Tag Archives: electrons

Electrons, Bonding, and the Periodic Table

The structure of the periodic table of elements is a bit weird the first time you see it, like a castle or a cake. If we just read the periodic table top to bottom and left to right, we are reading off the elements in order of increasing number of protons. However, if this were the only useful ordering on the periodic table, it could be a simple list. The vertically aligned groups on the periodic table actually represent the chemical properties of the elements. Dmitri Mendeleev developed the table in 1869 as a way to both tabulate existing empirical results, and predict what unexplored chemical reactions or undiscovered elements might be possible. It was revolutionary as a scientific tool, but the mechanism behind the periodicity was not understood until decades later. As it turns out, the periodicity of chemical behavior corresponds to the bonding type of the outer electrons in different atoms.

To understand what that means, we can start by looking at the elements on the left side of the periodic table. Hydrogen has only one proton, so the electrically neutral form of hydrogen has only one electron. This single electron is a point particle, jumping around the nucleus. The electron exists in a probability cloud, whose shape is given by the lowest energy solution to the quantum mechanical equations describing the system. These quantum states can be distinguished by differing quantum numbers for various quantities like spin and angular momentum, and we will talk about these in more depth later on. When we add additional electrons, they all want to be in the lowest energy state as well. Sadly for electrons but happily for us, no two electrons are able to occupy the same quantum state: they must differ in at least one quantum number. This is known as the Pauli exclusion principle, and was devised to explain experimental results in the early years of quantum mechanics. So while the single electron in hydrogen gets to be in the lowest energy state available for an electron in that atom, in an atom like oxygen, its eight electrons occupy the eight lowest energy states, as if they are stones stacked in a bucket.

But what’s really interesting about these higher energy electron states is that they have different shapes, as we can see by the mathematical forms that describe the possible probability distributions for electrons. So while the electron cloud in a hydrogen atom is a sphere, there are electron clouds for other atoms that are shaped like dumbbells, spheres cut in two, alternating spherical shells, and lots of other shapes.

The electron cloud shape becomes important because two atoms near each other may be able to minimize their overall energy via electron interactions: in some configurations the sharing of one, two, more, or even a partial number of electrons is energetically preferred, whereas in other configurations sharing electrons is not favorable. This electron sharing, which changes the shape of the electron cloud and affects the chemical reactivity of the atoms involved, is what’s called chemical bonding. When atoms are connected by a chemical bond, there is an energy cost necessary to separate them. But how atoms interact depends fundamentally on the shape of the electron cloud, determining when atoms can or can’t bond to each other. So the periodic table, which was originally developed to group atoms with similar chemical properties and bonding behaviors, actually also groups atoms by the number and arrangement of electrons.

Now, there is a lot more that can be said about bonding. You can talk about the inherent spin of electrons, which is important in bonding and atomic orbital filling, or you can talk about the idea of filled electron shells which make some atoms stable and others reactive, or you can talk about the many kinds of chemical bonds. It’s a very deep topic, and this is just the beginning!

Since every real world object is a collection of bonded atoms, the properties of the things we interact with, and what materials are even able to exist in our world, depend on the shape of the electron cloud. Imagine if the Pauli exclusion principle were not true, and all the electrons in an atom could sit together in the lowest energy state. This would make every electron cloud the same shape, which would remove the incredible variety of chemical bonds in our world, homogenizing material properties. Chemistry would be a lot easier to learn but a lot less interesting, and atomic physics would be completely solved. Stars, planets, and life as we know it might not exist at all.

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The Electron Cloud

There is a popular image of the atom that shows the nucleus as a collection of balls, with ball-like electrons following circular orbits around them. The parallels to our own solar system, to the orbits of the moon around the earth and the earth around the sun, strike a chord with most people, but the depiction is inaccurate. It is based on the ideas of several prominent early twentieth century physicists, developed after the discovery of the electron in 1897 showed that atoms were not the smallest building block of nature. There are two serious mistakes in this image, and the actual structure of the atom is a lot more interesting.

The first problem is that the proton itself is not an indivisible particle: it’s composed of three quarks, subatomic particles which were hypothesized in the early sixties and observed in experiments beginning in the late sixties. The same is true of the neutron: it’s also composed of three quarks, though the flavor composition is different than that of the proton. (“Flavor composition”? Yes, quarks come in different flavors.) So those giant balls in the nucleus are actually comprised of smaller particles. At this point we believe quarks to be themselves indivisible, not composed of another even smaller particle.

But the second reason this picture is incorrect is that the electron doesn’t follow a linear orbit around the proton, the way gravitationally orbiting bodies do. In fact, due to the small mass of the nucleus and the even smaller mass of the electron, gravity is the least important force in an atom. The electromagnetic force, between the oppositely charged proton and electron, is much larger than the gravitational force between these tiny objects. But wait, you might say, if there’s such a large attractive force, shouldn’t the electron just spiral into the proton? This quandary illustrates perfectly why we can’t rely on classical physics, which was built up for objects comprised of billions of atoms, for the particles within a single atom. Because yes, if we had two oppositely charged billiard balls that have a weak gravitational interaction and a strong electromagnetic interaction, they will crash into each other! But, the electron is so small and so light that we cannot treat it as a classical object.

Here is where quantum mechanics come into play. Quantum mechanics as a whole is a set of mathematical constructions used to describe quantum objects, and it’s quite different than what’s used for classical, large-scale physics. There are all sorts of interesting consequences of quantum mechanics, such as the Heisenberg Uncertainty Principle, which states that for some pairs of variables, such as energy and time or position and momentum (mass times velocity), how precisely you can measure one depends on how precisely you are measuring the other. For each variable pair, there is a basic uncertainty in the measurement of both, which is very small but becomes relevant at the quantum scale. This shared minimum uncertainty between related variables is a fundamental property of nature. For momentum and position, this leads to that old joke about Heisenberg being pulled over for speeding: the police officer asks, “Do you know how fast you were going?” and Heisenberg responds, “No, but I know exactly where I am!”

What the uncertainty principle means here is that the electron is actually incapable of staying in the nucleus. Imagine a moment in time where the electron is within the nucleus: now its position is very well known, so there is a large uncertainty in its momentum. Thus the velocity may be quite high, which means that a moment later the electron will have moved far from the nucleus. In fact, because of the uncertainty in position, we cannot ever really say where in space the electron is. It is more accurate to talk about its position as determined by a probability cloud, which is denser in places that the electron is more likely to be (near the nucleus) and less dense where it is less likely to be (far from the nucleus). This also takes into account the wave nature of the electron as a quantum object, which we’ll get into another time.

With this knowledge, we can discard that old image of an electron orbiting a nucleus. A single electron, even though it is measurable as an individual, indivisible particle, exists as a cloud around the nucleus. The shape of the cloud is described by quantum mechanics, and as we add more electrons to the atom, we will find a whole gallery of electron cloud shapes. These shapes are the heart of interatomic bonding, as we will see.

Thinking About Collections of Atoms

On a basic level, science is about asking why the world is the way it is, and engineering is about asking, how can we use that to better our condition? There is certainly a lot of interplay between the two; they inform each other and rely on each other. And in my mind, a good scientist should always be a reasonable engineer, and vice versa. So if we want to understand what the science is that underpins a lot of our current technology, we first have to ask a lot of “why” questions about the world around us. Such as, why do different objects and materials have different properties? Why are there different forms that matter can take? Why do some forms appear on Earth and some don’t? Then, once we know what makes materials different from each other, we can start talking about how to use that to do something useful.

So what is the difference between the atoms in a metal table, the atoms in a cup of coffee, and the atoms in our hands? There are two major differences that are relevant: first, the atoms themselves come in a wide variety of types, and second, they can be arranged with other atoms in many unique ways that affect the property of the resultant material. The image below shows how we can arrange the same silicon and oxygen atoms in a random way or an ordered way, to get either silica or quartz. This change in ordered affects the physical properties of the resultant material.

We touched on the many types of atoms before when we discussed the number of protons in an atom. Proton number affects electron number, because of the attractive force between protons and electrons due to their opposite charge. So, for a given number of protons, an atom will end up with a similar number of electrons. How many electrons an atom has is very important, because the cloud of electrons is much larger than the compact nucleus which contains the neutrons and protons, so electrons are the primary means by which an atom interacts with the world.

What “the world” means here is primarily other atoms. So to assemble a solid, we have lots of atoms whose electron clouds are interacting with each other. Atoms can share electrons, they can be attracted to each other if they have opposite charges, and they can form three-dimensional structures to allow many atoms to interact . These interactions are all based around electronic forces, which stem from charge as we discussed earlier. Different kinds of atoms will experience different forces in different environments, so we end up with a whole slew of ways to assemble atoms. We can pack carbon into sheets and get pencil lead, we can jam it together with no ordering and get charcoal, we can compress it until it has a dense, flawless periodic structure and get diamond, or we can mix it with hydrogen to get the long hydrocarbon chains that crude oil is made of. And that’s just carbon!

Now, the obvious question to ask here is why atomic species and ordering vary, and why those variations lead to different material types. We’ll get into the first question shortly, but the second will take a lot longer to answer.

Charged with Meaning

The further you delve into the physics of electronics and materials, the more you will hear about the importance of electric charge. What charge particles have determines much of how they interact with other particles. In materials many of the electronic and magnetic effects are, at a basic level, due to charge. So what is it?

Electric charge is a fundamental property of matter. How much charge a particle has determines the force it will experience from an electromagnetic field, and such a field can be generated either by other charged objects or by the motion of magnetic objects. This is similar to mass, which is another fundamental property that determines the gravitational force an object will experience as it interacts with other massive objects. There is one key difference between charge and mass, however: there are two types of charge, positive and negative, whereas mass can only be positive (or zero). From the particle perspective, we can have particles like protons that have a positive charge, particles like electrons with a negative charge, and particles like neutrons that have no charge. Anything with a charge creates an electromagnetic field, and other charged particles nearby will feel a force from that field.

Now, say that we have two particles sitting near each other. Each one will have an associated electromagnetic field, and the total field will be a sum of the individual fields. The size of the electromagnetic force experienced by each particle due to the other depends on the magnitude of the two charges. But whether the charge on each particle is positive or negative is important for the following two reasons:

  1. Similar charges repel.
  2. Dissimilar charges attract.

So with our two particles, if they both have positive charge, or they both have negative charge, they will each feel a force directed away from the other charge. But if one is negatively charged and one is positively charged, they will experience the same size force toward each other. This force is part of what holds atoms together. Protons and electrons have equal and opposite charge. In atoms, we have a nucleus of protons and neutrons surrounded by a cloud of electrons. If there are more protons than electrons, the atom as a whole will be positively charged and will be attractive to nearby electrons. But if there are more electrons than protons, the atom is instead negatively charged, and the electrons within it are not as strongly bound.

We can already see that the charge of a particle is extremely important on the atomic scale. As we look at collections of atoms, the interactions will get more complicated, but the pieces to remember are:

  1. Charge is an inherent property of matter.
  2. Charged objects create an electromagnetic field.
  3. How strong a force an object feels from such a field is determined by that object’s charge.