Science Questions with Surprising Answers
Answers provided by
Dr. Christopher S. Baird

Does an electron in an atom move at all?

Category: Physics      Published: December 1, 2014

hydrogen atom orbital
This image shows the mathematical plot of a single electron in a certain state in a hydrogen atom. Public Domain Image, source: Christopher S. Baird.

First of all, I assume you meant to ask the question, "Does an electron in a stable (non-transitioning) atomic state experience any movement?" Obviously, an electron that is transitioning between states is moving from one state to the other. But for an electron that is just staying in one stable state in an atom, the question is more interesting. Does it move? The answer could be yes or no depending on how we define motion and what form of the electron we consider to be truly real.

The problem is that an electron is not a solid little ball that we can watch zip around. An electron is a quantum object. As such, an electron is partially particle-like and partially wave-like, but is really something more complex that is neither a simple wave nor a simple particle. The electron is described by a probabilistic quantum wavefunction, which spreads out through space and vibrates, but in such a way that it still has certain discrete properties such as mass. When bound in a stable state in an atom, the electron wavefunction spreads out into a certain shape called an "orbital". The orbital does not contain the electron or describe the average location of a little hard electron orbiting around. Rather, the orbital is the electron.

When bound in a stable state in an atom, an electron behaves mostly like an oscillating three-dimensional wave, i.e. the orbital vibrates. It's a bit like a vibrating guitar string. When you pluck a guitar string, you get the string shaking, which is what creates the sound. Scientifically, we would say that you have excited a standing wave in the string. The guitar string is not moving in the sense of shooting off to the other side of the room. In this sense, the guitar string is not moving at all, but remains clamped to the guitar. But the guitar string is moving in the sense that it is vibrating when you pluck it. If you pick one spot on the plucked string and look at it closely, it is definitely moving from one location in space to another, back and forth repeatedly. By pulling the string, you transferred chemical energy in your arm to elastic energy in the stretched string. When you let go, the elastic energy was converted to motional energy (kinetic energy) as the string snapped back and started vibrating. The total kinetic energy of the entire string averaged over time is zero, since the overall string is not going anywhere with respect to the guitar. But the kinetic energy of any small part of the string at a given moment is not zero. In this way, a plucked guitar string experiences local motion but not overall motion.

animation of vibrating wavefunctions in hydrogen
Mathematical plots of the electron wavefunction in hydrogen, showing clearly its vibrational movement. The plots on the left and right each show a single electron in the ground state of a single hydrogen atom. The two plots in the middle show the two possible ground states that an electron wavefunction can take when two hydrogen atoms are bound into a hydrogen molecule. Each red dot shows the location of a nucleus. In each plot, the blue curve/pink curve pair shows the two different wavefunction components of a single electron. Note that these plots show a one-dimensional slice of a three-dimensional orbital. Public Domain Image, source: Wikipedia.

An electron in an atomic orbital state acts somewhat like a plucked guitar string. It is spread out in a three-dimensional cloud-like wavefunction that vibrates. Whereas a guitar string vibrates up and down, an atomic electron wavefunction simply vibrates strong and weak. The frequency at which the electron wavefunction vibrates is directly proportional to the total energy of the electron. Electrons in higher-energy atomic states vibrate more quickly. Because an electron is a quantum object with wave-like properties, it must always be vibrating at some frequency. In order for an electron to stop vibrating and therefore have a frequency of zero, it must be destroyed. In an atom, this happens when an electron is sucked into the nucleus and takes part in a nuclear reaction known as electron capture.

With all of this in mind, an electron in a stable atomic state does not move in the sense of a solid little ball zipping around in circles like how the planets orbit the sun, since the electron is spread out in a wave. Furthermore, an electron in a stable atomic state does not move in the sense of waving through space. The orbital electron does move in the sense of vibrating in time.

But the truth is more complicated than this simple picture depicts. There are two things that describe the electron in quantum theory: the electron's quantum wavefunction, and the magnitude squared of the electron's quantum wavefunction. (The "magnitude squared" operation just means that you drop phase factors such as negative signs and then take the square. For instance, the magnitude squared of negative three is nine.) Interestingly, experiments can only directly measure the magnitude squared of the electron wavefunction, and yet we need the original wavefunction in order to predict the outcome of many experiments. For this reason, some people say that the magnitude squared of the wavefunction is the only real entity, whereas the original wavefunction itself is just a mathematical crutch that is needed because our theory is inelegant.

Is the magnitude squared of the electron wavefuntion the real physical entity or is the original wavefunction the real physical entity? This question is really a philosophical one and not a physical one, so I will not pursue the question here. To scientists, the question, "What is actually real?" is unimportant. We are more concerned with making the equations match the experiments. So what does all this have to do with an electron in an atom? The point is that an atomic electron's raw wavefunction does vibrate, but the magnitude squared of the wavefunction does not vibrate. In fact, physicists call stable atomic electron states "stationary states" because the magnitude squared of the wavefunction is constant in time. If you consider the raw wavefunction to be the truly physical entity, then you have to say that an electron in an atom experiences motion in the form of a vibration. If you consider the magnitude squared of the wavefunction to be the truly physical entity, then you have to say that an electron in an atom experiences no vibration, and therefore no motion. I consider the first choice to make more sense. You can mathematically show that certain atomic electron states contain angular momentum (i.e. rotational momentum). It's hard to make sense of the claim that an atomic electron contains angular momentum and at the same claim that the electron is completely motionless in every sense of the word. For this reason, I prefer to view the raw wavefunction as the truly physical entity, and therefore an electron in an atom experiences motion in the form of vibrations. But, again, the question, "What is actually real?" is a philosophical one and is unimportant in science. The bottom line is that the raw wavefunction of an electron in a stable atomic state experiences vibrational motion. Whether you consider this motion real or not is up to you.

Topics: atom, atoms, electron, kinetic energy, move, movement, quantum, wavefunction