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Friday, February 23, 2024

Here's How You Can 'See' Molecules—on a Whole 'Nother Planet

So maybe you heard this thing about possible signs of life on Venus. Yes, it's Venus this time and not Mars. Scientists have detected the signature of the molecule phosphine in the atmosphere of this planet using rotational spectroscopy. As far as we understand it now, the only way to get phosphine is to make it in a lab or as a byproduct of some types of bacteria. Oh, bacteria on Venus? That would be kind of a big deal.

Now, some pretty awesome physics are involved in the possible detection of this molecule. Let me go over some of the coolest ideas so that you can fully understand it.

Radio Waves Are Light Waves

The signal for phosphine is a radio wave with a wavelength of 1.123 mm. So, how you do "see" radio waves? Yes, you use a radio telescope. In this case, that telescope was the James Clerk Maxwell Telescope at the Mauna Kea Observatory in Hawaii. Although a radio telescope might look quite different compared to an optical telescope, they are basically the same thing.

Both visible light and radio waves are types of electromagnetic wave. An electromagnetic wave starts with an electrically charged particle like a proton or an electron. These electric charges create an electric field around the particles—this field allows charges to interact with other charges without even touching. But something else happens if you could actually hold this charge and accelerate this charge back and forth (which you can't actually do with an electron—not with your hand). The accelerating charge changes the magnitude of the electric field. Here is the cool part—this changing magnetic field creates an electric field such that this changing electric and magnetic field can create a sustaining oscillation. I know, it's crazy but that's exactly what is known as an electromagnetic wave.

Then what makes a radio wave different than a visible light wave? The only difference is the wavelength. We typically classify radio waves as electromagnetic waves with a wavelength larger than 1 millimeter and smaller than the universe (that's just sort of a joke). Visible light has a wavelength of 680 nanometers for red light down to 380 nm for violet light. But all electromagnetic waves travel at the same speed—the speed of light at 300 million meters per second.

Although radio and visible light are both electromagnetic waves, there is one thing that is very different—the way that they interact with matter. Of course you already knew this. You know that the radio waves that your radio receives can travel through solid walls, but the visible light from the Sun or a lamp cannot. But it also means that instead of a shiny parabolic mirror for your telescope, you can use plain painted metal for a radio telescope lens. This makes it much easier to build very large diameter lenses like the James Clerk Maxwell Telescope (yup, same guy as in Maxwell's equations). Of course we always want a lens as big as possible for the best possible image, but you actually need the radio telescope to have a larger parabolic dish because the wavelength is bigger. The radio telescope would still work with a smaller lens, but you would get poor image resolution.

What the Heck Is Rotational Spectroscopy?

You obviously can't literally "see" the phosphine in the atmosphere of Venus. However, you can see evidence of it from the radio waves phosphine absorbs—the exact radio wavelength phosphine absorbs is a function of phosphine's particular rotational energy level.

Let me start with plain visible light spectroscopy for the simplest atom—hydrogen. Hydrogen consists of just a single proton in the nucleus and one electron in the orbital shell. Since the there is an attractive force between the negative electron and the positive proton, it's common to depict this atom as though it were a tiny solar system with the electron moving around in a circular orbit around the much heavier proton.

Of course this planetary orbit model isn't legit. If an electron was moving in a circle around a proton, it would have a centripetal acceleration and produce electromagnetic radiation which would cause it to lose energy and spiral into the proton—that would be bad. It turns out to be that super tiny stuff just doesn't follow the same rules as macroscopic objects like baseballs and puppy dogs. But, even though this planetary model isn't the best model, it's still fairly useful. In the planetary orbit, a planet could have any orbital energy, but for the electron orbit—it can only "orbit" at certain energy levels. Yes, that's weird but super small stuff often seems weird. But wait, it gets even wackier. It turns out that you can get this electron to move to a higher energy level if you disturb it with a light wave of a particular frequency. In fact there's even a relationship between the change in energy levels (ΔE) and the frequency of the light (we often use ν). Of course, there is also a relationship between the wave frequency and the wavelength (λ) so I can write this energy change as the following.

In this expression c is the speed of light and h is a constant called Plank's constant. For the electron in hydrogen to be excited from the ground state (lowest energy level) to the next level would require light with a 122 nanometer wavelength. But wait! If the electron is in the first excited energy level and drops back down to the ground state—it will create light with that same wavelength. Alas, this wavelength (121 nm) is not visible to the naked eye.

But there are some energy level transitions for hydrogen that actually do produce light with visible wavelengths. Each allowed orbit in the hydrogen atom is at a different energy value. This means that different transitions for this hydrogen atom will produce different, and unique, wavelengths of light. In fact, the light produced by an atom is sort of like its fingerprint. By looking at this spectrum, you can identify the atom.

By running electrical current through a gas, you can get the electrons in the atoms to get excited to different energy levels. Then they produce light when they go back down to the ground state. If you want to see what wavelengths of light are produced you can have the light pass through a diffraction grating. A diffraction grating is essentially a bunch of really small lines etched in glass and really close together. When light passes through it, the grating causes an interference pattern such that different wavelengths bend different amounts. It's like a glass prism that makes the spectrum of colors, but much better. Here is what it would look like for hydrogen. Each one of these colors of light correspond to an energy transition. For these visible wavelengths in hydrogen, it's a transition from higher orbits back down to the 2nd energy level. It's not the image that you would use to get actual measurements, but it's nice that you can see the different colors.

It's important to realize that these wavelengths essentially identify the element. If you replace the hydrogen atom with a helium atom, it can still produce light—but it will be with different wavelengths that correspond to the energy levels in helium. But you don't have to just look at light from the excited gas as a way to identify an atom. Instead of looking at the light the atom produces, you could instead look at the light the atom absorbs. Suppose you have a cloud of hydrogen gas. When light of all wavelengths passes through that gas, the wavelengths that match the energy level transitions can be absorbed by the hydrogen atom (it's the same wavelengths that it produces). So you would see dark lines instead of bright lines—but they would be in the same place with the same "fingerprint."

OK, but what does this have to do with phosphine and radio telescopes? When a molecule (like phosphine) interacts with electromagnetic waves, its rotational motion changes. However, just like the energy levels of the electron in a hydrogen atom, the rotational energy levels for phosphine are quantized. It can only have certain discrete energy levels. But it's still true that the change in rotational energy levels correspond to electromagnetic waves of a certain wavelength. And for one particular change in rotational energy levels you get an EM wave with a wavelength of 1.123 millimeters—a radio wave. In fact, it's a radio wave that uniquely identifies the change in rotational energy as that belonging to a phosphine molecule.

But where do these radio waves that get absorbed by phosphine come from? They come from the background radiation of the planet. Yes, Venus has a bunch of stuff going on in the lower atmosphere and on the very hot surface that produces all sorts of electromagnetic waves. Some of these are in the radio wavelength that pass through the gas (with phosphine) in the atmosphere and then travel all the way to Earth to be detected by a radio telescope. After the waves have been detected by the telescope, you can look at the intensities of radio waves at different frequencies to find which wavelengths are absorbed in the atmosphere of Venus.

That's how you can figure out there is phosphine on another planet. And with phosphine, there is evidence of life … on another frickin planet.

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