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# What is the velocity of an electron within an atom?

This is a trick question. An electron within an atom doesn’t have a velocity. Despite what we are usually taught in grade school, it isn’t a particle zipping in an orbit around the nucleus. An electron is better described as having an orbital rather than an orbit. “Orbital” sounds something like an orbit, but it isn’t.

An analogy for an orbital is a cloud. The image to the left is a computer-generated reconstruction of an electron orbital, also called an “electron cloud.”

The orbital has energy as illustrated in the animation to the right. But it doesn’t travel as a unit and so, doesn’t have velocity. Imagine it as a rain cloud that stores so much energy that lightning flashes out from time to time. But this is just a metaphor that doesn’t really do justice to the idea of an electron orbital. For a more precise understanding, see orbital.

Sometimes physicists calculate a velocity that corresponds to the amount of energy in the electron cloud. This approach is beyond my understanding. But I’ve read on-line in a couple of places that if the energy of an electron orbital in a hydrogen atom were translated into velocity, it would travel over 2,200 kilometers a second. At this speed, if the electron were to orbit, which it doesn’t, it would travel around the Earth in a little over 18 seconds. So, an electron orbital has a lot of energy, but it doesn’t have a velocity.

# What is the difference between an orbit and an orbital?

In the early 1900’s, when physicists were first probing the insides of the atom, they thought that electrons might travel around the nucleus of the atom in an orbit. This is the solar system model of the atom; the electron travels around the nucleus like the Earth around the sun. This model, illustrated by the animation below and to the left, can accurately describe some aspects of a hydrogen atom. However it does not fit the results of experiments with atoms of the other elements nor does it fit later discoveries about the hydrogen atom. So, almost 100 years ago, physicists threw out the idea of an orbit. A good metaphor for the current understanding of the electron is that it’s like a cloud around the nucleus (see image below). Physicists call this metaphorical cloud an “orbital.”

I’ve seen this image of an orbital touted on the Internet as “the first image of a hydrogen atom.” But it’s not an image of an entire atom as it does not include the nucleus; the red and yellow at the center do not represent the nucleus.

This image is a leap forward and exciting, but here are some other things the image is not: It’s not a photograph; it’s not of one electron; and it’s not of the electron wave function. (Many physicists consider the wave function to be solely a mathematical equation, not a physical object that could “look like something.”)

It should be noted that the scientists who created this image made none of these inaccurate claims. But on the Internet, the image has sometimes been mislabeled by others.

So, what exactly is this orbital thing of which this is an image? Explaining how the image was generated will help to explain what an orbital really is.

## How the Image of the Orbital Was Generated

Here is how the image was created: Scientists in a Dutch lab zapped hydrogen atoms with a laser. The laser shot photons at the electron within the atom. Photons add energy to the electron. In the experiment, energized electrons flew out of the atom and hit a detector half a meter away. The experimenters did this hundreds of thousands of times, each time with a new hydrogen atom. Each time the energized electron hit the detector, its position was mapped to the origin of the electron within the atom, that is, the point of interaction between the photon and the electron within the atom. The computer combined all the origin points within the atom to form the image of the orbital. Thus, the orbital is a mapping of all the interactions of photons and electrons over hundreds of thousands of runs of the experiment. The colors were added by the scientists. The orbitals are not material objects, so do not have color. The colors represent the frequency of electron interactions in any particular location within the atom. In the dark blue area, the fewest interactions occurred. In the red area, the most interactions occurred. The New Scientist article provides more details.

To summarize, the image was created by zapping hundreds of thousands of hydrogen atoms with a laser. The zap of a photon from the laser sent the electron flying out of the atom and onto a detector half a meter away. Based on the position of each detection, the computer reverse-engineered the location of the interaction between photon and electron. The cloudlike pattern is the sum total of all the locations where the photon-electron interactions occurred within the atom. Color coding represents the frequency of these interactions.

Thus, an orbital is a region in which the electron is likely to interact. The coloring of the orbital reflects the varying probabilities of interaction. Many physicists would say that the orbital is the region in which the electron is likely to be “detected.” This can carry the connotation that the electron is a tiny particle, and we’re detecting it. But there is no consensus that the electron ever takes the form of a particle even though most physicists call electrons (and other subatomic things) “particles.” In the view of many physicists, “particle” is a misnomer and only an attempt to communicate in a non-technical way. Many physicists, like Art Hobson,* maintain that the electron is a wave at all times. As a consequence of the lack of consensus on what an electron actually is, it’s safer to simply say the most that we know here—the orbital is the region of the atom in which the electron is likely to interact with a photon.

## Orbitals vary in shape depending upon the energy level of the electron.

The Dutch lab which created the above image created additional images of electron orbitals in hydrogen atoms (below).

Each image depicts an electron orbital at a different energy level, with (a) being the lowest of the four and (d) the highest energy level of the four. A low-energy electron orbital can be energized into a higher energy level with a laser. The laser emits innumerable photons. If the electron absorbs a photon, its energy level jumps up. Later, it may spit out a photon and settle back down to a lower energy level.

Sometimes, people wonder if the photon that was spit out is the same as the one that was originally absorbed by the electron. The simplest answer is no. A photon is not a material object; it is a unit of energy. The electron gains and loses energy but is not storing and, then, spitting out a photon as if it were an object.

(The animation of the Bohr model of the hydrogen atom shows its version this very behavior—an electron absorbing a photon and later spitting out a photon. When many electrons spit out a photon, specific colors of light, called its “spectrum” are emitted.)

As can be seen in the images, the orbitals of different energy levels take on different shapes and are at different distances from the center of the atom. Like the picture above, these images were created by repeatedly shooting laser light at one hydrogen atom after another.

Prior to creation of these images, physicists calculated the shapes of orbitals based on the mathematics of quantum physics. They generated drawings of orbitals like those below based on their calculations. In some cases, they used computers to help with the drawings. The Dutch computer-generated images derived from actual electron-photon interactions provide confirmation of scientists’ mathematical understanding of electron orbitals.

Footnotes

*Art Hobson, Tales of the Quantum, Understanding Physics’ Most Fundamental Theory; Oxford University Press, 2017, New York City.

# What does an electron orbital look like?

This image can cause some puzzlement. It is being touted on the Internet as “the first image of a hydrogen atom.” It is not an image of an atom as it does not include a picture of the nucleus; the red and yellow at the center do not represent the nucleus. They indicate the high probability of detecting the electron in the center of the atom. The colors refer only to frequency of detections of electrons. Here’s the color key:

The image is a leap forward and exciting, but here are some other things the image is not: It’s not a photograph; it’s not of one electron; and it’s not of the electron wave function (which is an equation, not a material object). It should be noted that the scientists who created this image made none of these claims. It’s just that the image has sometimes been mislabeled by others.

## Electron Orbital/Electron Cloud

Here is what the image shows: the region within a hydrogen atom in which the electron will most likely be detected. Red means “most likely,” and blue means “least likely.” The entire colored region is called an “orbital” or “electron cloud.”

Quantum physics tells us that an electron does not occupy a particular position until detected. This image of an orbital was reconstructed by computer based on detections of innumerable electrons.

Here is how the image was created: The experimenters in a Dutch lab zapped hydrogen atoms with a laser to energize the electron within the atom. This caused the electron to fly out of the atom and hit a detector half a meter away. The experimenters did this hundreds of thousands of times, each time with a new hydrogen atom. Depending on the frequency with which electrons hit different positions on the detector, the computer reconstructed an orbital, the region within the atom that the electron can occupy and where it might be detected. The New Scientist article provides more details.

## Electron orbitals vary according to energy level.

The Dutch lab which created this image created additional images of electron orbitals in hydrogen atoms (below). Each image depicts an electron orbital at a different energy level, with (a) being the lowest and (d) the highest energy level. A low-energy electron orbital can be energized into a higher energy level with a laser.  The laser emits innumerable photons. If the electron absorbs a photon, its energy level jumps up. Later, it may spit out the photon and settle back down to a lower energy level.

As can be seen in these images, the orbitals are of different shapes and distances from the center of the atom depending on the energy level. Like the picture above, these images were created by repeatedly shooting laser light at one hydrogen atom after another. When the energized electron responded by shooting out and hitting the nearby detector, the point within the atom that the electron originated from was calculated. The calculations are used to generate a computer image of all the points of origin of the electron. The collection of points of origin compose the electron cloud or orbital.

Prior to creation of these images, physicists calculated the shapes of orbitals based on quantum theory. They generated drawings like those below, sometimes using computers, based on the calculations.

# Are electrons waves or particles?

The accompanying video demonstrates how an electron can be both a particle and a wave. (The video has two unfortunate errors in it, which I’ll point out.) The video shows how different kinds of objects, including an electron, act when they speed towards a barrier perforated by two slits. Then, it shows the pattern the objects form on a detection screen after passing through the slits in the barrier. This is the famous Double Slit Experiment. Here’s what’s going on in this video, step by step:

## How Particles Act

“Particle” shows ordinary particles, let’s say pebbles. Particles are separate individual little things that at any one moment are in a tiny, very localized position. So, individual pebbles shoot through one slit or the other. Then, the pebbles hit the detection screen.

Here’s where the video goes off the rails. It shows a pattern on the detection screen of random dots all over the screen. Your common sense would tell you that the pebbles should form two clumps on the detection screen, one behind each slit. Real experiments show that your common sense is correct. Figure (1) by Fermilab is a more accurate depiction of what the detection screen should look like.

## How Ordinary Waves Act

“Wave,” in the video, shows an ordinary wave, let’s say a water wave. The water wave is spread out, so it goes through both slits. On the far side of the barrier, two waves emerge, one from each slit. The two waves interfere with each other. They form the crisscross pattern of ripples that we see if we throw two stones into a pond. This crisscross

pattern of ripples hits the detection screen and forms a striped pattern.

Figure (2) clearly shows how a water wave creates the crisscross “interference pattern” and marks the detection screen with a striped pattern. This is just like in the video. This striping is the signature pattern of waves interacting. When physicists see this pattern, they think “waves.”

To summarize, here are the differences from particle behavior: the wave is spread-out; goes through both slits, not just one or the other; forms two interacting waves on the far side of the barrier; and forms a striped pattern on the detection screen.

## How Electrons Act

“Quantum object” shows a subatomic particle, for example, our electron. It doesn’t act at all like an ordinary particle such as a pebble. At first, it acts more like a wave. It’s spread out and goes through both slits. It emerges as two different waves on the far side of the barrier, and these interfere with each other. The two waves form the same crisscross pattern that ordinary waves form.

But upon hitting the detection screen, the wave “collapses.” The electron wave hits the screen in one tiny spot as if it were a particle. The experiment is run over and over. One at a time, electrons flow wave-like through the barrier and collapse at the detection screen, each time hitting one tiny spot, that is, suddenly turning into a particle. Over time, a pattern on the detection screen emerges. It’s the striped pattern—the signature pattern of two waves interacting! Somehow the particles which hit the screen “know” where to land on the detection screen such that over time, they collectively seem to show the influence of the two interacting waves.

## The Quantum Wave vs. Ordinary Wave

Even though the electron acts in certain ways like a wave, there are significant differences between the wave of a quantum particle and an ordinary wave like a water wave. The electron type-wave is called a “quantum wave.” An ordinary wave is called a “classical wave.” The mathematical equations which describe the properties of a quantum wave and a classical wave are very different. While quantum waves share some similarities of behavior with classical waves, for example, creating a striped pattern on the detection screen, quantum waves also act significantly differently. Quantum waves and classical waves differ in both their mathematical descriptions and in their behavior.

Here’s a brief listing of differences between a quantum wave and a classical wave (for more detail see the article in this encyclopedia on wave):

• As shown in the video, the quantum wave collapses when it hits the detection screen and lands on it as a particle. This is called the “collapse of the wave function.” An ordinary wave retains its wave nature when it hits the detection screen.
• The amplitude of a quantum wave is proportional to the probability that the quantum particle will be detected in a specific position. In contrast, the amplitude of a classical wave is proportional to the wave’s strength.
• The equation of a quantum wave can include imaginary numbers. These are numbers that include the square root of negative 1. As no number times itself is a negative number, imaginary numbers do not refer to anything that has physical reality. The equations for classical waves do not include imaginary numbers and describe physically real things.
• It is when an electron is in the quantum wave state, rather than in its particle state, that it displays quantum weirdness: superposition (being in more than one place at the same time), entanglement (behaving in an instantaneously correlated manner with an electron as far as across the universe), quantum tunneling (appearing on the other side of a barrier despite having insufficient energy to cross the barrier), and other weirdnesses. Classical waves, of course, do none of these things.

## Wave-Particle Duality

The ability of electrons and other quantum particles to act like both a wave and a particle is called “wave-particle duality.” I’ve found that the Transactional Interpretation of quantum mechanics is able to make some sense of wave-particle duality.* This interpretation proposes that when the electron is in its wave-like state, it is not in our physical reality. That is, it’s not in spacetime but is in an underlying level of reality that we can call “Quantumland.” This level of reality, while not observable by us, is lawful in that it follows the laws of quantum mechanics. It underlies and determines the probabilities of what occurs in our spacetime.

*The Transactional Interpretation is explained in lay terms without math in  Ruth E. Kastner, Understanding Our Unseen Reality, Solving Quantum Riddles; Imperial College Press, 2015, London.

How does the electron enter our physical reality? It interacts with something physical that is made up of lots of particles—a “macroscopic object” like a detection screen. Upon interacting with the screen, it’s suddenly a particle. This is called the “collapse of the wave function.” Since, the electron always becomes a particle as soon as it interacts with a macroscopic object, we can never observe it in its wavy state. We’re like King Midas. He could never feel his daughter’s soft hand because she turns to gold the moment that he touches her. We can never observe the wavy state of an electron because the wave function collapses to a particle when we interact with it sufficiently to perceive it.

Figure (3) depicts Quantumland on the left, the collapse of the wave function, and the resultant objects in everyday spacetime on the right. This depiction is a gross simplification because the collapse from wave to particle does not occur at the scale of entire objects like homes and picnicking families. Instead electrons, quarks, and other quantum particles are continually moving from their wavy states, interacting with others, and collapsing to particles. When they collapse, the entire atom and molecule collapses with them. Then, quantum particles revert to their wavy state, collapse again, and on and on. So, at any one moment, many of the atoms and molecules of an object are in their wavy state and many are collapsed down to particles.

This brings us to the final part of the accompanying video, “Add an Observer.” This part of the video shows the electron wave approaching the barrier. But this time, there’s a detector at the barrier watching which slit the electron goes through. This could be a human with Superman vision or a Geiger counter or another device. The device interacts with the electron sufficiently to determine which slit, so the electron collapses down to a particle and goes through only one slit.

Once past the barrier, the electron, freed from interaction, reverts to its wavy state. Upon interaction with the detection screen, it again collapses down to a particle and lands as a tiny localized dot. Again, the video incorrectly shows that after repeated runs of the experiment, random dots cover the detection screen with no particular pattern. Experimental results show that the resulting pattern on the detection screen is, instead, two clumps as shown in Figure (1).

## Consciousness and Wave Function Collapse

The role of consciousness in the collapse of the wave function has had a controversial history. In the early days of development of quantum mechanics, many of the founding fathers of the field contemplated the possibility that consciousness played a role in collapsing the wave function. Over time, this view was rejected. Considerable work was done starting in the 1950’s on the theory of decoherence. This is the theory that interaction with macroscopic particles cause collapse of the wave function. While this is a well-accepted theory, experiments in recent years also point to the possibility that consciousness can also cause collapse of the wave function. For further discussion, see the article in this encyclopedia collapse of the wave function.

## In Summary

In summary, the electron is definitely a particle when it hits the detection screen. And at other times, it’s a wave. But it’s not a physical wave like a water wave or sound wave. It’s a wave that follows the laws of quantum mechanics.

# How Can an Electron Be in More Than One Place at the Same Time?

A single electron CAN have a pretty specific location at a special moment in time, the moment that it interacts with another particle and creates a physical change in our universe (more later). However, an electron has no specific location when it acts as a wave in a quantum field. A wave can also be called an excitation or a disturbance of the field. In any event, the electron, when in the wave state, is spread out over a region of space.

However, upon interaction with something else in our universe, it will assume a pretty specific location. (This is, by convention, called the moment in which the electron is “measured.”) And the location in which the electron will be found upon interaction, is more probable where the amplitude of the electron wave is highest. Its PERMITTED locations are calculated using Schrodinger’s Wave Equation. Its PROBABLE locations are calculated as the square of the amplitudes of Schrodinger’s Wave Equation.

[Note: Schrodinger’s Equation is used to calculate the probable locations of a group of electrons. Using it to calculate the location of a single electron would be something like using the average height of women to predict the height of the next woman you see – not too sensible nor accurate. The average height of a women, however, would be helpful in predicting the heights that you’re likely to find in a random sample of all women. Same thing with Schrodinger’s Equation—it makes more sense to use it to predict the probable locations of a group of electrons.]

Returning to a single electron… by definition, the location of the electron won’t be found until it’s detected. It might be detected, for example, by a “cathode ray tube,” which includes a screen, the same kind of screen as on our TVs. The electron wave interacts with a spot on the detector screen; its energy is absorbed by the screen; and the screen gives off a tiny flash of light. A computer hooked up to the screen could record the location of the flash.

In this way, a single electron could be recorded at a specific location. However, the location is specific only in our macroscopic world. This would become clear if one looked at the flash with an overwhelmingly powerful microscope, stronger than we can currently even dream up the design of. If one used this microscope to look at the exact location of the electron as it hit the screen, the location wouldn’t be an exact point. Instead, at best, the electron would vibrate within a tiny space at the Planck-length scale. This is because of the Heisenberg Uncertainty Principle.

It’s important to note that when in the wave state, and prior to detection, it’s not just that we don’t know where the electron is. It actually has no specific location. Once it interacts with another particle, however, it randomly assumes a (fuzzy) specific location within the permitted locations specified by Schrodinger’s Equation. (Only when detecting a group of electrons can it be seen that the calculated probabilities have somehow guided the locations that the individuals in the group assumed.)

The electron has, at the moment of interaction, created information as to its whereabouts. Once that information is created, our universe has experienced physical change. Our universe works on the principle that that which has created a physical change (created information) goes into the past. And, now, that change will be a factor in creating the future.

# What is the difference between an electron and a photon?

I had the same question. When I researched this at @Electricity is energy [the real title of the article is “Electricity Is NOT Energy”], I found out that electrons are tiny particles of matter. They are the bits of matter within an atom that vibrate around the nucleus of an atom. Electrons can also fly about freely or travel slowly and are not just found within atoms. In a copper wire, for example, they can be found loose, outside atoms, traveling slowly, a few inches per minute.

Electrons have a negative charge, which means only that they move away from other negatively charged matter (other electrons) and are drawn to positively charged matter (protons, often ones in the nuclei of atoms).

But photons are units (packets of energy) of an electromagnetic wave. They are not bits of matter. A type of photon that we experience very intimately all the time is the photons of visible light. These hit our retina and cause chemical changes or hit a photographic plate. In both cases, the photons create chemical changes which ultimately create images.

Light is just one type of electromagnetic energy. Other types of electromagnetic energy are X-rays (a high-energy wave), waves that carry radio signals and TV signals, microwaves in a microwave oven, etc. All of the bits of energy that are associated with these waves are photons.

Photons have neither negative nor positive charge. They are not matter and have no mass. They travel the speed of light when in a vacuum like in outer space (which is not a complete vacuum, really). But they can travel much slower when traveling through a medium like water or even air.

Photons and electrons interact to create flows of electricity. Both are involved. Electricity is not merely a flow of electrons in a wire; it is also a flow of photons in an electromagnetic wave.