s up close where the electromagnetic interaction does what it does, governing the motions of the granular parts and creating the atom’s volume along with the tendencies of atoms to attract and react.

Why the atom has volume – the quantized orbit

What happens when a body is far removed from Earth?  Gravitation interaction pulls the body towards Earth, causing it to accelerate.  The body’s total energy remains constant, as its potential energy is transformed 1:1 into kinetic energy.  Depending on the situation, it can fly past Earth (with a change in direction), it can go into orbit or it can crash. 

What happens when an electron is far removed from a proton?  Something similar but only up to a point.  The electromagnetic interaction pulls the negative electron towards the positive proton.  But this is where similarity ends and Feynman’s world of “strange behavior” begins.  Yes, if the electron is initially moving fast enough, as it was prior to the first 300,000 years of the universe, it will fly past with a change in direction.  So this isn’t that strange.  And if it’s moving slowly enough, it to can go into orbit.  So this isn’t strange either.  But it’s what happens next that’s strange.

A body orbiting Earth will remain at whatever radius it established based on its initial conditions (momentum plus location) and will then stay in this orbit (almost) forever.  Think of the planets orbiting Sun.  The total energy of the orbiting body stays the same; the swing back and forth from potential to kinetic and back to potential occurs on average in a 1:1 relationship.  But an orbiting electron experiences something different because it can lose energy (via photon ejection) while the orbiting body can’t.  Once the electron establishes an orbit at a certain maximum or outermost radius, it starts moving in discrete jumps closer and closer towards the proton, shedding energy as it does so by ejecting photons.  The electron moves inward from one orbital to the next, as if it were descending a staircase, sometimes one step at a time and sometimes skipping steps altogether, releasing one photon per each step equal in energy to the energy difference between the orbitals, until it can’t go any further.  Thus, as opposed to a free falling body experiencing gravitational transformation of potential to kinetic energy, a “falling” electron experiences electromagnetic transformation of potential energy to photon emission.

For each discrete “quantized” step of the electron towards the proton, a photon is ejected.  This process can be reversed if a photon of the same energy returns to the system to be absorbed by the electron and so energize it back up the stairs.  Thus the electron moves down and down until it reaches the lowest possible radius.  This movement is also sometimes referred to as an “energy minimization” process since the inward movement and corresponding photon ejection ultimately minimizes the total energy of the electron.¹⁴

Why a minimum radius?

The above still leaves us with the question, what stops the electron’s descent?  Why doesn’t it keep on going and crash into the proton?  Classical physics says it should.  As we’ll see later, this historic question was asked by Neils Bohr and the simple answer goes back to the electron’s wave characteristics.  In short, even though the electron is a particle, it has a wavelength.  The early quantum mechanical rulebook, prior to the more complicated rulebook of Schrödinger and Heisenberg and others which isn’t necessary to get into here, states that the electron can only establish stable orbits around the nucleus when the circumference (as determined by the radius) is equal to an integer multiple of the electron’s wavelength.  Thus, as it descends from orbital to orbital, the electron moves towards the nucleus in very precise integer steps, or multiple-integer steps if it makes larger jumps, from radius to radius, with each accessible radius corresponding to an orbital circumference equal to an integer multiple of the electron’s wavelength, ejecting one photon for each step taken, until it gets to a final orbital whose circumference equals the length of a single wavelength of the electron.  This “ground state” thus occurs at the minimum orbital circumference and thus the minimum orbital radius.  For hydrogen, this radius is called the Bohr radius.

Heisenberg Uncertainty

But the question still remains, why does such a minimum exist?  We return to Feynman’s concept of “strange” behavior.  While the electromagnetic interaction pulls the electron towards the proton, the electron’s wavelike character keeps it from crashing fully inward.  Very advanced mathematical equations show that as the electron starts moving closer to the nucleus than its minimum radius, its wave is compressed into a smaller region, causing its total energy to increase, which makes this step highly improbable.  Thus, the electron remains at the minimum radius where its total energy is minimized.

At the heart of these advanced mathematics is the famed Heisenberg uncertainty principle.  What this principle roughly says is that as a particle’s location becomes more defined, its momentum becomes less defined.  This is one of those strange parts of nature for which there’s no easy explanation.  It’s just so.  Thus, as the electron moves closer to the nucleus than the minimum radius, it moves within a tighter space, making its location more certain but its momentum less certain, and this leads to its energy increase.  The uncertainty principle explains why electrons don’t crash into nuclei and thus why atoms can’t be compressed.  It was quantum mechanics that explained this.

* * *

Because the bound electron’s potential energy decreases as it moves towards the proton (and ejects photons along the way), it has a lower potential and a lower total energy than it did at infinite distance.  The energy of an orbital electron is typically quantified by the energy required to pull it away from the atom to an infinite distance.  This energy is thus called the electron’s “binding energy.”  Since the energy at infinite distance is arbitrarily set to zero, the energy of orbital electrons is necessarily negative.  The ground state electron requires the highest removal energy; its “binding energy” is thus the most negative.

Pauli Exclusion

When we’re dealing with atoms having more than one electron and one proton, an additional principle steps in to govern things.  Modifying our previous examples, imagine releasing multiple electrons near a nucleus containing an equal number of protons (and associated neutrons).  Once released, the electrons cascade down the orbital energy levels, ejecting photons while doing so, until they eventually get to the point where they can’t go any further.  Now one might think that all the electrons would end up in the same bottom-most orbital of minimum radius.  But this doesn’t happen.  In yet another point of “strangeness,” it turns out that electrons have a property called spin,¹⁵ which has something to do with angular momentum, and this property has one of two possible values, +1/2 and -1/2.  According to something called the Pauli exclusion principle, two electrons of the same spin can’t co-exist in the same orbital, thus meaning that the maximum number of electrons in a given orbital is two, and they must have opposite spin.  So once the bottom-most orbital fills with two electrons, each of opposite spin, the next orbital up (larger radius) gets filled, again with two opposite-spin electrons, and this is repeated, again and again, until all the electrons have placed themselves in a bottom-up filling of the orbitals.

The behavior of orbiting electrons enables modeling the atoms as hard spheres

While the Pauli exclusion principle explains the electron housing rules, it also helps explain something else and brings us back to the start of this section.  It contributes to our understanding of how the behavior of orbiting electrons mathematically turns atoms into a billiard balls.  Why do atoms “collide” with each other?  Why don’t their electron clouds just pass through each other?  The answer?  Pauli exclusion, which roughly says that no more than two electrons (of opposite spin) can be in the same the same place.  The clouds aren’t allowed to overlap.  As Feynman said, “almost all the peculiarities of the material world hinge on this wonderful fact.” ¹⁶  But note that while Pauli exclusion prevents overlap, it doesn’t create the rebound effects of the collision.  Pauli exclusion is not a force itself; it’s a principle.

While Pauli exclusion doesn’t directly cause repulsion, and is not a repulsive force, it is because of Pauli exclusion that repulsion occurs.

Consider two helium atoms approaching each other. Each atom consists of two protons, two neutrons, and two electrons. As recounted in one of my previous posts (here), as they approach, their respective electron clouds overlap, and their individual orbitals merge into a bonding orbital, which is then populated by two of the electrons, one from each atom.

Now comes the critical point. What happens to the next two electrons? They can’t enter into this same bonding orbital with the others because of the Pauli exclusion principle. So they must enter into the next orbital available up on the energy ladder, which is an anti-bonding orbital. This orbital forms at the same time as the bonding orbital. The anti-bonding orbital is so named because the electrons in this orbital accumulate outside the region between the nuclei and so can’t contribute to bonding. Instead they contribute to anti-bonding since their location effectively decreases the pull of the two positively-charge nuclei toward the negative electrons between them, leaving the proton-proton repulsion force to dominate the situation.

The anti-bond negates the covalent-bond, leaving a very weak net bond. This is what happens when atoms “collide.” The bond between them is weak and they repel each other. Electron-electron interactions contribute to the net repulsion, but it’s the proton-proton interactions that dominate. Two helium atoms collide (and don’t react) because there is room in the bonding orbital for only one pair of electrons; the other pair must occupy the anti-bonding orbital.

The same general principles apply to all closed-shell molecules. Individual electron orbitals combine to form two orbitals, one bonding and one anti-bonding. Being closed-shell, two electrons are offered up by each atom. Two enter the bonding orbital, the other two the anti-bonding orbital, leaving a weak net bond that is easily broken by the strong proton-proton repulsion.

Atoms as stable hard spheres – summary

That the atom conceptually exists as a stable hard sphere is rather amazing since the electromagnetic interaction seeks both to explode the nucleus into fragments (proton-proton repulsion) and to collapse the electrons into the nucleus (electron-proton attraction).  Fortunately for us, the presence of the countering strong interaction prevents the nucleus explosion and the quirkiness of the quantum world prevents both collapse (Heisenberg uncertainty principle) and atom overlap (Pauli exclusion principle).  Acting together these principles explain why matter, despite being over 99.9999% empty of mass, has such strength and thus why atoms can be treated as hard, incompressible spheres, an extremely simplifying feature that opens the door to very powerful mathematical modeling.  The additional fact that mass is concentrated in the center and not spread evenly throughout the volume provides a further simplifying assumption: the thermal energy associated with rotation for a monatomic atom is effectively zero.  This fact impacts the heat capacity of monatomic elements.

Atom – why the attract

When the electron (E1) of the first hydrogen atom moves between the two protons (P1 and P2), it repels the electron (E2) of the second, forcing it to move away and behind P2.  E1 is attracted to P2 resulting in net attraction between the two atoms.  Since E1 is closer to P2 than P1 is, the attractive force between E1 and P2 is greater than the repulsive force between P1 and P2.  One could argue though, that E1 will eventually circle around behind P1, thus reversing this situation.  But one can’t ignore E2 in the process.  When E1 departs, E2 comes back out front again and creates a new net attractive force with P1.  In this way, the two electrons develop a synchronized motion, resulting in a net-net attractive force between the atoms that switches back-and-forth and back-and-forth at very high frequency.  This attractive force, called the van der Waals force or London dispersion, is a natural response between any two atoms.  The strength of attraction varies, but it’s always there.

In essence, each atomic hydrogen atom is a microscopic magnet containing a positive (proton) and a negative (electron) pole.  The opposite poles from the two magnets attract each other.  In the real atoms, even though the poles are spinning at very high speeds, the atoms sense their presence and so respond to each other, aligning their motions such that the opposite poles, although moving, can still line up in a synchronized way and create a net attractive force.

Between all atoms, not just atomic hydrogen, the attractive van der Waals attraction is always present.  If atoms approach each other slowly enough, these attractive forces will lead to weak van der Waals bonding (not covalent bonding) and can result in such physical phenomena as condensation.  When additional attractive forces are involved, such as exist in polar molecules where certain nuclei attract electrons more than others, an extreme case being polar water molecules in which the oxygen nuclei have much stronger attraction of the electrons than the hydrogen nuclei, the weak bonding tendency (again, not covalent bonding) increases.  In these situations, however, if the approach speed is too high, the atoms and molecules collide and bounce off each other like billiard balls.  With increasing speeds, the bounce is stronger and prevents weak-bonding attachment from occurring, much like two ‘sticky’ objects will bounce off of each other if you throw one at the other with high enough speed.  Replace the word ‘speed’ here with ‘temperature’ and this explains why changes in temperature cause transitions from solid to liquid to vapor.

The covalent bond

Returning to atomic hydrogen for now, as the two atomic hydrogen atoms attract each other and move closer to each other, they react since each electron has a new lower-energy orbital accessible to entry.  This new orbit is called a bonding orbit.  The sharing of the electron pair between the two atoms results in a very strong bond, called a covalent bond, and leads to the formation of a hydrogen molecule, denoted as H₂.  In a covalent bond, two electrons, one from each atom, occupy the same orbital, called a molecular orbital.  The orbital is shaped like an hourglass, with each proton located in its own bulb.  When the electrons’ orbit takes them to the center of the hourglass, they serve to pull the two nuclei towards each other.  The length of the resulting bond is determined by an equilibrium balance between the attraction of the two nuclei towards the centrally located electrons and the repulsion of the two protons for each other. 

The covalent bond is the strongest chemical bond.  There is none stronger because the Pauli exclusion principle limits the maximum number of electrons in the space between the nuclei to two—and they must be of opposite spin.  All other types of bonding, such as van der Waals bonding, hydrogen bonding, ionic bonding, and so on, involve the occurrence of less than two electrons between the nuclei.

The incomplete outer shell

To generalize for more complicated atoms, the reason why a bond could form between the two hydrogen atoms in the last example is that each had an unfilled outer orbital and the Pauli exclusion principle allows both electrons to form a new bonding orbital (lower energy than the two separate orbitals) so long as they are of opposite spin.  This generalization also applies to atoms comprised of multiple protons and thus multiple electrons but things get more complicated since increasing the number of electrons opens the door to increasing orbital shapes.  Orbitals are typically categorized by energy level, which is sometimes referred to as a shell.  The innermost energy shell, which is characterized by a principal quantum number and which I don’t need to get more into here, is the ground state and is comprised of a single orbital having a spherical shape.  The second energy shell is comprised of four orbitals—one sphere, three hourglasses—while the third shell is comprised of nine orbitals—one sphere, three hourglasses, five cloverleaves.  (Orbitals having the same energy level but different characteristic shapes are called degenerate.)  So it’s really more accurate to say that when the outermost energy shell isn’t full, meaning that one or more of the degenerate orbitals is not full, then the atom can react.  But if the outermost energy shell is full, then the element is inert.  There are chemistry subtleties here that I don’t want to get into as it would necessarily lead to a lengthy discussion of the rather complicated physics of electron orbital structures and chemical reactions.  But again, in general, because the housing rules are based on bottom-up filling, whether or not an element is reactive depends on whether or not the outermost energy shell is full.

These issues explain the structure behind the periodic table.  The chemical properties of the elements are governed largely by the extent of saturation (or valence) of the outermost energy shell.  The inner orbitals aren’t relevant because they’re full.  For example, elements of similar valence behave similarly in chemistry and are thus positioned in vertical columns in the periodic table.  Elements having a valence of zero have full outer shell(s) and are thus chemically inert.  These elements are the inert elements (noble gases) that populate their own column.

Given this, one can see why the discovery of the atomic number played such a crucial role in the development of the Periodic Table.  The chemical properties of an atom are largely dictated by the number of electrons it has, which is equivalent to its atomic number as defined by the number of protons it has. 

Alas, the fun and wonderful description of the elements as one marches through the Periodic Table is beyond the scope of this book but does fill many books and makes for fun reading.  The interested reader is encouraged to explore the works of, for example, John Emsley or Eric R. Scerri.

* * *

The totality of the above phenomena lies at the core of chemistry.  It’s the fact that negative electrons and positive protons are separated in space within a bound atom that gives rise to attractive forces between atoms and molecules.  It’s the fact that negative electrons continually seek to minimize total energy by moving as closely as possible to the positive protons that gives rise to chemical reactions.  It’s the fact that a negative electron can only get so close to the positive proton combined with the fact that orbiting electrons of colliding atoms can’t overlap that gives the atom volume.  And it’s the combination of all of these facts and others that give us chemistry.

Photons

Our eyes detect photons as colored light.  Our skin feels photons as heat from a red hot metal bar across the room.  Doctors fire photons called x-rays through our body to detect if a bone is broken.  We heat dinner using microwaves.  In each case, the photons, whether in the form of light, thermal radiation, x-rays, or microwaves, transfer energy between matter, typically through their interaction with orbital electrons.

Photons are discrete particles of electromagnetic energy that don’t sit still.  Ever.  They always move at the speed of light (186,000 miles/sec in a vacuum) and have zero mass. 

As an elementary particle, a photon is generated or destroyed as a single particle and once generated, remains this way, travelling vast distances in a straight line, not spreading out over distance and time as a wave would.

A sea of photons exists all around us.  On a sunny day, about a thousand billion (10¹²) photons of sunlight fall on a pinhead each second.  We don’t sense these discrete particles of energy; their overwhelming presence makes them appear to us as a continuum.  We can’t see the gaps.

Yet, while such language suggests that photons are particles, don’t be fooled.  Like the electron, or even the proton and neutron for that matter, each photon has both particle and wave properties, a wave-particle duality that we haven’t yet captured in a word.  Like a particle, each photon carries energy, linear momentum and angular momentum.  Like a wave, each photon displays both wavelength and frequency, the two linked together by the constant wave speed equal to the speed of light.  Many discrete photons added together form an electromagnetic wave.  Wave or particle?  It all depends on one’s perspective, neither perspective being more truthful than the other.  Once again, our language fails us in this small and strange world.

Why should we care about photons?  Because when photons are absorbed (or emitted), they increase (or decrease) the energy of matter.  Just because they have negligible mass doesn’t mean they have negligible influence.  Each photon is an electromagnetic wave that interacts with charged particles and causes them to move; thus, each photon has momentum; they cause motion; they affect the thermal energy of matter; they play an important role in any energy balance such as those based on radiative heat transfer.  When bound electrons move from orbit to orbit or when energy transitions occur inside the nucleus, photon absorption or emission is involved.  At the most fundamental level, photons are messengers of electromagnetic interactions, playing a key role in the events that occur between charged particles.  They really aren’t any different from the mass-carrying constituents of the atom.  Each shows wave-particle duality, some more so than others.  At these small scales, there is no distinction between wave and particle.

When photons are emitted or absorbed by matter, the rule of interaction is very specific.  The photon’s energy, as defined by its frequency, is exactly equal to the difference in energy between the two states involved.  There is no partial emission or partial absorption.  The science of spectroscopy is based on such phenomena as these.

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References

[1] Feynman, Richard Phillips, Robert B. Leighton, Matthew L. Sands, and Richard Phillips Feynman. 1989a. The Feynman Lectures on Physics.  Volume I.  Mainly Mechanics, Radiation, and Heat. Vol. 1. The Feynman Lectures on Physics 1. Redwood City, Calif.: Addison-Wesley., p. 1-2.

[2] The atomic number defines the element and equals the number of protons, while the atomic weight is equal to the combined weight of protons and neutrons.  The presence of isotopes reflects the fact that varying neutrons—and thus varying atomic weights—can exist for a given element.  A number following the element name denotes an isotope.  For example, carbon consists of 6 protons and so carbon-12 consists of 6 protons plus 6 neutrons.

[3] Other effective analogies include:  If the atom were the size of a soccer ball, its nucleus would be less than the size of the period at the end of this sentence.  Or, if the nucleus were the size of a golf ball, its electron would reside one mile away.

[4] While the atomic densities of the elements range from a minimum of 0.09 to a maximum of 22.5 gm/cc for hydrogen and osmium, respectively, the densities of the nuclei are constant at about 3 x 10¹⁴ gm/cc.  The range in atomic densities reflects the fact that density equals mass divided by volume.  As each nucleon is added to the nucleus, tight packing is maintained such that the increase in volume is directly proportional to the increase in mass, thus leaving the nucleus density the same.  For the atom, however, as each nucleon is added to the nucleus, mass increases while the volume of the atom doesn’t really change that much.  For example, the radius of hydrogen is about 0.8 x 10^-8 cm while that of osmium is 1.4 x 10^-8.  So the much higher mass of osmium (76 protons + 116 neutrons) relative to hydrogen (1 proton) is squeezed into a similar volume (only about 8 times larger), resulting in a much higher atomic density as shown above.  See Emsley, John. 1990. The Elements. Reprinted (with corrections). Oxford: Clarendon Press.

[5] Feynman, Richard Phillips, Robert B. Leighton, Matthew L. Sands, and Richard Phillips Feynman. 1989. The Feynman Lectures on Physics.  Volume II. Mainly Electromagnetism and Matter. Vol. 2. The Feynman Lectures on Physics 2. Redwood City, Calif.: Addison-Wesley. Volume II, p. 35-1.

[6] Simhony, M. 1994. Invitation to the Natural Physics of Matter, Space, and Radiation. Singapore ; River Edge, N.J: World Scientific, Chapter 5.

[7] Feynman et al., Volume II, p. 28-12.

[8] The four fundamental interactions—strong, electromagnetic, weak, gravitation—are sometimes referred to as the four fundamental forces.  In general, I use “force” when referring to the attraction or repulsion that occurs as a result of the interaction.

[9] Frisch, Otto Robert. 1973. The Nature of Matter. New York: Dutton, p. 135.

[10] Heavier elements do exist, but they are man-made using special equipment and their nuclei are so unstable that they live a very short life. 

[11] The reverse process is called electron capture and can occur inside atoms when the nucleus absorbs an inner bound electron.

[12] This particle was initially termed “neutrino” and was later changed to “anti-neutrino.”

[13] Feynman et al., Volume I, p. 2-4.

[14] The total energy of the electron, comprised of both kinetic and potential (electromagnetic) terms, is quantified in a mathematical function known as the Hamiltonian.  The mathematics here are complicated especially when more than a single electron is involved.  The Hamiltonian played a critical role in the development of quantum theory.

[15] The term ‘spin’ was coined during early research on electrons when they demonstrated properties associated with angular momentum, which implied that they must be spinning.  However, in order for something to spin, it must have an internal structure.  To the best of physicists’ understanding, electrons do not have an internal structure, which means they can’t actually spin.  They must truly be fundamental, irreducible particles without structure but with an inherent angular momentum.  Even if there were standing still, orbiting nothing, they would have an angular momentum, a property as fundamental as charge and mass.

[16] Feynman, Richard Phillips, Robert B. Leighton, Matthew L. Sands, and Richard Phillips Feynman. 1989. The Feynman Lectures on Physics.  Volume III. Quantum Mechanics. Vol. 3. The Feynman Lectures on Physics 3. Redwood City, Calif.: Addison-Wesley, p. 4-13.

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