If you go to any of the image search engine web sites on the internet and enter "atom", you will be shown many examples that share a common motif, although there are variations as well. Here is a very small sampling:

4.1

Every one of these is incorrect! Any depiction of an atom that shows electrons as well-defined particles moving in well-defined pathways or orbits is simply wrong. Neither is a nucleus composed of a large cluster of individual proton and neutron spheres. Atoms do not resemble tiny solar systems! They are much stranger than that.

Let's look at one accurate representation of the hydrogen atom. It's not like anything you would see in the course of normal life. It's not helpful to pretend that it isn't something completely outside of typical human experience. Here's hydrogen—one electron interacting with one proton:

4.2

The electron is a smeared out, three-dimensional, spherical cloud that becomes very diffuse around the edges. The fact that the image is tinted blue is arbitrary: atoms don't have any color. The nucleus—a bare proton, in this case—is too small to indicate with a dot, but it's at the center of the cloud. Where is the electron? It is the cloud—the entire cloud. The density of the cloud at a given position—the intensity of color—tells us how likely it is that the electron is there. All we know is that the electron is more likely to be present where the shading is darker, close to the nucleus.

Depictions such as the one above are called orbitals. This is another case—like spin—where the terminology that chemists use can be confusing. Figure 4.2 doesn't look anything like an orbit, but we call it an orbital nonetheless.

For the rest of the module, all of the images of orbitals you will see have been generated with quantum chemistry programs. These programs are used to solve the mathematical expression that describes the behavior of one or more electrons in the presence of one or more nuclei, the Schrödinger equation for electrons. We can do this for any atom or molecule of interest. Understanding the nuts and bolts of how this is done—the theoretical equations and the computer coding—is beyond the scope of an introductory chemistry course, but the programs represent our best current understanding of how matter behaves. The results have been corroborated many, many times against experimental data for measurable quantities.

We get two things directly out of solving the Schrödinger equation, the energy of the system in a given state (usually the lowest, most stable state, which is called the ground state) and something called the wavefunction. The wavefunction tells us where the electrons are but in a way that is very different from the way we usually understand the position of something. The wavefunction is represented with orbitals, like the one shown above for the hydrogen atom.

As a first step toward understanding why atoms behave like this, we will look at some of the differences between the hydrogen atom and something that will be familiar to most people, a spacecraft (such as the space shuttle shown below) in orbit around Earth. We'll look at four traits of each system.

4.3

(1) POSITION & SPEED: As a space shuttle orbited Earth, its position, speed, and the direction it is moving with respect to Earth were all known quantities. It was possible to use those numbers to predict where the space shuttle would be at a later time. None of these things are true about the electron in the hydrogen atom. We cannot pin down its position and velocity (its speed and direction of movement), and we cannot predict where it will be later. The reason for this is found in one of the fundamental principles of quantum chemistry, the uncertainty or indeterminacy principle derived by Werner Heisenberg.

(2) ENERGY LEVEL: Once a space shuttle or other powered spacecraft reaches the proper altitude, it will maintain that altitude unless a force acts upon it. One way this can happen is if the craft fires its engine. It can do this to decrease altitude and lose gravitational potential energy with respect to Earth, or it can climb to a higher altitude and gain gravitational potential energy. A spacecraft can have any value of potential energy ranging from zero when it is on the ground before launch to the energy required for it to effectively be outside of Earth's gravitational attraction. The electron in a hydrogen atom can have different energies, but unlike the spacecraft example, they will always be discrete values and it cannot ever be zero. We call this quantization. Observations in the 19th century and earlier found that atoms and molecules generate spectra with sharp lines instead of continuous emission. This was one of the first clues that matter behaves differently at the nanoscale level of atoms.

(3) MINIMUM ENERGY LEVEL: A third difference between an orbiting spacecraft and the H atom is that a spacecraft can land or crash on the surface, but the electron cannot crash into the nucleus. There is a minimum energy level atoms have that we call the ground state (or the ground electronic state). We now have three defining traits of the hydrogen atom: the position of the electron is indeterminate, it has discrete rather than continuous energies, and it cannot crash into the proton that comprises the ¹H nucleus.

(4) MULTIPLE OBJECTS: The fourth and final difference we will consider is what happens if a second spacecraft or electron is added to the two respective systems. If a second spacecraft approaches another one, they can dock or pass by one another. Aside from the chance of colliding, two spacecraft don't attract or repel each other strongly. The situation is very different in atoms. There are two factors that affect what happens. First, two electrons always repel each other strongly, even though they will both be attracted to the proton. But electrons have a property called spin that we mentioned above. Spin is one of the strangest things to come out of quantum mechanics. Two electrons with the same spin (up + up or down + down) interact differently than two electrons with opposite spins (up + down). We will return to this when we move on to atoms and ions with more than two electrons. We will start by examining systems with just one electron, where this is not a factor and trends are very well-defined.

Shown below are several other ways in which the hydrogen atom can be represented:

4.4

The first format (left)—known as a 3D isodensity contour—represents one low value of the density of the H atom's entire spherical cloud. This representation gives us a sense of the size and shape of the atom, but it may create the false impression that the electron moves around on the surface of the sphere at a constant distance from the nucleus, which is not the case. The middle representation is better. It shows a cross section of a set of density contours, with greater density indicated by darker color (as above, the choice of blue is purely arbitrary). We see that the density increases closer to the nucleus. The electron doesn't move only on the individual contours any more than it only moves on the outer surface in the depiction on the left. The final image is a 2D depiction of the functional dependence of the electron density around the nucleus, showing that it changes continuously at different distances from the nucleus. The density is greatest at the nucleus.

Let's see if you can answer a question about the electron in H based on what you've read so far.

The correct answer is (c). The first answer is incorrect because electrons do not ever move in well-defined orbitals, regardless of how frequently they are depicted that way by artists in books or on the internet. The second answer is also wrong, for two reasons: the electron in H is more likely to be found near the nucleus than to be as far away as possible, and the electron does not move on a surface.

The shape that depicts the many positions where the electron can be in H is known as an orbital. Like the term "spin", it is perhaps somewhat ill-advised to call something that has no connection to the usual meaning of the word orbit an orbital, but that is the word that is used. We shall see later than the orbital for H in its lowest energy state is the first in a sequence of spherical orbitals, hence it is called the 1s orbital (the s label come from the observations that lines involving s orbitals are sharp, though remembering that s orbitals are spherical is a useful mnemonic).

Based on what we've covered so far, can you answer the following question without any multiple choices to give you a clue?

Let's summarize our latest observations:

Follow-up: We've seen that the H atom consists of a nucleus surrounded by the cloud that represents all the positions where the electron can be located. The nucleus is tiny compared to the extent of the cloud.

The correct answer is (b) because electrons are much lighter than protons or neutrons. This is the reason why people say that most of an atom is empty space. It would be more accurate to say that an atom has a very small mass density except at the nucleus.