Of Particular Significance

Atoms: Building Blocks of Molecules

Matt Strassler [December 7, 2012; updated December 9]

If molecules — the main structures that are involved in chemistry — are the words from which all of the materials around us are built, then atoms are the letters, the building blocks for molecules.  Just as there are words of all lengths, a typical molecule may contain a few or a hundred or even a hundred thousand atoms.  A molecule of table salt (NaCl) contains two atoms, one of sodium (Na) and one of chlorine (Cl); a molecule of water (H2O) has two of hydrogen and one of oxygen; a molecule of table sugar (C12H22O11) is made from twelve atoms of carbon, eleven of oxygen and twenty-two of hydrogen in a very particular arrangement.

How do we know atoms exist?  In some cases, we can “see” them, much as we can see the molecules that they can form… not with our eyes, but with more advanced “seeing” devices.  One method involves a “scanning tunneling microscope”, which can show the atoms inside a crystal, or even move them around one at a time. Another method uses our ability to trap ions (atoms which are slightly altered, as explained below). Here is a photo showing evidence of three ions being trapped simultaneously. [Light is shined onto the ions, which is then absorbed by the ions and re-emitted. The re-emitted light can be detected, allowing us to “see” where the ions are, in a way somewhat analogous to how a reflection of light off a tiny but shiny diamond allows us to find it.]

How many types of atoms are there?  The types are called “chemical elements”, and the precise number depends on how you count, but let us say for the moment that the atomic alphabet consists of about a hundred chemical elements; we’ll return to the counting subtleties later.  Just as we could associate the letters in the alphabet, A to Z, with the numbers 1 to 26, every element is given not only a name but also a number, called the atomic number, and often written “Z”.  The simplest atoms are those of the element hydrogen; it has atomic number 1. The most complex atoms found in abundance in nature are those of the element uranium, which has atomic number 92.  Others include oxygen (8), nitrogen (7), calcium (20), krypton (36), lanthanum (57), platinum (78).  You can find the full list here, in the “periodic table of the chemical elements.”  Which element an atom represents determines its chemistry — how it behaves inside molecules — just as the member of the alphabet that a letter represents determines how that letter can function inside various words.

Now here’s a list of questions you might ask about atoms:

  1. What are atoms made of?
  2. What is the meaning (if any) of the atomic number?
  3. What is the main source of the difference in chemistry between an atom from one element and an atom from another element?
  4. To what degree are all atoms of a particular element similar or the same?
  5. What makes the parts of an atom stick together?
  6. Why do atoms stick together to make molecules?

It turns out that all of these questions are best answered by starting with question number 1: what are atoms made of? Atoms are made of objects usually called “subatomic particles”.  [Unfortunately the term is somewhat misleading, as we’ll see, for these “particles” have some properties that aren’t very particle-like at all.]  Specifically, atoms consist of a set of tiny featherweight electrons surrounding a very small but heavy atomic nucleus that contains most of an atom’s mass. The nucleus is made of other “particles”, which are made of yet other “particles”; we’ll get to them in future articles.

The Cartoon Atom

We often see cartoon pictures of atoms drawn on chemistry books, advertisements, and warning signs. An example is given in Figure 1. It conveys the very rough idea of what an atom is like: it has a certain number of electrons (drawn here in blue) on the outside, in orbit around a central atomic nucleus. The nucleus is a cluster of protons (drawn red) and neutrons (drawn white).

Fig. 1: A cartoon of an atom, showing electrons (e) on the outside orbiting a nucleus, made from protons (p) and neutrons (n), at center.
Fig. 1: A cartoon of an atom, showing electrons (e) on the outside orbiting a nucleus, made from protons (p) and neutrons (n), at center.  The numbers of protons equals the “atomic number”, often denoted “Z”; in its simplest, electrically neutral state, the atom has the same number of electrons as protons.

Now we can answer question 2: what does the atomic number Z mean? It is simply how many protons an atom has.  Oxygen has atomic number 8, so its nucleus has 8 protons.

Under the simplest circumstances (see below), the atomic number is also how many electrons an atom has.  (The number of neutrons is a more complicated story, to be covered later.) Electrons have a negative electric charge (an amount we call -e) while protons have a positive charge (+e); neutrons are neutral (i.e. carry no electric charge.)  When the number of electrons and protons is equal, the charges of the electrons and protons exactly cancel, so that atoms have no electric charge — they are electrically neutral.

However, it is not unusual — in the process of forming molecules, for instance — for an atom to gain or lose one or more of its outermost (or “valence”) electrons.  In this case the electric charges of the electrons and protons don’t cancel, and the resulting electrically-charged atom is called an ion.

A More Realistic Atom

Although the cartoon in Figure 1 vaguely captures the overall architecture of an atom — it is true that there are electrons on the outside and a nucleus made of protons and neutrons in the middle — it profoundly fails to convey the real shape and character of an atom, because (1) it’s not at all to scale, and (2) we live in a quantum world, in which objects often behave in ways that are hard to draw or visualize.

Problem (1) can be partly dealt with through the somewhat more accurate (though still highly imperfect) image shown in  Figure 2.

Fig. 2: A more accurate depiction of an atom, showing it is mostly empty space (grey area) traversed by rapidly moving electrons (blue dots, drawn much larger than to scale) with the nucleus (red and white dot, drawn larger than scale) at center.  This is somewhat analogous to a rural community, with expanses of uninhabited land, a few scattered farm houses, and a small village with closely packed houses at its center.
Fig. 2: A more accurate depiction of an atom, showing it is mostly empty space (grey area) traversed by rapidly moving electrons (blue dots, drawn much larger than to scale) with the heavy nucleus (red and white dot at center, drawn larger than to scale) at center. Its shape is like that of a rural community, with expanses of uninhabited land, a few scattered farm houses, and a small village with closely packed houses at its center.

Let me explain what I’ve tried to convey through this image. First, electrons are very, very tiny, so small that we have never been able to measure their size — for all we know they are point-like, with zero size, but certainly they’re at least 100,000,000 times smaller in diameter than atoms. Second, the nucleus (and the protons and neutrons that make it up) is also very tiny, though larger than the electrons; its size has been measured, and is about 10,000 to 100,000 times smaller in diameter than its atom. An atom is in some ways like a small rural community. You might think of the protons and neutrons that make up the atomic nucleus as somewhat larger houses that make up the village in the center of the community, and the electrons as the far-flung farmhouses scattered around the village. Most of the land of the community — analogous to the realm of the electrons — contains crops but no houses. Although the territory that is considered part of the town may be quite large, the actual amount of area occupied by houses is very small, as is the area occupied by the village at the center of the town.

The analogy only goes so far, since the electrons, unlike the farmhouses, are in rapid motion, moving through the greyish region in the figure and around the nucleus at speeds that are typically about one percent of the speed of light. Note also that the territory they tend to cover, the grey spherical cloud, is not accurately drawn; it often has a more complicated shape, and not all of the electrons travel in the same region.

But as I warned you, Figure 2 still isn’t really accurate.  First, I’d have to draw the nucleus thousands of times smaller, and electrons millions of times smaller, than I have, in which case you wouldn’t see them on the picture at all. For scale, if an atom were the size of your bedroom, its nucleus would be the size of a speck of dust (unless you’ve got a really big bedroom.)  Compared to the size of the objects out of which they are made, atoms are huge!  In a sense (but see below) atoms are mostly empty space!

And second, much more profound and subtle, the figure does not convey the murky nature of quantum mechanics.  We use the equations of quantum mechanics to describe and predict the behavior of molecules, atoms, and subatomic particles, and those equations tell us that “particles” can have very strange and counter-intuitive properties.  Even though electrons are point-like in one sense (for instance, if you try to bounce two electrons off each other, you will find you can get them arbitrarily close together without them revealing that they have any structure), there is a way in which, when left alone, they can spread out like a wave, and fill out the entire grey area in Figure 2.  If that sounds strange, it’s not because you’ve misunderstood; it is strange, and hard to think about.    I certainly don’t have an ideal way to draw it that wouldn’t be misleading, and experts still argue about what is the best way to think about it.  So please just accept this as a strange fact, for now.

Whereas the electron’s size (if it has one) is too small to measure, and its mass is so small that the electron can spread out over a whole atom, the nucleus, on the contrary, has a measured and well-known size, and its mass is so large — more than 99.9% of the whole atom’s mass — that it barely spreads out at all.   The nucleus mostly just sits at the center of the grey area as the atom moves about.

The Atom and Its Chemistry

So the best way to describe an atom that I can come up with is this: most of an atom’s mass is carried by the small nucleus that sits at its center, around which extremely tiny electrons, with much smaller mass, are spread out (through the weirdness of quantum mechanics) in a most un-particle-like way, filling the grey area in Figure 2.

The tiny size of the nucleus relative to the whole atom, and its tendency to sit at the center of the atom, explains why it plays a relatively minor role in chemistry. Chemistry occurs — molecules form and change — when atoms come close together, and that happens when the outermost (“valence”) electrons from one atom come close to those of another atom — when the edge of the grey region of one atom comes into the general vicinity of the grey region of another atom. In chemical processes, the atomic nuclei remain at the centers of their atoms, and never come anywhere near each other, relatively speaking.  The main roles of the nucleus are providing the positive charge that holds the electrons in the atom, and providing most of the atom’s mass (which determines how easy it is for other objects to push the atom around.)

And so this gives us the answer to question 3: what determines an atom’s chemistry is (mostly) the details of its outermost (“valence”) electrons.  These details can be determined (in a somewhat elaborate way, using quantum mechanics equations) from its atomic number Z.

Instead of pursuing chemistry itself, a subject for a whole college course, we’ll continue on down to the subatomic particles, addressing along the way the other questions that are still unanswered. Here are the ones we dealt with and the ones that we still have to get to:

  1. What are atoms made of? Answer: Electrons on the outside and an atomic nucleus (made from protons and neutrons) at dead center.
  2. What is the meaning (if any) of the atomic number? Answer: it is the number of protons in the nucleus of the atom, which under simple circumstances equals the number of electrons that surround the nucleus.
  3. What is the main source of the chemical difference between an atom from one element and an atom from another element? Answer: the properties of its outermost electrons, which are determined by the total number of electrons for each element, i.e. the atomic number.
  4. To what degree are all atoms of a particular element similar or the same? Answer: Click here for a discussion of isotopes, and click here to learn about how all atoms of a given isotope are truly identical.
  5. What makes the parts of an atom stick together? Answer: Click here to learn about the role of electric forces and quantum mechanics.
  6. Why do atoms stick together to make molecules? Answer: Click here [coming soon] to learn about the role of electrons and electric forces in building molecules out of atoms.

And here is another that may have occurred to you, based on Figure 2:

  • If an atom is mostly empty space, how is it that any objects can seem solid?  Why can’t I just put my hand right through my computer screen, if the screen is made from atoms which are mostly empty?

78 Responses

  1. > And here is another that may have occurred to you, based on Figure 2:

    > If an atom is mostly empty space, how is it that any objects can seem solid? Why can’t I just put my hand right through my computer screen, if the screen is made from atoms which are mostly empty?

    Did you ever write an article about this? I would love to know the answer to this question.

    1. I did not. However, it appears in the book that I will soon be publishing, and I will provide some supplementary material on this blog even before publication.

  2. ” “neutron as element zero”; I would say this is physically not an atom, because, lacking an electron, it is not in the same class as the other atoms. ” A hydrogen ion doesn’t have an electron but is still counted as a hydrogen atom ?
    I’m an accountant and not a scientist so apologies if this is a nonsensical comment.

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  9. Matt, you said that “electrons … are in rapid motion, moving … around the nucleus at speeds that are typically about one percent of the speed of light.” That would suggest that electrons have lots of kinetic energy. Is there any way to tap that energy? Thanks.

    1. Electrons do indeed have a massive amount of kinetic energy on a weight-by-weight basis. Sadly, just because something is there does not mean it can be used. The electrons are in their ‘ground state’; the lowest energy they can possibly be, so there is no way of getting that energy out. It is similar to the fact that a single iron nail, if converted to energy, would power your house for 50 years; there is just no way to actually convert it, to get the energy out. (Short of throwing it into a black hole.)

      Interestingly one exception is ‘k-capture’ radioactive decay where an electron is adsorbed by a nucleus. This happens in you all the time, it is how potassium, a vital component of organic life, decays into argon.

  10. Excellent tutorial. 1) A better pictorial would be an animation where the electron is a pixel at jumps around the nucleus 10 times per second. Then point out that the animation is slowed down 10^43:1. Fast chemical reactions may occur on attosecond time scales, but from the electron’s standpoint this is 10^26 time steps. You underteach if you don’t point this out. 2) re: your reply to ru(Dec 9) “..sense in which [the electron] spreads out around the hydrogen atom in a nice spherical shape.” This is the shape of the ‘hood where the electron hangs, not the shape of the electron.

  11. These results are very interesting, but I would hesitate to draw the conclusions you do from this data. This is possibly due to the article’s title, which, in the usual manner of such press release is not entirely accurate.

    What the simulation shows is that the same laws govern large and small systems. This is not obvious, but not surprising either. We often see in nature phenomena that do not change with scale. The emission of plasma from the black holes in the center of galaxies looks near identical to the squirting of ink by a squid, and is governed by similar laws (A high speed fluid slowing down as it interacts with surrounding matter.)

    While the headline focuses on two examples, and the most eye catching, we could equally say the universe is like the internet, a fern or fat congealing on a plate of leftovers. Rather than assume that the entire universe is somehow imitating a small lump of mush in the bodies of a few billion apes on a tiny rock in space, might we rather infer that our brains grow not by some sort of unique, consciously directed means, but via the same simple laws that govern the collection of cold gas clouds?

  12. Possibly, what I was wondering when I asked the question was how the energy of the electron was distributed through space. With water I can define a certain volume of space and state that a certain amount of mass (thus energy) is present in it, the density being the content divided by the volume.

    Similarly I wondered if I could define a certain volume of space that contained the electron with a known amount of energy. The smaller this volume of space was, the more energy per arbitrary unit it would contain. A point particle would then be infinitely dense, packing a finite amount of energy into an infinitely small volume.

    My error as far as I understand it currently was to assume that these measurements of ‘size’ were evidence of a particle’s energy being completely contained in a space. On reflecting on what it is that size may or may not mean however I have come to understand that it is a vague concept, especially when dealing with small entities.

  13. This is probably quite a bad analogy but I was thinking in terms of these differing behaviors as being similar in structure to a whirlpool in the electron field (as it would be in water) – the spread out ‘field’ being the aperture at the top, and moving towards a narrower and narrower focus at the ‘bottom’ as higher energies are utilized until reaching the terminal ‘point’ particle at the end (or what we are able to currently determine as the end, since it could extend further beyond our ability to ‘reach down’ that far).

    Extending the idea further: the ‘downward’ terminus of the funnel can move about, just as the particle element of an electron can move about within its waveform probability; the ‘downward’ nature of the funnel is negative charge whilst an inverted ‘upwards’ whirlpool could be seen as a particle with positive charge. (Maybe even the direction of whirlpool spin could be, well, spin or handed-ness?)

    Though this has problems with any attempt to make it fit mathematically (in that it wouldn’t at all) and so only works as well as the rural community description, though I suppose this would be true of any analogy for a complex phenomenon that has no ‘macro world’ equivalent.

  14. Aperiodic crystals have an ordered structure and symmetry, the point being on the fact that that ordered structure is not based on translational symmetry, which is the basis of traditional crystallography.

    Aperiodic crystals present more complex types of order and symmetry, and it is because of this order and symmetry that they present diffraction.

    Just as it has happened before with Physics, it was first that mathematicians found some “funny” properties with geometrical figures, with no special relation to nature, and then it took some time for the physicists to realize that those “necessary conclusions” found by mathematicians were useful to solve certain theoretical physics problems.

    For instance, Riemann discovered the metric tensor, differential geometry and non euclidean geometry (then to be extended by Ricci and Levi-Civita), and then it took a while for somebody (Einstein) to realize that that “funny” stuff was the math trick behind Gravitation (General Relativity).

    In the 1960s, mathematicians discovered aperiodic tilings, and it took a while for physicists to realize that these kinds of tilings were the “math trick” behind quasi-crystals.

    I do not see the relation between aperiodic crystals and Bose Einstein condensates (BECs require very low temperatures to be produced and they happen only with composite structures that present a specific quantum state, that is, composite bosons, while most crystals are produced at temperatures much closer to standard room temperature, and they are just normal atoms organizing according to geometrical lattices).

    Kind regards, GEN

    1. I believe the underlining theme is exactly what Schrödinger was inferring to, chaos to order, “a masterpiece”.

      Whether there is a “DNA” embedded in Nature’s laws which leads to higher and higher states of energies is hard to decipher, as of yet. But this is growing evidence that may suggest that order is not just a consequence of more complex structures which in-turn are a consequence of certain variables changing one way or another, i.e. entropy, universal cooling, etc.

      I wrote a post in another article on this website which expands on this theme and, in my opinion may very well lead to some real evidence of universal consciousness.

      I hope Prof Strassler will not be upset if I repeat it one more time.
      “The universe may grow like a giant brain, according to a new computer simulation.

      The results, published Nov. 16 in the journal Nature’s Scientific Reports, suggest that some undiscovered, fundamental laws may govern the growth of systems large and small, from the electrical firing between brain cells and growth of social networks to the expansion of galaxies.

      [“Natural growth dynamics are the same for different real networks, like the Internet or the brain or social networks,”]said study co-author Dmitri Krioukov, a physicist at the University of California San Diego. ” … NBC news.com

      A few months ago I posted this same observation but with a twist, that may have caused a negative impression, GOD. Of course, this is not what Dr. Krioukov is suggesting but he does like it open to conjecture.

      He is my post …

      If the is God then did God create the universe or did the universe create God?

      If God created the universe then that would be very problematic w.r.t. causality, what caused God? However, if the universe created God then that would be well within the realm of our real universe all our questions both from evolutionism and creationism would lead to a common goal.

      Given all that we know about our universe and ourselves:
      1. What could God be?
      2. Why would there be a need for God in the first place?
      3. How could God control the universe, which created Him?

      A curious observation is as the structures, atoms and molecules, become more complex the outcome, evolution of the universe, tends to life and beyond to consciousness, (we are very high up in the overall scheme of existence).

      We have a consciousness which is very difficult to define and formulate with the same math we use to formulate physical phenomena. Below is a very interesting video of a 3D formulation of what the known universe looks like. As you can see it has a striking resemblance to the structure of our brain, the structure that gives us consciousness.

      1. Do you believe that a universal consciousness (God) can exist given this data?

      2. Like our own consciousness can control our brain’s motor functions and hence our body functions, could the universal consciousness (once it “turned on”) create the more complex physical fields from the fundamental field (gravity or something else to the strong field) and hence drove the primordial chaotic universe to one of order and expanding, i.e. the expansion of the universe is not related to the initial conditions at the big bang but rather the universal consciousness is reinforcing and evolving to a higher and higher state. A principle of conscious advancement as the driving force for everything. No conservation laws need to be violated or invalidated.

      Is God the universal consciousness created by the magnificent structures of our universe, see the video below.

      http: //www.youtube.com/watch?feature=player_embedded&v=74IsySs3RGU

  15. Hello Prof,

    I would like to know your opinion on aperiodic crystals. Do you think the are a freak of Nature or a Nature’s natural progression from chaos to order?

    Erwin Schrödinger was wrote:

    “In physics we have dealt hitherto only with periodic crystals. To a humble physicist’s mind, these are very interesting and complicated objects; they constitute one of the most fascinating and complex material structures by which inanimate nature puzzles his wits. Yet, compared with the aperiodic crystal, they are rather plain and dull. The difference in structure is of the same kind as that between an ordinary wallpaper in which the same pattern is repeated again and again in regular periodicity and a masterpiece of embroidery, say a Raphael tapestry, which shows no dull repetition, but an elaborate, coherent, meaningful design traced by the great master.”

    “Schrödinger’s focus on what makes progeny from parent, on an as yet unknown crystalline molecule within the chromosome, amounted to a scientific prediction of the nature of the gene. It would take James Watson and Francis Crick ten years to unravel the workings of this “aperiodic crystal”—and identify the hereditary, helical molecule as deoxyribonucleic acid—DNA. …”

    Are we a freak of Nature or was the DNA inevitable every since the first Bose-Einstein condensate popped into existence?
    Is consciousness the end goal of all this orderly transformations of energy we see all around us in the universe?

    So many questions so little time … I wonder why Einstein ended his quest so prematurely?

    1. Aperiodic crystals are as inevitable in our universe as periodic ones. Their existence is dictated by the same laws of nature.

      However asking whether the universe has a goal or purpose in dangerous territory. What would set the goal? Th universe itself? God? You would need some sort of consciousness to do so. You may wish to check out this brief screed by Neil deGrasse Tyson: https://www.youtube.com/watch?v=7pL5vzIMAhs

      1. I wish I sketch that fast, … 🙂

        Neil deGrasse makes for good TV but I am afraid he failed in convincing me that there is no purpose in the majestic dance we see all around us. You see, he made the cardinal mistake of ending his sequence of questions short, short of the goal,…:-). He based the universal goal to humans as the end goal, far, far from it. Consciousness, universal consciousness, is the end goal because that would, I contend, would close the loop. From absolute chaos, the singularity, the Big Bang, to universal consciousness that could control it’s own destiny.

        Checkout my post below.

  16. Matt thanks very much for your efforts on this very useful project. It is helpful for the student to have a broad outline description of the landscape as you are providing. The fact that there are difficult/mysterious problems ahead is one of the attractions of this area. By raising that at the start you keep the student engaged and up to speed whilst you gradually advance towards the problems.

  17. Matt,
    I love your “Yes, this is weird” approach. As a science student trying to come to grips with all this 25 years ago I would loved to have read your article back then. Keep up the good work!

  18. The problem is, QM is a very vital, nay fundamental aspect of how atoms work, so there’s really no way to avoid mentioning it. It’s why we have a section on the cartoon atom (Looking very classical) and the more realistic atom (Looking far more quantum mechanical.)

    Crossing your fingers is problematic too, many readers will have their own questions raised elsewhere or will be smart enough to wonder when reading this article.

    1. Density, as in the density of water at 5 °C, is the end result of the interaction of billions of billions (“a la Carl Sagan”) of water molecules.

      So, in that specific meaning of density, it makes no sense to speak about the density of an electron.

      Kind regards, GEN

  19. Good outline and enlightening. Thank you Professor.

    /How does this relate to density? Obviously something of a given mass is denser if it is smaller, so does this limit how small an object may be (An object of sufficient density would be a black hole would it not?)/- Kudzu.

    Electron atmosphere and freedom of movement allowed in space arround nucleus: Two completely different particles (the electron and the anti-positron) are swapping back and forth(create mass). What does this mean? The physical thing which is propagating through space is a mixture of the two particles. When you observe the particle at one point, it may be an electron, but if you observe it a moment later, the very same particle might manifest itself as an anti-positron! This should sound very familiar, it’s the exact same story as neutrino mixing (or, similarly, meson mixing).

    The freedom of movement allowed is due to the “pull” created by the density of the nucleus, not by the Higgs vev?
    The Higgs “vev”(spontaneous electroweak symmetry breaking – occupying lower potential energy)- is same as back and forth movementum of photons(mass?) inside a closed system(black holes).
    Gravitation cannot contain “speed of the light”. In Black holes, the spacetime dimension is ruptured – the light had free fall into that rupture.

    Higgs(h) get the “mass” because it cannot escape closed system created by Big bang temperature(after cooling).
    Photons were massless because it already escaped closed system- but cannot escape the Roller coaster of spacetime metric.
    Inside closed system mass is conserved. But Higgs(h) mass is not conserved only for a while(abruptly zero) – thus react with spactime metric for a while. ?????

  20. In my many years as a physics student I have gotten the impression that, for all the lip service paid to the contrary, the three least favorite words of most physicists are “I don’t know.”

    Professor Strassler’s above post gingerly leans toward being an exception, but the hesitancy speaks volumes. I would suggest that the failure to and the difficulty in “explaining” the behavior of atoms is that we really don’t know what it is. We have no consistent answer to the question, “how big is an electron?”

    Our equations and their reliability with respect to a wide range of predictions provide useful clues. But we are nevertheless at a loss as to how to “explain” this success because of the irreconcilability of the facts into a story that consistently supports our preconceptions. Neither chunk-of-stuff-like particles nor fuzzy wavy particles make sense across the board.

    Nor do I find it convincing to blame the failure to explain these things on the mathematical limitations of the audience. The truth is that the math does not answer some of the biggest questions. It is a veritable cliche borne of quantum theory’s founding fathers that to utter an understanding of atomic reality based on quantum theory is to reveal one’s ignorance.

    Under such circumstances the most fruitful approach, it seems to me, is to be very humble and be very receptive to new ideas. Possibly the ultimate explanation will be of a less mathematical character and a more artistic or intuitive character. Maybe all the baggage carried along with the word, “particle” is an obstacle to a deeper understanding. Maybe the problem has to do with our failure to fully understand gravity.

    1. I think the challenge is to explain what we do know and what we don’t. That’s what’s behind my hesitancy; I don’t have the space in this article to be clear. If one says “we don’t know” in a general way, important details get lost : that we can predict some properties of the electron to one part in 10^12, that we can predict how electrons scatter off each other to one part in 1000, that we can predict how muons decay to electrons with comparably great precision, etc. And we can measure that the electron’s radius (as defined by how differently it behaves from a quantum point-like particle) is smaller than 100,000,000 times smaller than that of a typical atom. Now, that represents a huge amount of knowledge. And we know, therefore, that electrons are very well described as quanta of the electron field, just as other elementary particles are. That does not represent ultimate knowledge, and there are things we don’t understand… as there always are.

      The other problem is that quantum mechanics language is not quite the same as quantum field theory language. This is another reason for my being hesitant. One has to be very careful if one is to be accurate.

  21. I’ve never had a physics course so can only follow your simpler descriptions, but I have a strong interest in these things and have read several books over the years. Something you’ve said above confuses me, and I’m sure I must have a hole in my understanding. You describe the electron as being like a wave that fills the entire gray area. I thought the wave was not a physical object but instead a mathematical construct describing the probability of finding the electron in a given position within the atom.

    1. This is something even the experts argue over. It is often said that this wave is the probability of finding the electron in a particular place, in which case we could possibly say yes, the wave is math and the electron is ‘really’ whizzing about in one particular place at a time, but this is not entirely accurate. We can also imagine the electron itself smeared throughout that cloud or as the cloud, again not entirely accurately. As the professor states it’s a tricky area where our usual notions can easily confuse us.

      1. This makes me think of the blades of a fan rotating quickly. At rest you can see them as simple objects. When running they seem to be a cloud of metal.

    2. Whether the wave is a mathematical construct or something to be treated as physical is very subtle, and people don’t necessarily agree on the matter. I am going to have to write an article about this in future, but I want to make sure I do it right. In any case, the equations we use give correct predictions for atoms and how they behave; the issue in question is how you interpret what the equations signify, which is inevitably ambiguous.

  22. Thankyou for your reply. I hope one day to read these articles as they sound like they would be very enlightening on this topic, though your brief explanation does make perfect logical sense.

  23. apologies if you’ve addressed this in another article, but I remember being taught that electrons were point-like, having zero size. was this wrong?

    1. I have to be quite careful in my wording, don’t I! No, what you learned wasn’t really wrong, but it wasn’t complete.

      First, when someone says to you “an object has zero size”, what they really mean is that “if this thing has a size, it is too small for us to currently observe.” After all, everything we *know* comes from experiment. All we can do is look to see if the size can be measured; if we can’t observe any effects of a finite size, we know the object is smaller than we can measure with that particular experiment. So the correct statement is not quite that “electrons are point-like” but that “electrons are not known not to be point-like”. It’s an subtle but important distinction, because the first statement might prove to be wrong (we might someday run an experiment good enough to detect the electron’s size, if it has one), while the second statement is a correct and irrefutable statement about current knowledge.

      Second, in quantum mechanics the notion of point-like particle is inherently confusing. The idea that something is point-like is the statement that if and when you try to break it apart or detect its finite extent by banging something into it, you fail. But if a point-like object is left to its own devices to wander around a proton inside a hydrogen atom, there is a sense in which it spreads out around the hydrogen atom in a nice spherical shape. Now the problem is that what is really going on does not have any intuitive picture to go with it, and people interpret it differently. Should one say it is the electron that spreads out? Should one say that it is a wave that describes the electron that spreads out? Is it only the probability to find the electron that spreads out? None of these is really entirely accurate as far as it describes the equations we use, and we don’t know the equations are giving us quite the right picture for what nature is doing. Physicists and philosophers are still arguing, even today, over the right words to use. So my challenge (and yours) is to figure out how to sidestep this and move on. This website is not intended (nor am I prepared with the right pedagogical tools) to try to explain quantum mechanics to the public; and I think that’s too difficult a problem for anyone to solve, at least with current knowledge.

      1. “Now the problem is that what is really going on does not have any intuitive picture to go with it, and people interpret it differently. Should one say it is the electron that spreads out? Should one say that it is a wave that describes the electron that spreads out? Is it only the probability to find the electron that spreads out? None of these is really entirely accurate as far as it describes the equations we use, and we don’t know the equations are giving us quite the right picture for what nature is doing. ”
        I think it best to take a “Wittgenstein approach” and just lay everything out as you have done in the extract above.

  24. The analogy with Letters, words, sentences is a great one, I enjoyed it. However, maybe you are enforcing it a bit too much, stylistically speaking. In my experience its better to just tell it once and then let the reader make the analogy for himself.

    In reference to the part after the electron radius, I personally also would leave out remarks how weird or bizzare or hard to understand something is, because with that, you are creating a kind of “thinking-barrier” – at least for some people. (The thinking then goes: Oh ok this is weird! I cannot possibly understand it!) Also generally judgements, conclusions, meta stick most. One could as well emphasize how perfectly natural a certain behaviour is.

    But these are quibbles. I cannot thank you enough for your great articles, I enjoy reading you a great deal.

    Best regards.

    1. Thanks for your comments!

      I am still struggling with the issue of the electron radius. About the weirdness: The problem is that if you make statements that *are* bizarre and you don’t say “yes, this is weird”, that confuses one set of people; and if you say “yes, this is weird” that makes the thinking-barrier you mentioned. So what’s the best approach? I am trying “yes, this is weird — and it’s ok if it seems weird to you, because it seems weird to me too.” But I’m not confident that this is best. So you have added to the many voices in my head that push and pull in different directions.

      This is an amazingly difficult article to pull off; it’s supposed to be just a stage along the way to particle physics. It’s not an accident that the atom article took over six months to write after the molecule article.

      1. I suspect it would be much easier to write about atoms if you do not try to explain QM simultaneously. You refer to protons and neutrons with proper abstractness and you should not be afraid to do the same with electrons, regardless of the fact that they are elementary particles. The composition and the basic properties and ordening of the constituents are more important for understanding the atom casually.

        Concerning the size of an electron, could you simply not mention it and merely give the mass ratio between a nucleus and an electron as some kind of measure, and cross your fingers?

  25. I think it is not quite correct to say that the nucleus is not involved in chemistry, because the mass of the nucleus is sometimes important. Not so much that a single neutron makes much difference in a chemical reaction, but there are general trends in reactions due to mass. For example, see how heavy metals interact with polysaccharides.

    1. Proton-transfer reaction rate are quite sensetive to mass. Deuterium effects are well known, normally these reactions are slower. Also don’t forget NMR spectroscopy, where these aspects are crucial to elucidate the structure of molecules (e.g., Carbon 13 NMR).

  26. An excellent piece that prompts a few questions.

    Firstly a rather trivial one, but as a physicist what is your take on treating the neutron as element zero?

    Secondly, what is size exactly? Minute Physics recently produced a video on ‘What is touch?’ that concluded that perhaps touch was just being close enough to interact, and from this article I gather you suggest that the size of an object is the area of space that other particles will interact with it, bouncing off but possibly also including other interactions like scattering or fusing? Then the size of a proton would be given by the scale at which particles stopped scattering off the ‘proton’ and began to interact with the individual quarks within it?

    How does this relate to point particles? Are they just an idealization?

    How does this relate to density? Obviously something of a given mass is denser if it is smaller, so does this limit how small an object may be (An object of sufficient density would be a black hole would it not?)

    1. “neutron as element zero”; I would say this is physically not an atom, because, lacking an electron, it is not in the same class as the other atoms. For one thing, it is 100,000 times smaller in radius than any atom. It is, instead, in the class of nuclei, being related by near-symmetry to the hydrogen nucleus.

      Size: this turns out to be an astonishingly complicated business. That’s indeed why I’m struggling with it in this article. Size is not a characteristic of an object; it is a characteristic of the interaction between a probing object and the object that it is being probed , and it often comes with ambiguities. This is one of the very important things one learns in quantum particle physics. And this is very counter-intuitive, because in ordinary life it isn’t often true. I need a good analogy for this.

      So defining size, radius, point-like objects, density, etc. is something that turns out to be precise only with careful technical definitions, and ambiguous because there are different possible definitions that depend on what experiment you are carrying out. A famous example is that the proton size effectively grows (not a lot) as you increase the energy of the particles that you are scattering off of it. Another is that if you scatter an electron off of a magnetic monopole of a certain type, the monopole will appear to have a definite and finite size; but if you scatter a monopole off a monopole, they will act as though they are point-like. It’s well understood why, but that’s at least two or three articles deep to explain it.

      1. To a non-scientist like myself, size is dependent on distance from whatever is being measured – a house looks smaller seen from a distance. You have to get close to get the “true” size but there is a restriction on how close you can get so exact size is impossible to measure. Not sure that helps !

  27. From the perspective of chemistry, the atomic number for a given kind of atom is determined by the amount of protons in the nucleus of that type of atom. In such a way, you can avoid the “ion problem”, or what happens when an atom of a certain type in bound to some other atom (the arrangement of valence electrons in molecules is somewhat different, but the atoms remain being of a certain kind).

    Kind regards, GEN

  28. I can’t thank you folks enough for your wise comments. I have (at least temporarily) taken the ions out of this entry; I will put them somewhere else. And I’ve got my first attempt at dealing with the issue of orbitals up. It certainly won’t be the last version. Also thinking about whether additional figures would help or hurt.

  29. Great article, Matt. It does seem to be one of those situations where the only way to the truth is through a number of carefully-worded, er, half-truths. I like Figure 2 very much, but a variant of it showing the balloon-like shapes of the orbitals might be a useful companion. I would also echo Jon Lenox’s caveat–I too was worried that people might think you could perform alchemy by ionizing atoms. (In fact, it raises the rather interesting question about why that DOESN’T work. We all know that singly-ionized oxygen doesn’t turn into nitrogen, but I’m not sure I could state simply, clearly, and correctly why it doesn’t…as opposed to meandering on at great length!)

    1. Singly ionized oxygen is very close to nitrogen, it will readily bind three hydrogen atoms to produce an ammonia shaped H3O+ molecule and will pair up into strongly bonded O2.2+ molecules. Likewise O2- is very much like a noble gas atom.

      The electric charge on ions often acts as a modifier more to their physical properties than their chemical ones; and there are intriguing situations where this can be almost completely cancelled, carbon monoxide is much like nitrogen and boron nitride can exist in both graphite-like and diamond-like polymorphs.

  30. Thanks for your continued articles. I have a pedagogical quibble, however. I read reddit’s AskScience section, and people often ask, “If an atom is truly mostly empty space, then why don’t atoms just pass through each other? What am I touching when I touch a solid surface?” Another question that gets asked is, “Why don’t electrons fall inside the nucleus?” For this reason I think the picture of the atom as empty space with tiny electrons is not really helpful. It’s at this point that quantum physics has to be confronted (as it was by the physicists themselves at the turn of the century).

    I could be wrong about this because I’m not a physicist, but I’d like to suggest that maybe it’s better to present the electrons as literally having the shape of the orbitals that they occupy. It answers the first question (the atom is filled with the orbitals) and it answers the second (the lowest orbital is centered on the nucleus, and the other ones can’t get lower because of the Pauli exclusion principle). But then you have to also have the caveat that the electron behaves like a point particle under some circumstances.

    I came up with an analogy for this. Matter is like a tent, composed of tent poles (the nuclei) and the tent fabric (the electrons). The tent poles themselves don’t occupy much space but they “pin down” the tent fabric and give it shape. The tent fabric, on its own, tends to be shaped like a little ball, but when you stretch it on the poles, it begins to occupy space. This can be readily extended to explain how the orbitals in some solids become essentially distributed throughout the whole material, and the Rutherford experiment that initially created the idea that atoms are mostly empty space.

    Perhaps something from your series on particles as ripples in fields could be brought in here to explain orbitals in a more consistent way.

    1. Your pedagogical quibble is well taken: these are indeed questions that always get asked and that I have to answer in these articles. I was going to answer them later, but your point is that probably I need to bring them up — at least pose them, with links to answers — in this article directly. I think you are right, and I will make a revision.

      I think that if you say the electrons have the shape of their orbitals, you will generate all sorts of problems later in explaining particle physics. You definitely do not want to say that an electron is the same size as a hydrogen atom. At some level this is a fundamental problem in explaining quantum mechanics and the nature of particles… and indeed I am in danger of inconsistency within the website. Will ponder.

      Your tent fabric analogy is an interesting one.

      Thanks for your comments. It’s a challenge, definitely, to put in all the pictures and caveats in the right order.

  31. I understand why you’re describing the atomic number in terms of the electron count, because it’s what matters for chemistry, but it seems to me it opens up the possibility of a lot of confusion when it comes to ions. People might think that a -2 oxygen ion with 10 electrons and a neutral neon atom with 10 electrons should behave similarly…

      1. The outer layer of electrons of atoms (valence electrons) have many interesting behaviours, and all of these behaviours are related to chemistry.

        These behaviours determine the types of bondings that a given atom may have when binding to other atoms to form molecules and other arrangements (like lattices).

        The types of possible bondings that some kind of atom may have are determined (in a rather complex way) by the atomic number.

        Nature always behaves in such a way that it is always looking the most stable state that could be achieved under current conditions. The available types of bondings for a given kind of atom are related to this tendency to look for the most stable state that can be achieved by a given atom under current conditions.

        Chemistry is all about this tendency to look for the most stable state that could be achieved under current conditions, and under certain conditions, the formation of ions is the most stable state for a given kind of atom.

        Electrons are fermions, which means that they are affected by Pauli’s exclusion principle. What that means is that on a given atom, each electron has a unique set of quantum numbers, and they “want to stay as far away” from any other electron as they can. To be able to “stay as far away as possible” from each other, electrons are arranged within certain “slots” called orbitals.

        These “slots” are not precise places, but rather fuzzy regions where it is more probable that certain electron with certain energy level could be found (quantum mechanics rules, so everything is about uncertainty and probabilities!).

        So, electrons in an atom are organized by energy levels, and for a given level, there is an arrangement of electrons that is the most stable. The most stable arrangements is achieved by a certain kind of elements, the noble gases (like Hellium, or Argon, just to name two such noble gases).

        As these elements present the most stable arrangements, they do not have a very strong need to bind with other atoms to look for a more stable state (because they already are in a confortable enough state). Atoms of other kinds of elements that have too few electrons or too many electrons in the outermost layer (valence electrons) are very close to the stable state of the noble gases, so it is very easy for these atoms to either shed their valence electrons and be similar to a noble gas (when they have too few electrons) or to “steal” electrons from some other atom to complete the electron count to emulate a noble gas.

        The atoms that behave this way (either shedding electrons or stealing electrons to emulate noble gases) are the ones that can become ions under certain conditions.

        So, just like Prof Strassler described, chemistry is all about the behaviour of the valence electrons (and all electrons behave according to quantum mechanics).

        Kind regards, Gastón

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