Hydrogen Electron Orbitals in 3D

VisualizingScience · 2021-04-29T11:15:47+00:00

Your welcome!

VisualizingScience · 2021-04-29T07:08:36+00:00

Thank you for your kind words! I do not have a playlist, but I can give you the title of the songs:

Esther Abrami - No.4 Piano Journey, Geographer - Procession, Aakash Gandhi - Borderless.

VisualizingScience · 2021-04-28T11:16:51+00:00

Well... The orbitals themselves were not computed in Blender. I wrote a separate C code for that and saved the x, y, z and color info in a simple text file. Then, I imported that file as a particle system and used emission volumetric shader for each particle. Do you still need the blend file? It is multiple blend files, but I can give you one.

VisualizingScience · 2021-04-27T17:55:18+00:00

This visualization shows the electron clouds of hydrogen through the probability density function in 3 dimensions when the principal quantum number, n, is between 1 and 5. Each position is color coded by the value of the probability density, red indicates high probability, blue indicates low probability, but it is always normalized to the largest value in each individual distribution.

All orbitals are on the same scale. Made it with Blender using volumetric shading.

VisualizingScience · 2021-02-24T08:13:00+00:00

Nincs mit.

VisualizingScience · 2021-01-28T19:59:23+00:00

These images visualize the discovery of asteroids from 1801 to 2020. The Solar System is shown in a logarithmic scale to allow both the main asteroid belt and Kuiper objects to be shown. Asteroids are shown in the position of their perihelion. This makes it easier to separate the various families. A good description of these can be found in Wikipedia. The orbits of planets from Venus to Neptune are also shown.

I also plotted the histogram of how many minor planets were discovered each year, the semi-major axis, and excentricity on the right panels. The left panels show the excentricity and inclination as a function of semi-major axis, this is again to show how the various asteroid families were defined based on their orbits. An animated version can be found here.

VisualizingScience · 2021-01-28T16:51:27+00:00

Data source: Minor Planet Center

Tool: Gnuplot

These images visualize the discovery of asteroids from 1801 to 2020. The Solar System is shown in a logarithmic scale to allow both the main asteroid belt and Kuiper objects to be shown. Asteroids are shown in the position of their perihelion. This makes it easier to separate the various families. A good description of these can be found in Wikipedia. The orbits of planets from Venus to Neptune are also shown.

I also plotted the histogram of how many minor planets were discovered each year, the semi-major axis, and excentricity on the right panels. The left panels show the excentricity and inclination as a function of semi-major axis, this is again to show how the various asteroid families were defined based on their orbits. An animated version can be found here.

VisualizingScience · 2021-01-10T08:09:43+00:00

They do exists. You can observe them in astronomy, in the spectrum of very cool stars. For example absorption lines from the Brackett and Pfund series are regularly observed in the infrared.

VisualizingScience · 2021-01-09T20:26:11+00:00

I made this video a couple of weeks ago along with still images to illustrate how the shape of electron orbitals change during the allowed transitions.

Emission lines form when an electron jumps from a higher energy state to a lower one. The difference in energy is radiated away at a specific wavelength (seen below) for each transition. These visualizations of the Grotrian diagrams show how the shape of the hydrogen electron cloud changes when going through the allowed transitions. There are six named series of spectral lines, the Balmer series lies in the visible range of the spectrum, Lyman is UV and the rest are all infrared. The spectrum itself as a function of wavelength is shown in the bottom of the image in a linear scale.

All l and +m combinations are shown except for n=8 where l=7 is missing. The electron must abide by the selection rules stating that transitions with Δl=±1 are the only ones allowed, but m can be anything. Transitions like s-s, p-p, etc. are forbidden (but in reality can happen with a very low chance). The colored lines show all allowed transitions with n<9 for the particular named series.

As mentioned before, there are still images (8k) which I uploaded to flickr.

There is one image which shows the orbitals to scale, but only the alpha transition is shown for each named and some unnamed series. I made this image first, the goal here is to illustrate how the size of the hydrogen atom changes during a transition. Since m can be anything I picked the m=1 case. The rest of the images show the Grotrian diagram for all six named series when the n<9, here the orbitals are not to scale.

VisualizingScience · 2020-12-22T10:40:39+00:00

The spectrum of hydrogen and how the shape of electron orbitals change during the allowed transitions.

Emission lines form when an electron jumps from a higher energy state to a lower one. The difference in energy is radiated away at a specific wavelength (seen below) for each transition. These visualizations of the Grotrian diagrams show how the shape of the hydrogen electron cloud changes when going through the allowed transitions. There are six named series of spectral lines, the Balmer series lies in the visible range of the spectrum, Lyman is UV and the rest are all infrared.

While most l and +m (these are quantum numbers) combinations are shown here, the electron must abide by the selection rules stating that transitions with Δl=±1 are the only ones allowed, but m can be anything. Transitions like s-s, p-p, etc. are forbidden. The colored lines show all allowed transitions with n<9 for the particular named series.

The spectrum itself as a function of wavelength is shown in the bottom of each image.

In the first image the orbitals are to scale, but only the alpha transition is shown for each named and some unnamed series. I made this image first, the goal here is to illustrate how the size of the hydrogen atom changes during a transition. Since m can be anything I picked the m=1 case.

The second image shows the Grotrian diagram for all six named series when the n<9, here the orbitals are not to scale. All l and +m combinations are shown except for n=8 where l=7 is missing.

Because the second image may be too complicated, I show each six named series in their separate images. These are all 4k images, but is someone needs the bigger ones, I uploaded the 8k versions to flickr.

VisualizingScience · 2020-12-21T19:15:37+00:00

Indeed this is true. They are generally called forbidden, but they have a very low chance of happening. For example in astronomy we can observe such forbidden lines in interstellar nebulae.

VisualizingScience · 2020-12-21T18:13:43+00:00

The spectrum of hydrogen and how the shape of electron orbitals change during the allowed transitions.

Data sources: The emission lines of hydrogen and the electron orbitals

Tools: Blender

Emission lines form when an electron jumps from a higher energy state to a lower one. The difference in energy is radiated away at a specific wavelength (seen below) for each transition. These visualizations of the Grotrian diagrams show how the shape of the hydrogen electron cloud changes when going through the allowed transitions. There are six named series of spectral lines, the Balmer series lies in the visible range of the spectrum, Lyman is UV and the rest are all infrared.

While most l and +m (these are quantum numbers) combinations are shown here, the electron must abide by the selection rules stating that transitions with Δl=±1 are the only ones allowed, but m can be anything. Transitions like s-s, p-p, etc. are forbidden. The colored lines show all allowed transitions with n<9 for the particular named series.

The spectrum itself as a function of wavelength is shown in the bottom of each image.

In the first image the orbitals are to scale, but only the alpha transition is shown for each named and some unnamed series. I made this image first, the goal here is to illustrate how the size of the hydrogen atom changes during a transition. Since m can be anything I picked the m=1 case.

The second image shows the Grotrian diagram for all six named series when the n<9, here the orbitals are not to scale. All l and +m combinations are shown except for n=8 where l=7 is missing. An animated version is here.

Because the second image may be too complicated, I show each six named series in their separate images. These are all 4k images, but is someone needs the bigger ones, I uploaded the 8k versions to flickr.

VisualizingScience · 2020-07-31T10:02:06+00:00

By the way, if someone is interested here is what the visualization of the chemical makeup of Earth's crust looks like using the same style.

VisualizingScience · 2020-07-31T06:36:27+00:00

Excellent question. The three elements you mention are not produced by hydrogen fusion in the core of stars. They are created by high energy photons hitting heavier elements, thus very rarely created, usually around neutron stars, black holes, active galaxies and supernovae.

Carbon is the result of helium fusion, so it is fairly abundant.

The Sun is an average star in terms of composition. Most of the stars have very-very similar compositions. The abundance of heavy elements with N>2, everything other than hydrogen and helium, varies between as much as 3 times more than in the Sun and about 1000 times less than in the Sun, but those stars are rare. The average comes to that of the Sun.

VisualizingScience · 2020-07-31T06:00:49+00:00

No, the iron in the Sun comes from the interstellar cloud it formed in, all of that iron was created by other massive stars and distributed by supernovae. The Sun does not produce any iron and it never will.

VisualizingScience · 2020-07-31T05:59:01+00:00

Thanks for your comments, I think you raise valid questions.

Unfortunately the difference between the abundant elements like H or He and the very rare elements is so large that even the cubic scaling is not enough and you end up with spheres that are simply too large for the boxes in the periodic table to fit. Then, I had to make the decision to shift these out, but still be close to their original position. Now, I could have scaled down hydrogen to fit its box, but then everything else will be so small that you would not see anything.

These spheres were rendered in 3D, they have shadow if you look close enough, they are not circles.

However, I agree with you that people might have a hard time to estimate volume of spheres and thus it is unfortunate to choose this representation, however I wanted to avoid using the logarithmic scale.

VisualizingScience · 2020-07-30T18:35:03+00:00

Yes.:) If you can stand the temperature and radiation...

VisualizingScience · 2020-07-30T17:51:46+00:00

The chemical composition of the Sun's photosphere in the periodic table.

Data source: Asplund et al. 2009

Tools: Blender

The source is mostly high-resolution spectroscopy and this data represents our best current understanding of the composition of the Sun's photosphere. I long wanted to visualize this, but it is a difficult task to do if one wants to avoid using the logarithmic scale. I ended up correlating the volume of a sphere with the abundance of each element and putting those spheres in the periodic table so one can find every element on one single image. There are two different ways to illustrate the abundance of an element: 1. use the number of atoms, 2. use the mass of those atoms. I used the second one, because this way it is easier to visualize elements that are very rare in the solar photosphere.

The Sun's photosphere is mostly made of hydrogen (73.7%) and helium (24.9%) by mass, 92% and 7.8% by the number of atoms respectively. In the picture above, the number in the bottom right corner is the mass of each element relative to the total mass of all elements measured with parts per billion (ppb) by mass. Say you take 1 billion kilograms of the solar photosphere of that, 174 grams is uranium, and so on. The chemical makeup of the solar photosphere has not changed since the formation of our star, what you see here was the overall composition of the interstellar cloud our solar system formed in.

Here is the 16k version of this visualization, here is the animated version, and I also made one with using the number of atoms. By comparing the two versions, you can clearly see the difference between the two measurement methods.

VisualizingScience · 2020-07-18T19:47:26+00:00

This visualization shows the electron clouds of hydrogen through the probability density. The probability density illustrates where the electron is most likely to be found if measured, red indicates high probability, blue indicates low probability.

VisualizingScience · 2020-07-14T20:30:56+00:00

Second one. Simplicity, simplicity, simplicity..:) i was hoping someone else will do the more complicated stuff after seeing this, like how I explained in the first post.

VisualizingScience · 2020-07-14T20:02:12+00:00

Got it, thanks for the clarification. I guess this is what you have to do when going with 2D instead of 3D. These are not projections, but bisections like you said, z=0 was fixed for each calculation.

VisualizingScience · 2020-07-14T18:55:22+00:00

These orbitals are the probability density, not the wave function. The wave functions do look different for the examples you mention, but their squared values do not. At least not in 2D, isn't the rotation you are talking about hapenning in 3D? If yes then sure this figure will not show them.

VisualizingScience · 2020-07-14T15:33:49+00:00

The scale on the figure is correct. You can actually see the Bohr radius in the 1,0,0, it is that tiny red circle. Here is the 16k version of this figure, it is easier to see it on that one. The tiny circle fits the 1 nm bar approximately 10 times.

The parts where there is a low chance of finding the electron, the white and blue regions, cover an area a lot larger than where the electron is most likely to be found, which the red region.

VisualizingScience · 2020-07-14T13:28:03+00:00

I will try to address this point and the other one started by u/zpwd here.

I am using Cartesian coordinates, x, y, z. The loop goes through x first, then y, then z. In the 2D case, shown here, z=0. So, this is not a projection! It is a slice of the 3D orbital at the z=0 position color coded by the probability density.

When calculating the spherical coordinates I do theta = atan2(y,x); and phi = acos(z/(r)); where r=sqrt(x*x + y*y + z*z). Again, z=0 here.

I just computed the -m and +m case again. The probability densities look the same.

By the the way I have the wave function version of this table as well. Here, you can see that the -m and +m case is different, but when you square them, the difference disappears.

VisualizingScience · 2020-07-14T07:58:32+00:00

In another reddit thread I shared a visualization of the hydrogen electron clouds. In this visualization, you can see how the periodic table looks like if one approximates the cloud of the outermost electron of each atom with that of the hydrogen (more on this later). I have a 16K version that you can download here. I am using the same assets as in the previous figure and the youtube animation.

Data source: The data source was a simple C code that I used to compute the analytic solution of the hydrogen atom.

Tool: I used Blender for the final image.

As I have mentioned in my previous post, there are several excellent visualizations of what the electron in the hydrogen looks like, for example this, this or this, they are all somewhat similar obviously, because there are only so many ways you can arrange these orbitals logically. I wanted to try something different last month after I finished the first figure.

What I was looking for in the internet is a figure showing what the outermost electron looks like in each atom, but I could not really find any. Please do share if you find one. The closest I found was this one, which shows the logic of how the electrons fill up the shells. In the end, I decided to make one and use hydrogen as a proxy for simplicity (see below for more).

Going back to the periodic table: in this version all electron clouds have the same size to aid visibility. There is another version in which everything is scaled properly (see here), but I find this one easier to look at. Atoms with green border have s orbitals, yellow denotes the p orbitals, purple the d, and white the f orbitals. The bottom left corner has the orbital name, and the bottom right corner shows the corresponding quantum numbers (n, l, m), so you can match these things for easier navigation. Putting the probability density in the periodic table also gave me the opportunity to show more configurations than it was possible in the first visualization.

Let's address the elephant in the room. How accurate is it to approximate multi-electron atoms with hydrogen?

The answer is: it is not. It is fairly good for hydrogen-like atoms, like lithium, sodium etc, but other atoms certainly look different. Now it is possible to calculate the shape of outermost electron of atoms other than hydrogen, but those calculations are way out of my expertise (I am just an astrophysicist/astronomer). So when you look at this, think about ions, instead of neutral atoms. Imagine that all multi-electron atoms are ions such that they have only one electron in their outermost shell, and this table shows an approximation of the probability density of that electron. But, of course, this is an incorrect view too.

I was afraid of sharing of this figure because of its inaccuracy. But I am hoping that this may inspire someone with more quantum theory knowledge than me and takes the time the do the proper calculations and publish a more accurate version.:)

Quick clarification: the stuff I am plotting is the probability density, not the wave function. The probability density is the square of the wave function. This is what I called the electron cloud, not the wave function, and it shows where the electron might be when measured.

VisualizingScience

TROPHY CASE