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Is a Hydrogen Atom’s Electron Orbit Circular?

While fully amazing, does this image really show a hydrogen atom? Does it show the probability cloud a hydrogen atom’s single electron makes around its center, a circle, or is this circle just an effect of the technique used?

Visualizing the Hydrogen Atom

This is claimed on PhysicsWorld to be the orbital structure of a hydrogen atom, made with a “quantum microscope”:

The first direct observation of the orbital structure of an excited hydrogen atom has been made by an international team of researchers. The observation was made using a newly developed “quantum microscope”, which uses photoionization microscopy to visualize the structure directly. The team’s demonstration proves that “photoionization microscopy”, which was first proposed more than 30 years ago, can be experimentally realized and can serve as a tool to explore the subtleties of quantum mechanics.

A “Camera” Effect?

There is another possible explanation, however. If you had a tennis player hitting tennis balls in all different directions at random, you might get an oval shape or different patten over time if you were high in the air looking down on 10,000 serves, but if your detector could only snap the location of each tennis ball when it got about 5 feet from the tennis player, you’d see a perfect circle like this.

How did they do this?

This image of a hydrogen atom was created with a sort of electrostatic zoom lens.

… In the new work, Aneta Stodolna, of the FOM Institute for Atomic and Molecular Physics in the Netherlands, along with Marc Vrakking at the Max-Born-Institute in Berlin, Germany, and other colleagues in Europe and the US have shown that photoionization microscopy can directly obtain the nodal structure of the electronic orbital of a hydrogen atom placed in a static electric field. In the experiment, the hydrogen atom is placed in the electric field E and is excited by laser pulses.

The ionized electron escapes from the atom and follows a particular trajectory to the detector – a dual microchannel plate (MCP) detector – that is perpendicular to the field itself. Given that there are many such trajectories that reach the same point on the detector, interference patterns can be observed, which the team magnify by a factor of more than 20,000 using an electrostatic zoom lens. The interference pattern directly reflects the nodal structure of the wavefunction. The experiments were carried out with both resonant ionization involving a Rydberg state and non-resonant ionization.

The team chose the hydrogen atom thanks to its unique properties. “These [hydrogen atoms] are very peculiar…as hydrogen has only one electron, which interacts with the nucleus via a purely Coulombic interaction, it has a particular structure when we place it in a DC electric field,” says Vrakking.

The creator of this image seems to say above that the shape of the orbital is a result of the field used.

He goes on to explain that thanks to its single-electron status, hydrogen’s wavefunction can be written as the product of two wavefunctions, which describe how it changes as a function of two coordinates – the so-called parabolic coordinates. That is, the Hamiltonian of the hydrogen atom (in an external electric field) describes a splitting of its energy levels, which is known as the “Stark effect”.

Lost? Here’s a link with more about the Stark effect. If you still don’t get it, here is a picture of the fictional character Tony Stark, aka Iron Man.

Apparently every hydrogen atom has something called a Hamiltonian. Here is the man for which this function of atomic states is named, William Rowan Hamilton.

Just think how many Hamiltonians you have in your little finger. Dude, a lot.

This next sentence will take you on a journey deep into quantum space.

More importantly, though, this “Stark Hamiltonian” is exactly separable in terms of the two parabolic coordinates, which are linear combinations of the distance of the electron from the hydrogen nucleus r and the displacement of the electron along the electric-field axis z.

Who understands this? I read it a few times. I read it as if I were viewing an exotic animal in a zoo. Okay. Move along.

Did you know that there are Stark-like Hamiltonians? Now you do.

On this walk in the quantum physics fun house, we wander into the next room …

Vrakking told physicsworld.com that the shape of the two parabolic wavefunctions is therefore “completely independent of the strength of the field, and so it is invariable – it stays the same as the electron travels for more than half a metre in the experiment – all the way from where the ionization occurs up to the 2D detector”. This, he explains, is crucial to scaling up the spatial distribution to magnify the nodal patterns to millimetre-scale dimensions, where they can be observed with the naked eye on the 2D detector and recorded with a camera system.

“What you see on the detector is what exists in the atom,” he says. The group observed several hundreds of thousands of ionization events to obtain the results, with the same preparation of the wavefunction for each.


We hope you enjoyed the tour. The take home message is that this image is what exists in the atom, according to the photographer. A counter argument says that this is not exactly what it seems.

Circular averaged Nadir and Zenith – not orbitals

Atom orbitals are not likely to be stationary even if the center of the nucleus is held in place with a magnetic field. What the experiment shows is that the extent of the excited state is further from the nucleus. Averaging K-bits/measurement and combining 4 different measurements blurs (smears as several have commented) orbital structure and thus shows elevated levels circularly. This does not prove the circular nature of the orbitals – only that the outer levels where the electrons are essentially stopped with regard to movement away from and towards the nucleus


With apologies to real physicists, my gut says this is not the true shape of a hydrogen atom. Camera effect or not, however, this is an amazing piece of work to visualize a single instance of the most abundant atom in the universe.


About Xeno

E pluribus unum.


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